qqad in 2006

This document is created by Crazyfootballer – member of PaGalGuy.com QQAD

Quant Question a Day 1- 50 (Feb. – Nov. 2006)

----------------------------------------------------------- Quant Question # 1 ------------------------------------------------------------

Let n be positive integer and g(n) denotes the gcd of n^2 + 11 and (n+1)^2 + 11, then max(g(n)) is (a) 15 (b) 45 (c) 75 (d) 105

----------------------------------------------------------- Quant Question # 2 ------------------------------------------------------------

The points P, Q, R lie on a line in that order with PQ=9, QR=21. Let O be a point not on PR such that PO=RO and the distances PO and QO are integral. Then sum of all possible perimeters of triangle PRO is (a) 320 (b) 350 (c) 380 (d) 410

------------------------------------------------------------ Quant Question # 3 ------------------------------------------------------------

Which of the following statements about the functions A(x, y, z) = x² + 3y² - 4xy - 2yz + 2zx and B(x,y,z) = |x-|x-y|| + |y-|y-z|| + |z-|z-x|| is necessarily true? (a) B(x,y,z) <= |x-y| + |y-z| + |z-x| (b) (B(x,y,z))^2 > A(x,y,z) for x > y > z > 0 (c) A(x,y,z) > -6 (d) None of the above

------------------------------------------------------------ Quant Question # 4 ------------------------------------------------------------

Let [x] denotes the greatest integer that is less than or equal to x, e.g. [3.45] = 3, then [1/3] + [2/3] + [2^2/3] + [2^3/3] +...+ (101 terms) equals (a) 1/3( 4^50 - 1) - 50 (b) 1/3( 4^51 - 1) - 51 (c) 2/3( 4^50 - 1) - 50 (d) none of the above

Funda [-1/3] = 0 [2/3] + [2^2/3] = (2+2^2)/3 - 1 [2^3/3] + [2^4/3] = (2^3+2^4)/3 – 1


------------------------------------------------------------ Quant Question # 5 ------------------------------------------------------------

There are 11 books on a shelf. How many ways are there to choose 4 of them so that no two of the chosen books stand next to each other? (a) 70 (b) 165 (c) 495 (d) none of these

------------------------------------------------------------ Quant Question # 6 ------------------------------------------------------------

We are given a system of n linear equations in n variables, n > 1. Which of the following statements MUST BE FALSE? (a) The system of equations has an odd number of solutions. (b) The system of equations has no solution. (c) The system of equations has an infinite number of solutions. (d) The system of equations has exactly n solutions.

------------------------------------------------------------ Quant Question # 7 ------------------------------------------------------------ Let m = 1^2/1 + 2^2/3 + 3^2/5 + ... + 500^2/999, and n = 1^2/3 + 2^2/5 + 3^2/7 + ... + 500^2/1001, then the integer closest to m - n is (a) 250 (b) 500 (c) 1000 (d) 1500

------------------------------------------------------------ Quant Question # 8 ------------------------------------------------------------ If the equation (x^2 - 2ax -4(a^2 + 1))(x^2 - 4x -2a(a^2 + 1)) = 0 has exactly 3 different roots, then how many values can "a" take? (a) 4 (b) 3 (c) 2 (d) 1

------------------------------------------------------------ Quant Question # 9 ------------------------------------------------------------ In a wedding 101 people meet. The 1st person shakes hand with only 1 other person, 2nd with 2 others,..., 100th with 100 others. With how many persons does the 101th person shake hands?

(a) 100 (b) 1 (c) 51 (d) none of these


------------------------------------------------------------ Quant Question # 10 ------------------------------------------------------------ Two statements are made about the set A = {1, 2, 3, ..., 100}. (1) More 4 element subsets of A have sum greater than 201 than have sum less than 201. (2) More 4 element subsets of A have sum greater than 203 than have sum less than 203. Then which among the following is right? (a) Only (1) is true (b) Only (2) is true (c) Both (1) && (2) are false (d) Both (1) & (2) are true

------------------------------------------------------------ Quant Question # 11 ------------------------------------------------------------ For all real x, f(x) satisfies 2f(x) + f(1-x) = 2*x^2 + 1. Then which among the following is true for all x? (a) f(x) <= 1 (b) f(x) >= -1 (c) f(x) >= 1 (d) f(x) <= -1

------------------------------------------------------------ Quant Question # 12 ------------------------------------------------------------ Let 123abc231bca312cab be a 18 digit number in base 7. How many ordered pairs (a,b,c) exist such that the given 18 digit number is divisible by 4? (a) 62 (b) 74 (c) 86 (d) none of these ------------------------------------------------------------ Quant Question # 13 ------------------------------------------------------------ If |x^2-1|/(x-2) = x, then what value can x take? (a) (1-5^1/2)/2 (b) (1-2^1/2)/2 (c) (1-3^1/2)/2 (d) (1+2^1/2)/2

------------------------------------------------------------ Quant Question # 14 ------------------------------------------------------------ Two brothers, each aged between 10 and 90, "combined" their ages by writing them down one after the other to create a four digit number, and discovered this number to be the square of an integer. Nine years later they repeated this process (combining their ages in the same order) and found that the combination was again a square of another integer. What was the sum of their original ages? (a) 37 (b) 55 (c) 63 (d) 71


------------------------------------------------------------ Quant Question # 15 ------------------------------------------------------------ If f(n) = (24n + 1)^1/2, where n is a positive integer, then what can be said about f(n) ? (a) f(n) is prime for some n, but not infinite n (b) f(n) is composite for some n, but not infinite n (c) both (a), (b) are true (d) both (a), (b) are false

------------------------------------------------------------ Quant Question # 16 ------------------------------------------------------------ a, b, c, d are non-zero reals and f(x) = (ax + b)/(cx + d). If f(-1) = 0, f(1) = 1 and f(f(x)) = x for all x (except -d/c). The unique value which is not in the range of f(x) is (a) 1/3 (b) 2 (c) 0 (d) -1/2

------------------------------------------------------------ Quant Question # 17 ------------------------------------------------------------

If x^6 + 5x^3 + 8 = 0, then which among the following is true? (a) x + 2/x = 1 (b) x + 2/x = -1 (a) x - 2/x = 1 (a) x - 2/x = -1

------------------------------------------------------------ Quant Question # 18 ------------------------------------------------------------

Let ABCD is a square of length unity. A point Q is taken on BC and joined with P which is the mid-point of AB. If (< PDQ) = 45 degrees, then the area of traingle PBQ is: (a) 1/8 (b) 1/9 (c) 1/4 (d) 1/6

------------------------------------------------------------ Quant Question # 19 ------------------------------------------------------------ There are 6 straight lines in a plane, no 2 of which are parallel and no 3 of which pass through the same point. If their points of intersection are joined, then the number of additional lines thus introduced is

(a) 45 (b) 78 (c) 105 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 20


------------------------------------------------------------ The length of 2 altitudes of a triangle are 3 and 5 respectively. Which among the following can not be the length of the third altitute? (a) 7.5 (b) 2 (c) 4 (d) 6

------------------------------------------------------------ Quant Question # 21 ------------------------------------------------------------ If a,b,c,d are positive integers and a+b+c+d = 99, and A = (-1)^a + (-1)^b + (-1)^c + (-1)^d then, the total possible number of values of A are (a)99 (b) 98 (c) 3 (d) 2

------------------------------------------------------------ Quant Question # 22 ------------------------------------------------------------ Letters of the word BLACKI are arranged in order such that B is not at 1st, A is not at 3rd and K is not at 5th. In how many ways can this be done? (a) 336 (b) 426 (c) 486 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 23 ------------------------------------------------------------

9 contestants for Miss India are seated on around circular table. Aditya(HAHAHAH)wants to date 3 of them such that he doesn't select any 2 neighbouring contestants. The number of ways in which Aditya can do this is

(a) 24 (b) 33 (c) 27 (d) 30

------------------------------------------------------------ Quant Question # 24 ------------------------------------------------------------

Let [x] denotes the greatest integer that is less than or equal to x, e.g. [5.43] = 5. Let x be any number selected randomly such that [x^1/2] = 10. The probability that [(100x)^1/2] = 100 is (a) 1/7 (b) 1 (c) 67/700 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 25 ------------------------------------------------------------


The sequence 1, 3, 4, 9, 10, 12, ... includes all numbers that are a sum of one or more distinct powers of 3. Then the 50th term of the sequence is (a) 252 (b) 283 (c) 327 (c) 360

------------------------------------------------------------ Quant Question # 26 ------------------------------------------------------------

Let Q be the quotient obtained on dividing 31^29 by 41. Then Q is divisible by (a) 6 (b) 15 (c) 21 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 27 ------------------------------------------------------------

At the start of a weekend a player has won 50% of the matches he has played. At the end of the week after playing another 10 matches, 9 of which he wins, he has won more than 51% of his matches. What is the largest number of matches he could have played till the end of weekend?

(a) 378 (b) 287 (c) 216 (d) 185 ------------------------------------------------------------ Quant Question # 28 ------------------------------------------------------------

If x, y, z are any real numbers then the minimum possible value of x^2 + 2y^2 + z^2 + 2yz subject of x + 2y + z = –6 is (a) –6 (b) 6 (c) 12 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 29 ------------------------------------------------------------ In the triangle PQR, PQ = PR and the bisector of angle Q meets PR at A. If QR = QA + AP then < (P) equals (a) 90 degrees (b) 120 degrees (c) 135 degrees (d) none of the foregoing

------------------------------------------------------------ Quant Question # 30 ------------------------------------------------------------


n people vote for one of 27 candidates. Each candidate's percentage of the vote is at least 1 less than his number of votes.

What is the smallest possible value of n?

------------------------------------------------------------ Quant Question # 31 ------------------------------------------------------------

The curve y^2 +2xy + 4|x| = 4 divides the x-y plane into regions. Then the area bounded by the closed region of the curve is (a) 8 (b) 8*(2)^1/2 (c) 16 (d) 16*(2)^1/2

------------------------------------------------------------ Quant Question # 32 ------------------------------------------------------------

8 players compete in a tournament. Everyone plays everyone else just once. The winner of a game gets 1, the loser 0, or each gets 1/2 if the game is drawn. The final result is that everyone gets a different score and the player placing second gets the same as the total of the four bottom players. What was the result of the game between the player placing third and the player placing seventh?

(a) Third player wins (b) Seventh player wins (c) The match ends ina draw (d) can not be determined

------------------------------------------------------------ Quant Question # 33 ------------------------------------------------------------

Two circles of radius 4cm, and 9cm touch each other externally. A common tangent AB is drawn to these two circles, A and B lie on the two circles respectively. Then the radius of the circle which touches the given circles, and also whose tangent is line AB is

(a) 1.32 cm (b) 1.44 cm (c) 1.56 cm (d) 1.68 cm

------------------------------------------------------------ Quant Question # 34 ------------------------------------------------------------

N contestants numbered 1, 2, 3, ..., n are running a race around a circular track.

I. If the speed of the nth(n > 1) contestant is n times the speed of the (n-1)th contestant then the nth contestant meets (n+1)th contestant at the starting point n times as frequently as he meets the (n-1)th contestant.


II. If the speed of the nth(n > 1) contestant is n times the speed of the 1st contestant then the 2nd contestant and 4th contestant meet each other twice as frequesntly as the 6th and the 7th contestant.

Which of the following is correct?

(a) Only I (b) Only II (c) Both I and II (d) none of the foregoing

------------------------------------------------------------ Quant Question # 35 ------------------------------------------------------------

Let f(x,y) = 1 if |x - y| <= 1/2 = 0 otherwise Then g(y) = f(1/4,y)f(3/4,y) is maximized with respect to y if only if

(a) y = 1/2 (b) y >= 3/4 (c) 3/8 <= y <= 5/8 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 36 ------------------------------------------------------------

How many pairs of positive integers a, b have b < a < 1000 and their arithmetic mean equal to their geometric mean plus 2? (a) 2 (b) 3 (c) 29 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 37 ------------------------------------------------------------

p,q,r,s are natural numbers in increasing order such that p, q, r is an arithmetic progression; q, r, s is a geometric progression, and s - p = 30. Then p + q + r + s is (a) 129 (b) 139 (c) 149 (d) 169

------------------------------------------------------------ Quant Question # 38 ------------------------------------------------------------

Which among the following 3 statements is/are true? I. The minimum value of (x+5)(x+2)/(x+1) is 9 for x > -1 II. The maximum value of (100^n)/n! occurs at n = 100 only III. For any real numbers x, y > 1, x^2/(y - 1) + y^2/(x - 1) >= 8

(a) Only II (b) Only III (c) Both I and II (d) none of the foregoing


------------------------------------------------------------ Quant Question # 39 ------------------------------------------------------------

The sum of the infinite series 1 + 3x + 4x^2 + 10x^3 + 18x^4 + ... at x = 1/3 is (a) 28/9 (b) 25/8 (c) 49/16 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 40 ------------------------------------------------------------

The number of unordered positive real solutions to x^3 + y^3 + z^3 = 4(x + y + z), and x^2 + y^2 + z^2 = xyz are (a) 1 (b) 0 (c) more than 1 but finite (d) infinite ------------------------------------------------------------ Quant Question # 41 ------------------------------------------------------------

x(i) are reals such that -1 < x(i) < 1 and |x(1)| + |x(2)| + ... + |x(n)| = 99 + |x(1) + ... + x(n)|. What is the smallest possible value of n? (a) 200 (b) 100 (c) 201 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 42 ------------------------------------------------------------

Between 2 station the first, second and the third class fares were fixed in the ratio 8:6:3, but afterwards the first class fares were reduced by 1/6 and second class by 1/12. In a year the number of first, second and third class passenger were in ratio 9:12:26 and the money at the booking counter was 1326. How much in all was paid by first class passengers? (a) 320 (b) 360 (c) 420 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 43 ------------------------------------------------------------

I. A right angled triangle with integer sides has one side as 18 cm. Let M be the maximum possible area, and let N be the smallest possible area of this triangle. Then M-N is greater than 600 sq. cm II. A square of maximum possible area is put inside an equilateral triangle of side (2+3^1/2) cm. The area of the circle inscribed within this square is less than 2 sq. units Which of the above two statement(s) is/are true?


(a) Only II (b) Both I and II (c) Only I (d) none of the foregoing ------------------------------------------------------------ Quant Question # 44 ------------------------------------------------------------

The houses of 3 of my friends - Anupam, Shrikant and Nilesh - are located at the three vertices of the colony(triangular in shape) near my home. Given below are the directions to reach each of their houses from my home. Anupam's house: 12 m to the South and 40 m to the East Shrikant's house: 13 m to the West and 110 m to the North Nilesh's house: 15 m to East and 14 m to the North There is a temple passing through the houses of Nilesh and Shrikant. Anupam starts from his house and takes the shortest possible route to reach the temple. What is the distance travelled by Anupam? (a) 16.72 m (b) 24.56 m (c) 18.64 m (d) none of the foregoing

------------------------------------------------------------ Quant Question # 45 ------------------------------------------------------------

I. The remainder when 28! is divided by 62 is 46 II. Let N be a positive integer such that N when divided by 9, 10, and 11 leaves remainder as 4, 5, and 6 respectively. The remainder when N^3 + 2N^2 - N - 3 is divided by 60 is 47. Which of the above two statement(s) is/are true? (a) Only I (b) Only II (c) Both I and II (d) none of the foregoing

------------------------------------------------------------ Quant Question # 46 ------------------------------------------------------------

Four circles with radii 5, 5, 8, a are mutually externally tangent. Then the value of a is (a) 8/9 (b) 2/3 (c) 16/9 (d) 14/9

------------------------------------------------------------ Quant Question # 47 ------------------------------------------------------------

There are 100 children numbered 1 to 100 and 100 boxes numbered 1 to 100. Each box contains 1000 toffees. The first child takes 1 toffee each from boxes numbered 1, 2, 3,...,


100. The second child takes two toffees each from boxes numbered 2, 4, 6, ..., 100, the third child takes three toffees each from boxes numbered 3, 6, 9, ..., 99 and so on till the hunderedth child. Which among the following is/are false? I. The box left with minimum number of toffees is box numbered 64. II. The number of boxes from where exactly 2 children took toffee is 25. III. The number of boxes from where twice the number of toffees were taken as the number on the box is 2. (a) I and III (b) Only I (c) II and III (d) I, II and III

------------------------------------------------------------ Quant Question # 48 ------------------------------------------------------------

The integer solutions (a,b) to a^4 + 2(a^3) + 2(a^2) +2a + 1 = b^2 is/are (a) 0 (b) 1 (c) more than 2 but finite (d) infinitely many

------------------------------------------------------------ Quant Question # 49 ------------------------------------------------------------

Let x = (n^4 + 256 + 4n(n^2 + 16))/(n+4)^2. If 4 <= n^2 <= 49 then, (a) 12 <= x <= 95 (b) 28 <= x <= 95 (c) 12 <= x <= 37 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 50 ------------------------------------------------------------

Nokia maufactures mobile handsets and marks a price which is 8 times the manufacturing price, and prints it on the handset. They sell it to a distributor at a certain discount. The distributor then sells it to the wholesaler and offers him a discount equal to 3/4th of the discount that he received from the manufacturer. The wholesaler then sells it to the retailer at a discount equal to 2/3rd of the discount he received from the distributor. The retailer finally sells it to the customer at a discount equal to 1/2 the discount that he received from the wholesaler. If all the discounts are given on the price printed on the box and if the wholesaler made a profit of 50%, then who made the least profit? (a) Manufacturer (b) Distributor (c) Wholesaler (d) Retailer



------------------------------------------------------------ Quant Question # 51 ------------------------------------------------------------

Allwin went to the market and bought some chikoos, mangoes, and bananas. Allwin bought 42 fruits in all. The number of bananas is less than half the number of chikoos; the number of mangoes is more than one-third the number of chikoos and the number of mangoes is less than three-fourths the number of bananas. How many more/less bananas did Allwin buy than mangoes?


------------------------------------------------------------ Quant Question # 52 ------------------------------------------------------------

The roots of x^4 – x^3 – x^2 – 1 = 0 are a, b, c, d. The numerical value of f(a) + f(b) + f(c) + f(d), where f(x) = x^6 – x^5 – x^3 – x^2 – x is

(a) –4 (b) 2 (c) 6 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 53 ------------------------------------------------------------

If a +4b + 9c + 16d + 25e + 36f + 49g = -1; 4a + 9b + 16c + 25d + 36e + 49f + 64g = -2; 9a + 16b + 25c + 36d + 49e + 64f + 81g = 3.

Then 16a + 25b + 36c + 49d + 64e + 81f + 100g is


------------------------------------------------------------ Quant Question # 54 ------------------------------------------------------------

The number of roots of the equation x + | x^2 - 1 | = k, where k is a real constant is/are

(a) 4 for k = 6/5 (b) 3 for k = 5/4 (c) 2 for -1 < k < 1 (d) All of the foregoing

------------------------------------------------------------ Quant Question # 55 ------------------------------------------------------------

Vineet and Amar are 100m apart. Vineet runs in a straight line at 8m/s at an angle of 60 degrees to the ray towards Amar.


Amar runs in a straight line at 7m/s at an angle which gives the earliest possible meeting with Vineet. How far has Vineet run when he meets Amar?

(a) 20 s (b) 33.33 s (c) 40 s (d) 30 s

------------------------------------------------------------ Quant Question # 56 ------------------------------------------------------------

A non-constant polynomial f(x) satisfies 8(x-1)*f(x) = (x-8)*f(2x), then f(x) is the polynomial of degree

(a) 3 (b) 4 (c) either 3 or 4 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 57 ------------------------------------------------------------

x and y are complex numbers such that x^2 + y^2 = 7, x^3 + y^3 = 10. What is the smallest possible real value of x + y?

(a) -5 (b) -1 (c) 4 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 58 ------------------------------------------------------------

A road network is in shape of a regular hexagon ABCDEF with centre O. There are 6 more roads OA, OB, OC, OD, OE, and OF. Anupam starts at A and continually travels along ABCDEFA, while Shruti starts simultaneously at O and continually travels along OABOCDOEFO. If by the time Anupam crosses C for the second time, Shruti overtakes Anupam on each of the roads AB, CD and EF, then which of the following is the ratio of speed of Shruti and Anupam?

(a) 3:2 (b) 5:3 (c) can not be determined (d) none of the foregoing

------------------------------------------------------------ Quant Question # 59 ------------------------------------------------------------

Varun has to call his friend Amar, but he doesn't remember Amar's phone number. He has two options, first to try calling Amar directly and in case he doesn't get the number right he could try the second option of calling up Vineet, another friend of his who would in turn give cosmic_glitch's number of who finally give him Amar's number. Alternatively, Varun can try the second option first. Given Varun needs to minimize the total number of calls he has to make, what should be the minimum level of certainity that Varun should have regarding the number he already has so that it would be advisable for him to try the first option before the second?


(a) 25% (b) 75% (c) 100/3% (d) 200/3%

------------------------------------------------------------ Quant Question # 60 ------------------------------------------------------------

ABC is a right-angled triangle. P, Q, R are the points of contact of the incircle of ABC on the sides AB, BC, CA respectively. If AP/PB and CQ/QB are both integers, then AP/PB + CQ/QB is

(a) 3 (b) 5 (c) 6 (d) 4

------------------------------------------------------------ Quant Question # 61 ------------------------------------------------------------

Two functions are defined on xy plane for any arbit point(x, y) where x, y, a, b are positive. Given, f(x, y) = (ax, y) and g(x, y) = (x, by). If the quadrilateral formed by (3, 4), f(3, 4), (5, 6) and g(5, 6) is convex then which among the following is true?

(a) If b > 1, then a < 5/3 (b) If a > 5/3, then b > 2/3 (c) If 1 < a < 5/3 then b < 2/3 (d) Atleast two of the foregoing

------------------------------------------------------------ Quant Question # 62 ------------------------------------------------------------

A bird starts flying from a place O towards B via A. There is no wind resistance from O to A. But there is uniform wind resistance between A and B. To travel from O to B the bird takes 12 minutes, whereas to travel from B to O via A, the bird takes 14 minutes. Had there been wind resistance between O and A also (which equals that between A and B), the bird would have taken only 11 minutes to travel from O to B. O, A and B are collinear.If there was the same wind resistance between O and A as between A and B, what would be the time taken by the bird to travel from B to O?

(a) 12.5 min (b) 15.4 min (c) 18.2 min (d) none of the foregoing

------------------------------------------------------------ Quant Question # 63 ------------------------------------------------------------

The mid-points of triangle ABC are joined to form another triangle PQR along with three other triangles. Again the mid-points of the triangle PQR are joined to form another triangle along with three other triangles. This process is repeated infinite times. If the area of triangle ABC is 6 sq. cm then what is the sum of the area of all the triangles formed in the figure?

(a) 12 sq. cm (b) 14 sq. cm (c) 18 sq. cm (d) none of the foregoing


------------------------------------------------------------ Quant Question # 64 ------------------------------------------------------------

In a class the number of students who do not play hockey, volleyball, cricket, football are 16, 21, 11, 15 respectively. The number of students who do not play any of the games mentioned is 9. What can be the maximum number of students in the class who do not play one or more of the four games mentioned?

(a) 36 (b) 54 (c) can not be determined (d) none of the foregoing

------------------------------------------------------------ Quant Question # 65 ------------------------------------------------------------

What is the volume closest to an integer of a right circular cone that can be formed from a strip ABC(which is in shape of a right-angled triangle) with C as vertex of length AB=10 cm and other two sides as 6cm and 8cm?

(a) 9 (b) 11 (c) 7 (d) 13

------------------------------------------------------------ Quant Question # 66 ------------------------------------------------------------

Let [x] denotes an integer less than or equal to x e.g. [1.23] = 1. How many different values are taken by the _expression [x] + [5x/3] + [2x] + [3x]+ [4x] for x in the interval [0, 100]?

(a) 224 (b) 334 (c) 624 (d) 734

------------------------------------------------------------ Quant Question # 67 ------------------------------------------------------------

A cube of edge 12 ft is placed on the floor with one of the faces touching a wall. A ladder of length 35 ft is resting against that wall and is touching an edge of the cube. At what height does the end of the ladder touch the wall, given that it is more than the distance of the foot of the ladder from the wall?

(a) 12 ft (b) 16 ft (c) 24 ft (d) 28 ft

------------------------------------------------------------ Quant Question # 68 ------------------------------------------------------------

What is the least number of cuts required to cut a cube into 100 identical pieces, assuming all cuts are made parallel to the faces of the cube?



------------------------------------------------------------ Quant Question # 69 ------------------------------------------------------------

Let S be the set of first 999 natural numbers. What is the smallest number n such that given any n distinct numbers from S, one can choose four different numbers x, y, z, k such that x + 2y + 3z = k?

(a) 667 (b) 835 (c) no such value of n exists (d) none of the foregoing

------------------------------------------------------------ Quant Question # 70 ------------------------------------------------------------

From a solid cone of height 2 cm and radius 2*(2^1/2) cm, the maximum possible cube is cut. What is the volume(approximately) of the remaining portion in cubic cm? Assume pi = 22/7.

(a) 10.5 (b) 12 (c) 13.5 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 71 ------------------------------------------------------------

There is an empty conical tank(with its vertex facing downwards). A tap was opened into this tank, so as to fill it in a certain time. After, some time when the tank was full upto half its height, a leak was detected at the vertex and was immediately plugged. If the leak was detected exactly at the moment was the tank was supposed to be half full, then the time in which the leak alone can empty a full tank is how many times that in which the tap alone can fill the empty tank?

(a) 4/3 (b) 8/7 (c) 3/2 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 72 ------------------------------------------------------------

The number of real roots of the equation |1 - |x|| - (1.01)^(1.01x) = 0 is/are


------------------------------------------------------------ Quant Question # 73 ------------------------------------------------------------

Let x be real and f(x) be the largest value of |y^2 - xy| for y in [0, 1]. What is the minimum value of f (x)?

(a) 1/4 (b) 3 - 2*(2^1/2) (c) (2^1/2 - 1)/2 (d) none of the foregoing


------------------------------------------------------------ Quant Question # 74 ------------------------------------------------------------

ABCDEF is a regular hexagon. Points P and Q are on AB and CD respectively such that AP/BP = CQ/QD = 3. What is the ratio area(BPQC)/area(ABCDEF)?

(a) 5:24 (b) 11:54 (c) 19:96 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 75 ------------------------------------------------------------

The inhabitants of Planet-X measure time in hours and minutes which is different from out measurement of earth. The day in Planet-X consists of 36 hours with each hour having 120 minutes. The dials of their clock shows 36 hours. What is the angle(in Planet-X degrees) between the hours and the minute hands when it shows a time of 11:24? The angle around a point in planet-X is 720 degrees.

(a) 100 (b) 80 (c) 120 (d) 60

------------------------------------------------------------ Quant Question # 76 ------------------------------------------------------------

The digits of a four digit number form an arithmetic progression, not necessarily in the same order. How many such four digit numbers are possible if the arithmetic mean of all the digits is an integer?

(a) 72 (c) 84 (c) 90 (d) 96

------------------------------------------------------------ Quant Question # 77 ------------------------------------------------------------

Let f: R -> R and f(x+2) = 1/2 + (f(x) - (f(x))^2)^1/2. Then which among the following is always true?

(a) f(2) = f(4) (b) f(3) = f(7) (c) f(4) = f(10) (d) Atleast 2 of the foregoing

------------------------------------------------------------ Quant Question # 78 ------------------------------------------------------------

A natural number is abundant if its proper divisors (not including itself) add up to more than the number. (For example: 24 is abundant because the divisors of 24 are 1, 2, 3, 4, 6, and 12, 24 and 1 + 2 + 3 + 4 + 6 + 12 = 28 > 24) . How many divisors does the smallest abundant odd number has?


(a) 18 (b) 12 (c) 16 (d) 8

------------------------------------------------------------ Quant Question # 79 ------------------------------------------------------------

Shrikant and Sachin start running simulataneosly from the diametrically opposite ends of a circular track towards each other at 15km/h and 25km/h respectively. After every 10 minutes their speed reduce to half of their current speeds. If the length of the circular track is 1500m, how many times will Shrikant and Sachin meet on the track?


------------------------------------------------------------ Quant Question # 80 ------------------------------------------------------------

At Pizza-Hut pizzas are made only on an automatic pizza-making machine. The machine continually makes different sorts of pizzas by adding different sorts of toppings on a common base. The machine makes the pizzas at the rate of 1 pizza per minute. The various toppings are added to the pizza in the following manner. Starting from every pizza, every fifth pizza is topped with pepperoni, every seventh with olive and baby corn, every eigth with mushroom, and the rest with chesse and tomatoes. The machine works for 13 hours per day without any breaks in between. How many pizzas per day are made with cheese and tomatoes as topping?


------------------------------------------------------------ Quant Question # 81 ------------------------------------------------------------

What is the least perimeter of an obtuse-angled triangle with integer sides, whose one acute angle is twice the other?

(a) 45 (b) 56 (c) 65 (d) 77

------------------------------------------------------------ Quant Question # 82 ------------------------------------------------------------

If the real numbers p, q satisfy p - 3p + 5p - 17 = 0, q - 3q + 5q + 11 = 0. Then the numerical value of p+q is

3 2 3 2

(a) -5 (b) 2 (c) 8 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 83 ------------------------------------------------------------


Tushar wants to buy a total of 100 toffees with exactly a sum of Rs 100 that he has with him. He can buy snickers, eclairs, and pan-pasand at Rs 2, 0.5 and Rs 0.1 per toffee respectively. If Tushar has to buy one toffee of each type, then in how many distinct ways can Tushar make his purchase?


------------------------------------------------------------ Quant Question # 84 ------------------------------------------------------------

How many 6-letter sequences are there which use only A, B, C (and not necessarily all of those), with A never immediately followed by B, B never immediately followed by C, and C never immediately followed by A?


------------------------------------------------------------ Quant Question # 85 ------------------------------------------------------------

ABC is a triangle with sides AB = 4, BC = 5, and CA = 6. D and E are the foot of the altitutes from the vertices A and B to the respective opposite sides. What is the values of the ratio CD/CE?

(a) 2/3 (b) 3/4 (c) 4/5 (d) 5/6

------------------------------------------------------------ Quant Question # 86 ------------------------------------------------------------

The integer sequence a1, a2, a3, ... satisfies a(n+2) = a(n+1) - a(n) for n > 0. The sum of the first 1492 terms is 1985, and the sum of the first 1985 terms is 1492. The sum of the first 2001 terms is


------------------------------------------------------------ Quant Question # 87 ------------------------------------------------------------

Harish and Manish run back and forth from Model colony to Kothrud at the speeds 12km/h and 18km/h respectively. They start simultaneously - Manish from Model colony and Harish from Kothrud. If they cross each other for the first time in 14 minutes from the start, at what distance from Kothrud will they cross each other for the fifth time?

(a) 2.8 km (b) 3.5 km (c) 4.2 km (d) 4.8 km


------------------------------------------------------------ Quant Question # 88 ------------------------------------------------------------

A point is selected at random from the four quadrants of the XY plane. For each of the points selected, all possible lines are drawn which pass through the point and only two quadrants. What is the maximum number of points at which these lines can intersect?

(a) 55 (b) 41 (c) 29 (d) 19

------------------------------------------------------------ Quant Question # 89 ------------------------------------------------------------

Consider the function f(x) =(1- x)^(-1) + (1 - x)^(-2)+ (1 - x)^(-3) + (1 - x)^(-4) defined over the range 0 < x < 1. Then the number of real roots of f(x) = 2 is/are

(a) 0 (b) 1 (c) 2 (d) 4

------------------------------------------------------------ Quant Question # 90 ------------------------------------------------------------

In a parallelogram ABCD, the bisector of angle ABC intersects AD at a point M. IF MD = 5 cm, BM = 6 cm and CM = 6 cm, then the length of AB(in cm) is

(a) 4 (b) 4.5 (c) 6 (d) 7.5

------------------------------------------------------------ Quant Question # 91 ------------------------------------------------------------

A task is assigned to a group of 11 men, not all of whom have the same capacity to work. Every day exactly 2 men out of the group work on the task, with no pair of men working together twice. Even after all the possible pairs have worked once, all the men together had to work for exactly one day more to finish the task. What is the number of days that will be required for all the men working together to finish the job?


------------------------------------------------------------ Quant Question # 92 ------------------------------------------------------------

N!(N > 100) is divided by 10^x to leave a remainder of r (r >= 0). If x is the maximum possible and r is the minimum possible, then the last digit of the quotient is (a) always odd (b) odd when x is even (c) always even (d) even when x is odd


------------------------------------------------------------ Quant Question # 93 ------------------------------------------------------------

If positive integers a, b, c are such that the quadratic equation ax^2 - bx + c = 0 has two distinct real roots in the open interval (0, 1), find the minimum value of a.

(a) 2 (b) 3 (c) 5 (d) 9

------------------------------------------------------------ Quant Question # 94 ------------------------------------------------------------

The midpoints of the sides AB, BC, CD, DA of the parallelogram ABCD are E, F, G, H respectively. Each midpoint is joined to the two vertices not on its side. What is the ratio of the area outside the resulting 8-pointed star to the area of the parallelogram?

(a) 1/3 (b) 2/5 (c) 3/8 (d) 2/3

------------------------------------------------------------ Quant Question # 95 ------------------------------------------------------------

Find the maximum value of 3x + 4y if x^2 + y^2 = 6x - 4y - 4


------------------------------------------------------------ Quant Question # 96 ------------------------------------------------------------

The surface of a right circular cone is painted black. The cone has height 4 and its base has radius 3. It is cut into two parts by a plane parallel to the base, so that the volume of the top part (the small cone) divided by the volume of the bottom part (the frustrum) equals the painted area of the top part divided by the painted are of the bottom part. The height of the small cone is


------------------------------------------------------------ Quant Question # 97 ------------------------------------------------------------

How many 4-digit positive integers have the sum of their two leftmost digits equal to the sum of their two rightmost digits? (a) 615 (b) 485 (c) 545 (d) none of the foregoing


------------------------------------------------------------ Quant Question # 98 ------------------------------------------------------------

Rahul walks down an up-escalator and counts 150 steps. Aarav walks up the same escalator and counts 75 steps. Rahul takes three times as many steps in a given time as Aarav. How many steps are visible on the escalator? (a) 180 (b) 150 (c) 210 (d) 120

------------------------------------------------------------ Quant Question # 99 ------------------------------------------------------------

How many natural numbers less than 100 are there such that n^2 does not divide n!?


------------------------------------------------------------ Quant Question # 100 ------------------------------------------------------------

For real m, n the function f(x) = 1/(mx+n). What is the relation between m and n such that there exist distinct real p, q, r where f(p) = q, f(q) = r, f(r) = p?

(a) n= -m^2 (b) n = m^2 (c) m = -n^2 (d) m = n^2



------------------------------------------------------------ Quant Question # 101 ------------------------------------------------------------

At his normal speed, Shirish can travel 18 km downstream in a fast flowing stream in 9 hours less than what he takes to travel the same distance upstream. The downstream trip would take 1 hour less than what the upstream trip would take provided he doubles his rate of rowing. What is the speed of the stream in km/hr? (a) 20/3 (b) 8 (c) 33/4 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 102 ------------------------------------------------------------

If a, b, c, d are real numbers with a^2 + b^2 + c^2 + d^2 = 100, then what is the maximum value of 2a + 3b + 6c + 24d? (a) 240 (b) 250 (c) 300 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 103 ------------------------------------------------------------

On the first day of GMP course in XLRI, the class registered cent percent attendance from the students for the 2 hour introduction lecture. Some students arrived late for the class while some left early before the lecture could get finished in 2 hours. A third of who arrived on time for the class left early, and the rest left on time. Of those who arrived early for the class, a fourth left early while an equal number left late and the rest left on time. Also, half of the number of students arriving late left on time and the rest left late. It is know that the students who left early is half the number who arrived early while the number of students who left on time is 4 less than twice the number who arrived on time and the number of students who left late is exactly 1 less than the number who arrived late. How many students had enrolled for the GMP course? (a) 31 (b) 41 (c) 47 (d) can not be determined ------------------------------------------------------------ Quant Question # 104 ------------------------------------------------------------

A triangle has sides 13, 14, 15. It is rotated through 180 degrees about its centroid to form an overlapping triangle. Find the area of the union of the two triangles. (a) 84 (b) 56 (c) 126 (d) none of the foregoing


------------------------------------------------------------ Quant Question # 105 ------------------------------------------------------------

The distance AB is 12. The circle center A radius 8 and the circle center B radius 6 meet at P (and another point). A line through P meets the circles again at Q and R (with Q on the larger circle), so that QP = PR. Then the length of QP is

(a) (120)^1/2 (b) (130)^1/2 (c) (160)^1/2 (d) none of the foregoing

------------------------------------------------------------ Quant Question # 106 ------------------------------------------------------------

What is the largest possible number of elements in a subset S` of S = {1, 2, 3, ... , 9} such that the sum of every pair of distinct elements in S` is different?


------------------------------------------------------------ Quant Question # 107 ------------------------------------------------------------

How many solutions does n - [n ] = (n - [n]) have satisfying 1 ≤ n ≤ 5 where [n] denotes 2 2 2

greatest integer less than or equal to n?


--------------------------------------------------------- Quant Question # 108 ---------------------------------------------------------

Let P(a) = ab + b -a -1, then numerical value of P(1)*P(2)*P(3)*...*P(100) where b = (a^2 + 3a +1)/(a^2 + 2a +1) is

(a) 1/100 (b) 101 (c) 1/101 (d) 101

--------------------------------------------------------- Quant Question # 109 ---------------------------------------------------------

There are 2 vertical flagposts of heights 5*(3^1/2) m and 10*(3^1/2) m respectively, which are 10 meters apart. Vineet picks up a random point on the ground between the flagposts and observes the angle of elevation of the 2 flagposts. What is the chance that Vineet will find both the falgposts subtending an angle of atleast 60 degrees? (a) 50% (b) 75% (c) 100% (d) none of the foregoing


--------------------------------------------------------- Quant Question # 110 ---------------------------------------------------------

What is the sum of all positive rationals p/30 (in lowest terms) which are less than 10?


--------------------------------------------------------- Quant Question # 111 ---------------------------------------------------------

ABCDE is a 5-sided convex figure such that each triangle formed by 3 adjacent vertices of ABCDE has area 1. What is the area of the convex figure?

(a) (5 + 5^1/2)/2 (b) 3 (c) 2 + 3^1/2 (d) 5^1/2 + 2

--------------------------------------------------------- Quant Question # 112 ---------------------------------------------------------

A washerman can wash 6 trousers or 8 shirts in 1 hour while his wife can wash 6 trousers or 8 shirts in 2 hours. The couple get a work of 160 trousers and 200 shirts to wash. The man and the woman work on alternate hours and for a total of 12 hours daily. Every morning except the first the lady starts the work. If the couple worked for only 5 hours on the first day with the man starting the work at noon, then (a) the man finishes the work on 7th day (b) the woman finishes the work on 6th day (c) the man finishes the work on 8th day (d) the woman finishes the work on 8th day

--------------------------------------------------------- Quant Question # 113 ---------------------------------------------------------

The remainder when 17^83 + 83^17 is divided by 1411 is

(a) 0 (b) 66 (c) 1 (d) 100

--------------------------------------------------------- Quant Question # 114 ---------------------------------------------------------

Four dices(6-faced) are thrown. How many different arrangements can one get if the order is unimportant(e.g. 2356 is same as 2635 or 1124 is same as 4211)?



--------------------------------------------------------- Quant Question # 115 ---------------------------------------------------------

The maximal possible value of the product of certain pairwise distinct positive integers whose sum is 100 is (a) 15!/48 (b) 14!/4 (c) 4*(3^32) (d) none of the foregoing

--------------------------------------------------------- Quant Question # 116 ---------------------------------------------------------

Let [n] denotes greatest integer less than or equal to n. The number of real solutions to the equation 4n^2 - 40[n] + 51 = 0 are


--------------------------------------------------------- Quant Question # 117 ---------------------------------------------------------

A car X starts from a town A and goes towards point C. At the same time, car Y starts from a town B(lying between A and C) and goes towards town C. X catches up with Y at a town M between B and C. A car Z starts from town A when the cars X and Y meet. The cars X and Z meet at a point N where CN=AB. The cars Y and Z meet at a point O where MO= 20 miles. Then the length of AB given AC = 140 miles and BM = 20 miles is (a) 20 miles (b) 60 miles (c) 30 miles (d) 40 miles

--------------------------------------------------------- Quant Question # 118 ---------------------------------------------------------

ABCD is a rectangle. The points P, Q lie inside it with PQ parallel to AB. Points X, Y lie on AB (in the order A, X, Y, B) and W, Z on CD (in the order D, W, Z, C). The four parts AXPWD, XPQY, BYQZC, WPQZ have equal area. If BC = 19, PQ = 87, XY = YB + BC + CZ = WZ = WD + DA + AX, then the length of AB is (a) 241 (b) 163 (c) 217 (d) 193

--------------------------------------------------------- Quant Question # 119 ---------------------------------------------------------

The area enclosed by the graph of |x - 60| + |y| = |x/4| is (a) 240 (b) 360 (c) 480 (d) none of the foregoing


--------------------------------------------------------- Quant Question # 120 ---------------------------------------------------------

Let N be the largest integer divisible by all positive integers less than its cube root. The number of divisors of N are (a) 16 (b) 24 (c) 18 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 121 ---------------------------------------------------------

A right circular cone has base radius 1. The vertex is V. C is a point on the circumference of the base. The distance VC is 3. A particle travels from C around the cone and back by the shortest route. Its minimum distance from V is (a) 5/4 (b) 2 (c) 5/3 (d) 3/2

--------------------------------------------------------- Quant Question # 122 ---------------------------------------------------------

Sanjog and Rahul took part in a two-day maths contest. At the end both had attempted questions worth 500 marks. Sanjog scored 160 out of 300 attempted on the first day and 140 out of 200 attempted on the second day, so his two-day success ratio was 3/5. Rahul's attempted figures were different from Sanjog's (but with the same two-day total). Rahul had a positive integer marks on each day. For each day Rahul's success ratio was less than Sanjog's. What is the largest possible two-day success ratio that Rahul could have achieved? (a) 81/125 (b) 349/500 (c) can not be determined (d) none of these

--------------------------------------------------------- Quant Question # 123 ---------------------------------------------------------

The number of solutions of |||||n^2-n-1| - 2| - 3| - 4| - 5| = n^2 + n - 30 is/are

(a) 0 (b) 2 (c) more than 2 (d) none of these

--------------------------------------------------------- Quant Question # 124 --------------------------------------------------------- How many 5-digit numbers are there such that each number contains the block '15' and is divisible by 15? (a) 479 (b) 487 (c) 515 (d) none of the foregoing


--------------------------------------------------------- Quant Question # 125 ---------------------------------------------------------

A positive integer p is divisible by positive integer q if the sum of divisors of p is divisible by the number of divisors of q. How many positive integers less than 200 is 200 divisible by? (a) 14 (b) 25 (c) 31 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 126 ---------------------------------------------------------

The equation x^8 + y^8 = 8xy - 6 has N solutions where x, y are real numbers. Then N is


--------------------------------------------------------- Quant Question # 127 ---------------------------------------------------------

A leaf is torn from a paperback novel. The sum of the remaining pages is 15,000. What can be the page numbers on the torn leaf, given that it has only one page?

(a) 12 (b) 200 (c) 113 (d) atleast 2 of the foregoing

--------------------------------------------------------- Quant Question # 128 ---------------------------------------------------------

PQR is a triangle. QA is the angle bisector. The point B on PQ is such that <(PRB) = 2/5* <(PRQ). QA and RB meet meet at C. AB=AR=RC. The <P measures (in degrees)

(a) 30 (b) 45 (c) 60 (d) 75

--------------------------------------------------------- Quant Question # 129 ---------------------------------------------------------

The number of ordered pair (x, y) solutions to (logx/log2)*(logy/log4) + log(4-x)/log4, log(x+y)/log3 = (logx/y)/log3 is/are


--------------------------------------------------------- Quant Question # 130 ---------------------------------------------------------


PagalGuy starts training institute in one room. The room had a fixed capacity of less than 35 seats. The number of students enrolling for the first course was only half of the room's capacity. For the second course half of those enrolled for the first course did not take re-admission, while some more joined and the class was to two-third of the capacity. For the third course, half of the existing students did not take the re-admission, but because some more students joined the course, the class the 75% full. For the fourth course, half of the existing students did not take re-admission, but as some new students joined the course, the class had just one student less than the full capacity. How many students did PagalGuy train the whole year? (a) 46 (b) 56 (c) can not be determined (d) none of the foregoing --------------------------------------------------------- Quant Question # 131 --------------------------------------------------------- Let I be the set of integers. f is a function from I-> {1, 2, 3, ... , n} such that f(X) and f(Y) are unequal whenever X and Y differ by 5, 7 or 12. The smallest possible n is (a) 4 (b) 5 (c) 7 (d) none of the foregoing --------------------------------------------------------- Quant Question # 132 --------------------------------------------------------- The remainder when 22^23 + 10^35 is divided by 45 is (a) 2 (b) 11 (c) 8 (d) none of the foregoing --------------------------------------------------------- Quant Question # 133 --------------------------------------------------------- CAT 2010 quant section had three sections consisiting of 8, 7, and 6 questions respectively. A total of 17 questions are to be answered with a minimum of three from each section. The number of questions answered from the second section(which has 7 questions)should be more than the number of questions answered from each of the other two sections. In how many ways can a candidate answer 17 questions from quant section of CAT 2010? (a) 336 (b) 840 (c) 1176 (d) none of the foregoing --------------------------------------------------------- Quant Question # 134 ---------------------------------------------------------

A book contains 30 stories. Each story has a different number of pages under 31. The first story starts on page 1 and each story starts on a new page. What is the largest possible number of stories that can begin on odd page numbers?



--------------------------------------------------------- Quant Question # 135 ---------------------------------------------------------

A milkman had a mixture of milk and water with him. the ratio of milk to water is 4:5. He then boils the mixture so as to achieve a concentration of 50%. But, since he was distracted by the world cup finals being telecast live on T.V., he boiled the milk and realised that the initial ratio of milk to water has been reveresed. If, by then he has boiled the milk for exactly 90/7 minutes, find the extra time for which the milk has boiled, given that the rate of evaporation of water is 50% more than that of milk.


--------------------------------------------------------- Quant Question # 136 ---------------------------------------------------------

Two cars A and B started from P and Q respectively towards each other at the same time. Car A was travelling at a speed of 54km/h but due to some problem reduced its speed by 1/3rd after travelling for 60 minutes. Car B was travelling at a speed of 36km/h. Had the technical problem in car A had arisen 30 minutes later, they would have met at a distance which is (1/30*PQ) more than towards Q than where they met earlier(PQ > 120km). Anothet car C starts from P, 90 minutes after car B started at Q, and car C travels towards Q with a speed of 36km/h, at what distance from P will cars B and C meet?

(a) 63 km (b) 48 km (c) 40.5 km (d) none of the foregoing

--------------------------------------------------------- Quant Question # 137 ---------------------------------------------------------

Eight people each has a unique piece of news. They make a series of phone calls to one another. In each call, the caller tells the other party all the news he knows, but is not told anything by the other party. What is the minimum number of calls needed for all eight people to know all eight items of news?


--------------------------------------------------------- Quant Question # 138 ---------------------------------------------------------

Chetna and Apple have some marbles with each of them, such that the number of marbles with Apple is thrice that with Chetna. If Chetna distributes her marbles equally among certain number of bags, then she is left with 31 extra marbles. If Chetna and Apple were to pool the marbles and then distribute the total marbles equally among the same number of bags as Chetna did, they will be left with 16 marbles. The number of


marbles with Apple is the largest possible three digit number. How many bags are needed to equally divide all the marbles with Apple, if the number of those bags is the largest two digit number?


--------------------------------------------------------- Quant Question # 139 ---------------------------------------------------------

Let n be a positive integer such that the product of the digits of n is 25n/8 - 211. How many values can n assume?


--------------------------------------------------------- Quant Question # 140 ---------------------------------------------------------

ABC is an equilateral triangle and P satisfies AP=2, BP=3. The maximum value of CP is

(a) less than 5 (b) (26)^1/2 (c) 5 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 141 ---------------------------------------------------------

Rohit, the marketing head of PaGalGuy decides to print QQAD questions where pages are numbered from 2 to 400. The pages are to be read in the following order. Take the last unread page (400), then read (in the usual order) all pages which are not relatively prime to it and which have not been read before. This process is repeated until all pages are read. So, the order would be 2, 4, 5, 6, ... , 400, 3, 7, 9, ... , 399,... . What is the last page to be read?


--------------------------------------------------------- Quant Question # 142 ---------------------------------------------------------

Let C1 and C2 be two concentric circles with C2 in the interior of C1. From a point A on C1 is drawn a tangent AB to C2(B lies on C2). Let C be the second point of intersection of AB and C1, and let D be the mid-point of AB. A line passing through A intersects C2 at E and F in such a way that the perpendicular bisector of DE and CF intersect at a point M on AB. the ratio AM/MC equals

(a) 3/2 (b) 9/4 (c) 5/3 (d) 2


--------------------------------------------------------- Quant Question # 143 ---------------------------------------------------------

If a, b, c are real numbers such that a < b < c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(a) 0 < a < 1 (b) 1 < b < 3 (c) 3 < c < 4 (d) All of them

--------------------------------------------------------- Quant Question # 144 ---------------------------------------------------------

The sum of five real numbers is 8 and the sum of their squares is 16. What is the largest possible value for one of the numbers?

(a) 16/5 (b) 2 (c) 25/8 (d) none of these

--------------------------------------------------------- Quant Question # 145 ---------------------------------------------------------

The set of points x, y which satisfies x^3 - 3xy^2 >= 3x^2*y - y^3 and x+y = -1 is a line segment whose length is

(a) 1/2 (b) (2/3)^1/2 (c) 3^1/2 - 1 (d) 1

--------------------------------------------------------- Quant Question # 146 ---------------------------------------------------------

The children are touring Teen Murti Bhavan. All the children have formed two queues. In every row there are two children. But the first row and in last row there is one teacher. The children are moving at a speed of 10m/min and the length of the queue is 300m. If the teacher in row one wants to send some message, she sends one child from the first row to deliver the message to the teacher in the last row., the child delivers the message and comes back. If the child who delivered the message travelled 1.08 km, then what is the total time required by that child to come back?

(a) 48 minutes (b) 64 minutes (c) 72 minutes (d) 84 minutes

--------------------------------------------------------- Quant Question # 147 ---------------------------------------------------------

ABC is a triangle. D is the midpoint of BC. E is a point onfiltered= 2AD. BE and AD meet at F and <FAE = 60o. then <FEA in degrees is

(a) less than 60 (b) 60 (c) more than 60 (d) can't be determined


--------------------------------------------------------- Quant Question # 148 ---------------------------------------------------------

x, y, z are distinct reals such that y = x(4-x), z = y(4-y), x = z(4-z). The possible value of x+y+z is

(a) 4 (b) 6 (c) 7 (d) 9

--------------------------------------------------------- Quant Question # 149 ---------------------------------------------------------

a, b, c are positive integers forming an increasing geometric sequence, b-a is a square, and (loga + logb + logc)/log6 = 6. Then a + b + c is


--------------------------------------------------------- Quant Question # 150 ---------------------------------------------------------

100 numbers are written around a circle. The sum of every 8 consecutive numbers is 25/2. The 9th number is -1/2, the 19th number is 3/4 and 20th number is 2. What is the 50th number?




--------------------------------------------------------- Quant Question # 151 ---------------------------------------------------------

A quadratic with integral coefficients has two distinct positive integers as roots, the sum of its coefficients is prime and it takes the value -55 for some integer. The sum of the roots is

(a) 32 (b) 20 (c) 24 (d) none of the these

--------------------------------------------------------- Quant Question # 152 ---------------------------------------------------------

Let f(x) = x^3 - 16x^2 + 17x, if f(a) = 16, f(b) = 20, then a+b equals

(a) 16 (b) 4 (c) 8 (d) none of the these

--------------------------------------------------------- Quant Question # 153 ---------------------------------------------------------

A is a series of n terms with x(a natural number) as the first term and every term y(a natural number) is less than the next term. If the product of all the terms of A is always divisible by the product of the first n natural numbers then, which among the following regarding x, y and n must be true always?

(a) x^n = y^n (b) y^n = 1 (c) x is a multiple of y (d) x^n and y^n are co-prime

--------------------------------------------------------- Quant Question # 154 ---------------------------------------------------------

The _expression (52^1/2 + 5)^1/3 - (52^1/2 - 5)^1/3 is

(a) an integer (b) a rational, not integer (c) an irrational (d) irreducible

--------------------------------------------------------- Quant Question # 155 ---------------------------------------------------------

Bus A leaves the terminus every 20 minutes, it travels a distance 1 km to a circular road of length 10 km and goes clockwise around the road, and then back along the same road to to the terminus (a total distance of 12 km). The journey takes 20 minutes and the bus travels at constant speed. Having reached the terminus it immediately repeats the


journey. Bus B does the same except that it leaves the terminus 10 minutes after Bus A and travels the opposite way round the circular road. The time taken to pick up or set down passengers is negligible. A man wants to catch a bus a distance 0 < x < 12 km from the terminus (along the route of Bus A). Let f(x) the maximum time his journey can take. The value of x for which f(x) is a maximum is

(a) 3 (b) 5 (c) 8 (d) 10

--------------------------------------------------------- Quant Question # 156 ---------------------------------------------------------

How many ordered pairs of positive integers m, n satisfy m <= 2n <= 50, n <= 2m <= 50?

(a) 313 (b) 328 (c) 344 (d) 359

--------------------------------------------------------- Quant Question # 157 ---------------------------------------------------------

F is a fixed point in the plane. P, Q, R are points such that FP = 3, FQ = 5, FR = 7 and the area PQR is as large as possible. Then F must be (of PQR)

(a) incentre (b) orthocentre (c) circumcentre (d) centeroid

--------------------------------------------------------- Quant Question # 158 ---------------------------------------------------------

A milkman had two cows. The daily collection of milk from each cow varies randomly and the combined collection of milk from them varies between 20 litres and 50 litres. On Sunday the milkman had a total milk collection of 30 litres. Harry bets Rs 100 on the possibility that the total milk collection on Monday will not differ from that on Sunday by more than 5 litres, while the milkman thinks otherwise. What is the maximum amount the milkman can bet if he can not afford to make a loss?

(a) Rs 200 (b) Rs 250 (c) Rs 300 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 159 ---------------------------------------------------------

Quadrilateral ABCD is inscribed in a circle with diameter AD = 4. If sides AB=BC = 1 then CD equals

(a) 3 (b) 7/2 (c) 4 (d) none of the foregoing


--------------------------------------------------------- Quant Question # 160 ---------------------------------------------------------

If 5 indistinguishable red balls and 4 indistinguishable black balls are placed into 3 cells, then how many distinguishable arrangements are possible?


--------------------------------------------------------- Quant Question # 161 ---------------------------------------------------------

The total ordered pair of positive integers (a, b) such that the roots of equations x^2 -ax + a + b - 3 = 0 and x^2 -bx + a + b - 3 = 0 are also positive integers are


--------------------------------------------------------- Quant Question # 162 ---------------------------------------------------------

John Abrahm is on a bike at the intersection of two straight highways in the desert. He can travel at 50 km per hour on the highway and at 14 km per hour over the desert. The area (in sq. km) John can reach in 6 mins on his bike is

(a) 500/27 (b) 600/29 (c) 700/31 (d) 800/33

--------------------------------------------------------- Quant Question # 163 ---------------------------------------------------------

A class has certain number of students each having 1 to 6 books. the total number of students having 2 to 5 books each is 10. A total of 7 students have 4 to 6 books each. the total number of students having 2 to 3 books is 4.

Which among is following is/are false?

I. If the total number of students in the class is 13, then only 2 students have one book each II. If 6 students have 3 to 4 books each and 4 students have 5 to 6 books each, then only 1 student has 2 books III. If the class has 14 students, and 5 students have 5 to 6 books each, then 9 students have 1 to 4 books each IV. Only 1 student has 6 books

(a) I and III (b) only III (c) II (d) none of these


--------------------------------------------------------- Quant Question # 164 ---------------------------------------------------------

Ten test papers are to be prepared for an exam. Each paper has 4 problems, and no two papers have more than 1 problem in common. At least how many problems are needed?


--------------------------------------------------------- Quant Question # 165 ---------------------------------------------------------

N students are seated at desks in an p x q array, where p, q = 3. Each student shakes hands with the students who are adjacent horizontally, vertically or diagonally. If there are 327 handshakes, what is N?


--------------------------------------------------------- Quant Question # 166 ---------------------------------------------------------

If f(x) = 9^x/(3 + 9^x), then the numerical value of f(1/100) + f(2/100) + f(3/100) + ... + f(99/100) + f(100/100) lies between

(a) 50 and 51 (b) 51 and 52 (c) 100 and 101 (d) none of these

--------------------------------------------------------- Quant Question # 167 ---------------------------------------------------------

How many subsets of {1, 2, 3, ..., 10} exist in which the equation x + y = 11 has no solutions?


--------------------------------------------------------- Quant Question # 168 ---------------------------------------------------------

ABCDE is a regular pentagon. The star ACEBD has area 1. AC and BE meet at P, BD and CE meet at Q. The area of APQD is

(a) 5^1/2 -3^1/2 (b) 2/5 (c) 1/2 (d) none of these


--------------------------------------------------------- Quant Question # 169 ---------------------------------------------------------

There are a certain facts about the software engineers working with an IT firm. Total number of software engineers is 70 out of which 30 are females. 30 people are married. 24 software engineers are above 25 years of age. Out of all married software engineers, 19 are above 25 years, of which 7 are males. 12 males are above 25 years and overall 15 males are married. How many unmarried females are there which are above 25?


--------------------------------------------------------- Quant Question # 170 ---------------------------------------------------------

11 B-schools participate in a LSR festival to be telecasted 3 weeks later on TV. Each day any B-schools not performing watch the others (but B-schools performing that day do not watch the others). What is the smallest number of days for which the LSR festival can last if every B-school watches every other B-school at least once during the festival?


--------------------------------------------------------- Quant Question # 171 ---------------------------------------------------------

In a class of 100 students 70 passed in physics, 62 passed in mathematics, 84 passed in english and 82 passed in chemistry. 37 students passed in all 4 subjects. How many maximum students could have failed all four subjects?


--------------------------------------------------------- Quant Question # 172 ---------------------------------------------------------

There exists a 5 digit number N with distinct and non-zero digits such that it equals the sum of all distinct three digit numbers whose digits are all different and are all digits of N. Then the sum of the digits of N is a perfect

(a) square (b) number (c) cube (d) none of the foregoing

--------------------------------------------------------- Quant Question # 173 ---------------------------------------------------------


Consider two distinct positive integers m and n having integer arithmetic, geometric and harmonic means. The minimum value of |m - n| is


--------------------------------------------------------- Quant Question # 174 ---------------------------------------------------------

ABCD is a rectangle. O is the midpoint of CD. BO meets AC at M. E is a point outside the rectangle such that AE = BE and <(AEB) = 90 degrees. If BE = BC = 2, then area of AEBM is

(a) 6-(12)^1/2 (b) 2+3^1/2 (c) 8/3+(3)^1/2 (d) 2+(32^1/2)/3

--------------------------------------------------------- Quant Question # 175 ---------------------------------------------------------

Amirchand is selling some articles. Amirchand is offering a discount of 33.33% if one pays by credit card. Amirchand has marked on the article in such a way that after giving a discount, he still manages to get a profit of 25%. Garibchand uses false weighing balance and decieves Amirchand by 20% and he also pays the amount by credit card. If Garibchand gives the same article to another customer at 40% discount on marked price of Amirchand and Garibchand has a profit of Rs 20, then what is the cost price of the article in rupees?

(a) 160 (b) 200 (c) 240 (d) 300

--------------------------------------------------------- Quant Question # 176 ---------------------------------------------------------

f(x) is a polynomial such that f(t^2+1) = 6t^4 - t^2 + 5. Then the constant term of f(t^2) is

(a) 3 (b) 4 (c) 6 (d) 12

--------------------------------------------------------- Quant Question # 177 ---------------------------------------------------------

An ant moves around a thread which is in the shape of a triangle. At each vertex it has 1/2 chance of moving towards each of the other two vertices. Let A be the probability that after crawling along 8 edges the ant reaches its starting point. Let B be the probability that after crawling along 10 edges the ant reaches its starting point. Let C be the probability that after crawling along 12 edges the ant reaches its starting point. Then

(a) A > B > C (b) C > A > B (c) C > B > A (d) none of these


--------------------------------------------------------- Quant Question # 178 ---------------------------------------------------------

A taper roller (like frustum of cone) rolls on flat ground. What is the area it is covering on the floor when it rotates one rotation? Here small radius = 6, large radius = 12, and frustum height =8.

(a) 180*pi (b) 300*pi (c) 192*pi (d) none of these

--------------------------------------------------------- Quant Question # 179 ---------------------------------------------------------

Each of the numbers 1, 2, 3, 4, 5, 6, 7, 8 is written at a distinct corner of a cube. Assume that the sum of any three numbers written on a face of the cube is no less than 10. What is the minimum value of the sum of numbers written on a face of the cube?

(a) 13 (b) 14 (c) 15 (d) 16

--------------------------------------------------------- Quant Question # 180 ---------------------------------------------------------

The harmonic mean of two positive integers is 2006. The greatest possible value of their arithmetic mean is


--------------------------------------------------------- Quant Question # 181 ---------------------------------------------------------

A triangle is split into 144 smaller triangles by evenly spaced lines parallel to its sides. Two small triangles that share a side are said to be adjacent. The task is to count the small triangles by first selecting one of them and then moving from a triangle to an adjacent one without stepping twice into the same triangle. What is the maximum number of smaller triangles that can be counted this way?

(a) 133 (b) 144 (c) 72 (d) 134

--------------------------------------------------------- Quant Question # 182 ---------------------------------------------------------

Exactly three of the interior angles of a complex polygon are obtuse. What is the maximum number of sides of such a polygon?

(a) 12 (b) 6 (c) 7 (d) 10


--------------------------------------------------------- Quant Question # 183 ---------------------------------------------------------

For any positive integer n, let f(n) denote the index of highest power of 2 which divides n!. Then the numerical value of f(1) + f(2) + ……. + f(1023) is

a) 518656 b) 518652 c) 508656 d) 418656

--------------------------------------------------------- Quant Question # 184 ---------------------------------------------------------

Prade and Warrior were both given the same 5 digit number (N) but for Prade the thousands digit was concealed while for warrior the hundreds digit was concealed. Both were told that N was divisible by 7. While Warrior could determine the hundreds digit, Prade wanted more information. Which of the following is not a possible value of N?

a) 22428 b) 71323 c) 88564 d) 64624

--------------------------------------------------------- Quant Question # 185 ---------------------------------------------------------

Let a(1), a(2), . . . be a sequence defined by a(1) = a(2) = 1 and a(n+2 )= a( n+1) + a( n) for n >= 1. The value of the summation a(n)/4^(n+1) where n varies from 1 to infinity is

a) 1/11 b) 2/13 c) 1/2 d) none of the foregoing

--------------------------------------------------------- Quant Question # 186 ---------------------------------------------------------

Points A and B are selected onfiltered= -x^2/2 so that triangle ABO is equilateral. The length of one side of triangle ABO (point O is at the origin) is

a) (12)^1/2 b) (18)^1/2 c) (48)^1/2 d) none of the foregoing

--------------------------------------------------------- Quant Question # 187 ---------------------------------------------------------

In a class of 210 students with roll numbers 1 to 210; each student has as many sheets of paper as his roll number. The Math’s teacher takes away all the sheets of paper from all the students whose roll numbers are even. After this, the science teacher takes away all the sheets of paper from all the students whose roll numbers are multiples of 3. Then the English teacher takes away all the sheets of paper from all the students whose roll numbers are multiple of 5. Finally the Hindi teacher takes away all the sheets of paper from all the students whose roll numbers are multiples of 7. What is the total number of sheets of paper left with all the students together?



--------------------------------------------------------- Quant Question # 188 ---------------------------------------------------------

The polynomial x^(2n) + 1 + (x+1)^(2n) is not divisible by x^2 + x + 1 if x equals

(a) 16 (b) 17 (c) 20 (d) 21

--------------------------------------------------------- Quant Question # 189 ---------------------------------------------------------

Square ABCD has side length 6. Circle Q is tangent to sides AB and BC, and is externally tangent to circle P. Circle P is tangent to sides CD and DA, and is externally tangent to circles O1 and O2. Circle O1 is tangent to side CD, circle O2 is tangent to side DA, and circles O1 and O2 are externally tangent to each other and to circle P. If the radius of circle P is twice the radius of circle Q, and if circles O1 and O2 both have radius r, then r is (upto 2 places of decimal)

(a) 0.29 (b) 0.36 (c) 0.47 (d) 0.54

--------------------------------------------------------- Quant Question # 190 ---------------------------------------------------------


There are 100 points in a plane and some pairs of points are connected by lines. There are 1000 lines altogether. A Point is called a “Pagal” if it is directly connected to every other point. What is the largest possible number of Pagals?


--------------------------------------------------------- Quant Question # 191 ---------------------------------------------------------

Consider sequences of infinite positive real numbers of the form a, 4, b….. in which every term after the first is 1 less than the product of its two immediate neighbors. For how many different values of “a” does the term 5 appear somewhere in the sequence?

(a) 1 (b) 3 (c) More than 3 but finite (d) none of the foregoing

--------------------------------------------------------- Quant Question # 192 ---------------------------------------------------------

How many 5 digit numbers are there such that product of its digits is 180?


--------------------------------------------------------- Quant Question # 193 ---------------------------------------------------------

Let function f satisfies f(x) + f(x-1) = x^2 for all x. If f(11) = 40, then the remainder when (f(40))^11 is divided 51 is


--------------------------------------------------------- Quant Question # 194 ---------------------------------------------------------

There are 100 objects in a row on. A painter comes and paints every object red. Then, another painter comes and paints every third object (starting with object number3) blue. Another painter comes and paints every fifth object red (even if it is already red), then another painter paints every seventh object blue, and so forth, alternating between red and blue, until 50 painters have been by. After this is finished, how many objects will be red?


--------------------------------------------------------- Quant Question # 195 ---------------------------------------------------------


Triangle ABC is such that, AB = 4, BC = 5, and AC = 6, and a point D is on BC. B and C are reflected in AD to B” and C”, respectively. Suppose that lines BC” and B”C never meet (i.e., are parallel and distinct). The length of segment BD is

(a) 2 (b) 5/2 (c) 3 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 196 ---------------------------------------------------------

In a chess tournament each player plays every other player once. A player gets 1 point for a win, ½ point for a draw and 0 for a loss. Both men and women played in the tournament and each player scored the same total of points against women as against men. The total number of players in the tournament can be

(a) 31 (b) 16 (c) 21 (d) 36

--------------------------------------------------------- Quant Question # 197 ---------------------------------------------------------

Square PQRS has side length 2. A semicircle with diameter PQ is constructed inside the square, and the tangent to the semicricle from R intersects side PS at E. What is the length of RE?

(a) (2 + 5^1/2)/2 (b) 5^1/2 (c) 5/2 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 198 ---------------------------------------------------------

The average value of |a - b| + |c - d| + |e - f| for all possible permutations a, b, c , d, e, f of 1, 3, 5, 7, 9, 11 is


--------------------------------------------------------- Quant Question # 199 ---------------------------------------------------------

If p, q, r are the roots of x^3 -x -1 = 0, then the numerical value of (1-p)/(1+p) + (1-q)/(1+q) + (1-r)/(1+r) is

(a) 1 (b) -2 (c) 2 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 200 ---------------------------------------------------------


In a certain class of 300 students , the number of students who either do not study at home or do not attend classes is a third more than of those who either study at home or attend classes. the number of students who do not study at home but attend classes is two fifths more than those who study at home but do not attend classes, while the number of students who study at home as well as attend classes is half of those who neither study at home nor attend classes. If the number of students who only study at home or only attend classes is a third less than those who do either, then how many students who either do neither or do both?




--------------------------------------------------------- Quant Question # 201 ---------------------------------------------------------

Let 0 <= x, y <= 1. The positive difference between the maximum and minimum value of (x-2y+1)^2 + (x+y-1)^2 is

(a) 4 (b) 16/3 (c) 25/4 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 202 ---------------------------------------------------------

How many ways are there of determining 6 positive integers a1, a2, ... , a6 such that 1 <= a1 <= a2 = ... <= a6 <= 6?


--------------------------------------------------------- Quant Question # 203 ---------------------------------------------------------

A quadrilateral is obtained by joining the midpoints of the adjacent sides of the rhombus ABCD with <(A) = 60 degrees. The process of joining the mid-points is continued infinitely. If the sum of the areas of all the above said quadrilaterals including ABCD is 64*(3)^1/2 sq. units, what is the sum of the perimeters of all the quadrilaterals including the rhombus ABCD?

(a) 15(5+3^1/2) (b) 32(2+3^1/2) (c) 16*3^1/2 (d) none of these

--------------------------------------------------------- Quant Question # 204 ---------------------------------------------------------

There are three gears having 30, 45 and 60 teeth meshed with each other and are in a straight line. The product of the number of teeth and the rpm(revolutions per minute) are always constant. At a certain point of time, the teeth which are meshing are marked red and whenever the initial arrangement repeats, a beep sound is produced. The second gear is running at 60 rpm. After 5 minutes the sound system is changed and now whenever the arrangement repeats the number of beeps produced is one more than the previous repetition. What is the number of beeps produced in the first 6 minutes?


--------------------------------------------------------- Quant Question # 205 ---------------------------------------------------------


The total number of positive integer solutions to x^3 - y^3 - z^3 = 3xyz, x^2 = 2(x + y + z) is/are

(a) 1 (b) 6 (c) 0 (d) 3

--------------------------------------------------------- Quant Question # 206 ---------------------------------------------------------

Several B-schools took part in a tournament. Each player played one match against each player from a different B-school and did not play anyone from the same B-school. The total number of men taking part differed from the total number of women by 1. The total number of matches with both players of the same gender differed by at most one from the total number of matches with players of opposite gender. What is the largest number of B-schools that could have sent an odd number of players to the tournament?

(a) 3 (b) 5 (c) 6 (d) 11

--------------------------------------------------------- Quant Question # 207 ---------------------------------------------------------

7 professors decide to hold daily meetings such that (i) at least one professor attend each day (ii) a different set of professors must attend on different days. (iii) on day N for each 1 <= d < N, at least one professor must attend who was present on day d. How many maximum days can meetings be held?


--------------------------------------------------------- Quant Question # 208 ---------------------------------------------------------

The best description for the set of points (x, y) such that p^2 + py + x >= 0 for all real p satisfying |p| <= 1 is

(a) The area in the right half plane between y=x+1, y=-x-1, excluding the area left to the arc of the curve 4x=y^2 between (1, -2) and (1, 2)

(b) The area in the right half plane between y=-x+1, y=x-1, excluding the area right to the arc of the curve 4x=y^2 between (1, 0) and (-1, -2)

(c) The area in the right half plane between y=x+1, y=-x-1, excluding the area right to the arc of the curve 4x=y^2 between (1, -2) and (1, 2)

(d) The area in the right half plane between y=-x+1, y=x-1, excluding the area left to the arc of the curve 4x=y^2 between (1, 0) and (-1, -2)


--------------------------------------------------------- Quant Question # 209 ---------------------------------------------------------

If ab = 2^n -1 and 2^k is the highest power of 2 dividing 2^n -2 +a -b then k is always

(a) composite (b) a power of 2 (c) a prime (d) none of the foregoing

--------------------------------------------------------- Quant Question # 210 ---------------------------------------------------------

Let ABC be an equilateral triangle. What is the locus of the point P(outside ABC) in the plane that PA, PB, and PC form the sides of a right-angled triangle?

(a) a triangle (b) a circle (c) a non-convex polygon (d) none of these

--------------------------------------------------------- Quant Question # 211 ---------------------------------------------------------

A railway line passes through (in order) the 11 stations A, B, ... , K. The distance from A to K is 560 km. The distances AC, BD, CE, ... , IK are each <= 120 km. The distances AD, BE, CF, ... , HK are each >= 170 km. The distance between G and K is

(a) 220 km (b) 290 km (c) greater than 290 km (d) none of these

--------------------------------------------------------- Quant Question # 212 ---------------------------------------------------------

a, b, c are reals such that if p1, p2 are the roots of ax^2 + bx + c = 0 and q1, q2 are the roots of cx^2 + bx + a = 0, then p1, q1, p2, q2 is an arithmetic progression of distinct terms. The value of a + c = equals

(a) 0 (b) -1 (c) 1 (d) exactly two of the foregoing

--------------------------------------------------------- Quant Question # 213 ---------------------------------------------------------

The triangle ABC has length(AB) > length(AC) . The angle bisector of A meets the perpendicular bisector of BC at X. The line joining the feet of the perpendiculars from X to AB and AC meets BC at D. The ratio BD/DC is

(a) greater than 1 (b) 1 (c) less than 1 (d) indeterminate

--------------------------------------------------------- Quant Question # 214 ---------------------------------------------------------


The year is 2008 and a new system(base n > 2) is used in place of decimal for making calculations. Priyanka, one day receives twice the number of questions in "Quant questions a week" b'coz the digits of the original number of questions which was a two digit number got reversed. Let x be the least possible value of n and y is the next possible value of n.

The 4 digit number abab is a perfect cube in base z. Let z be the smallest possible such base.

Then y+z equals


--------------------------------------------------------- Quant Question # 215 ---------------------------------------------------------

The least number of positive divisors of a 6-digit number abbabb, where a, b represent distinct numbers are


--------------------------------------------------------- Quant Question # 216 ---------------------------------------------------------

Let E = (22^1/2 + 5)^1/2 + (8 - 22^1/2 + 2*(15 - 3*22^1/2)^1/2)^1/2. Then E also equals

(a) 3^1/2 + (10 + 2*3^1/2)^1/2

(b) 11^1/2 + 2*3^1/2 - 2^1/2

(c) (19 +4*33^1/2 -2*22^1/2 -4*6^1/2)^1/2

(d) Atleast 2 of the foregoing

--------------------------------------------------------- Quant Question # 217 ---------------------------------------------------------

A, B and C start running simultaneously from the points P, Q and R respectively on a circular track. The distance between any two of the three points P, Q and R is L and the ratio of the speeds of A, B and C is 1:2:3. If A and B run in opposite directions while B and C run in the same direction, what is the distance run by A before A, B and C meet for the third time?

(a) 10 L (b) A, B and C never meet (c) 40/3 L (d) none of the foregoing


--------------------------------------------------------- Quant Question # 218 ---------------------------------------------------------

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with 3 points of degree 2 each. Let S be the sum of degrees of all the points in a graph. Consider a graph with 12 points. It is possible to reach any point from any other point except 2 points through a sequence of edges. S in the graph must satisfy the condition

(a) 19 < S < 98 (b) 16 < S < 91 (c) 18 < S < 96 (d) 17 < S < 93

--------------------------------------------------------- Quant Question # 219 ---------------------------------------------------------

How many 5 digit numbers are divisible by 3 and contain the digit 6?


--------------------------------------------------------- Quant Question # 220 ---------------------------------------------------------

The line l contains the distinct points A, B, C, D in that order. A rectangle is constructed whose sides (or their extensions) intersect the line l at A, B, C, D and such that the side which intersects line l at C has length 5 cm. How many such rectangles are possible?


--------------------------------------------------------- Quant Question # 221 ---------------------------------------------------------

On the occasion of Jay's 64th birthday, Veeru, Basanti and Gabbar play the following game. There are three cards each with a different positive integer. In each round the cards are randomly dealt to the players and each receives the number of counters on his card. After two or more rounds, Veeru has received 20, Basanti 10 and Gabbar 9 counters. In the last round Basanti received the largest number of counters. Who received the middle number on the first round?

(a) Basanti (b) Veeru (c) Gabbar (d) Can not be determined

--------------------------------------------------------- Quant Question # 222 ---------------------------------------------------------


For how many reals r does the equation x^2 + rx + 6r = 0 have only integer roots?


--------------------------------------------------------- Quant Question # 223 ---------------------------------------------------------

Let x, y be reals such that (x^2 + y^2)/((x^2 - y^2) + (x^2 - y^2)/((x^2 + y^2)) = 1, then (x^8 + y^8) /(x^8 - y^8) + (x^8 - y^8) /(x^8 + y^8) is

(a) 41/20 (b) 2 (c) 25/12 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 224 ---------------------------------------------------------

n students played a tournament. Each pair played each other once. A player scored 1 for a win, 1/2 for a draw and 0 for a loss. Two students scored a total of 8 and the other players all had equal total scores. What can be the sum of all the possible values of n?


--------------------------------------------------------- Quant Question # 225 ---------------------------------------------------------.

Each of the numbers 1, 2, ... , 10 is coloured green or blue. 5 is green and at least one number is blue. If p, q are different colors and p+q <= 10, then p+q is blue. If p, q are different colours and pq <= 10, then pq is green. Then which among the following is not true?

(a) 3 is blue (b) 10 is green (c) 7 is blue (d) more than 2 numbers are green

--------------------------------------------------------- Quant Question # 226 ---------------------------------------------------------

ABCD is an isosceles trapezium with AB || CD. The length of AB, BC, CD, DA is 7 cm , 3 cm , 5 cm , 3 cm respectively. The exterior bisectors of <B and <C meet at P, and the exterior bisectors of <A and <D meet at Q. The length of PQ is

(a) 8 cm (b) 9 cm (c) 10 cm (d) none of the foregoing

--------------------------------------------------------- Quant Question # 227 ---------------------------------------------------------

The positive integers are grouped as follows: 1, 2+3, 4+5+6, 7+8+9+10, ..... and so on. The value of the 15th term is



--------------------------------------------------------- Quant Question # 228 ---------------------------------------------------------

ABC is acute-angled. AD and BE are altitudes. Also area BDE ≤ area DEA ≤ area EAB ≤ ABD. Then which among the following is necessarily true about the triangle ABC?

(a) isosceles (b) equilateral (c) scalene if <ACB is not 60 degrees (d) none of the foregoing

--------------------------------------------------------- Quant Question # 229 ---------------------------------------------------------

Let each of x(i) be non-negative real and not more than 1. Let S be defined as sum of all |x(i) - x(j)| where i is not equal to j. If i takes 15 consecutive values from 1 to 15 then what is max(S)?

(a) 52.5 (b) 56 (c) 60 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 230 ---------------------------------------------------------

4 spheres of radius 1 are placed so that each touches the other three. What is the radius of the smallest sphere that contains all 4 spheres?

(a) 3 (b) 3^1/2 + 1 (c) (3/2)^1/2 + 1 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 231 ---------------------------------------------------------

Let n be such that the number of integers less than or equal to n and divisible by 3 equals the number divisible by 5 or 7 (or both). Then the largest n is divisible by

(a) 3 (b) 5 (c) 7 (d) all of the foregoing

--------------------------------------------------------- Quant Question # 232 ---------------------------------------------------------

The hands of a strange clock move such that they would meet thrice as frequently if they run in opposite directions than if they run in the same direction. How many times would the faster hand meet the slower hand in the time that the slower hand completes 10 rotations, given that the hands run in opposite directions?



--------------------------------------------------------- Quant Question # 233 ---------------------------------------------------------

Let ABCDE be a regular pentagon and M be a point inside the pentagon such that <(MBA) = <(MEA) = 42 degrees.Then <(CMD) equals

(a) 54 degrees (b) 60 degrees (c) 66 degrees (d) 72 degrees

--------------------------------------------------------- Quant Question # 234 ---------------------------------------------------------

Let a, b, c be non-zero real numbers such that a^2 + b^2 + c^2 = 1 and a(1/b + 1/c) + b(1/c + 1/a) + c(1/a + 1/b) = -3, then a+b+c equals

(a) -1 (b) 0 (c) 1 (d) all of the foregoing

--------------------------------------------------------- Quant Question # 235 ---------------------------------------------------------

S is a set of positive integers containing 1 and 99. No elements are larger than 99. For every n in S, the arithmetic mean of the other elements of S is an integer. What is the largest possible number of elements of S?


--------------------------------------------------------- Quant Question # 236 ---------------------------------------------------------

Let the equation (x-4)^(1/(3x-1))^(1/(4x-5)) = (x^2 -5x +4)^(1/(19-2x)) has n solutions. Then n equals

(a) 3 (b) 2 (c) 1 (d) all of the foregoing

--------------------------------------------------------- Quant Question # 237 ---------------------------------------------------------

Let x, y, z be real, consider a system of equations 2x + y + 4z = 2, x + z = -3, x + 2y + Mz = 13. Which of the following is not true?

I. There is a value of M for which the system has more than one solution II. The system will become inconsistent for atleast one value of M

(a) I (b) II (c) I && II (d) none of the foregoing


--------------------------------------------------------- Quant Question # 238 ---------------------------------------------------------

Grass grows in a field at some rate r1, where r1 is the units of grass grown per day. It is know that 10 cows are turnedout in the field, the grass will be gone in 20 days. If 15 cows are turned out in the field, the grass will be gone in 10 days. If 25 cows are turned, let p be the days in which the entire grass be gone.

Raveena has a pack of fortune cards, which are numbered with consecutive natural numbers starting from 1. One card of this pack is lost and the average of all the remaining card numbers is 15. Let q be the distinct possible card Raveena could have lost.

A shopkeeper buys 10 biscuit packets, each packet containing 10 biscuits. Each packet is bought at the same price. he then sells off r packets, each at a profit of 20%, while all the remaining packets are opened and the biscuits there in are sold separately, each biscuit sold at a profit of 50%. Each biscuit withing any packet costs a whole number of rupees and the total revenue obtained is Rs 144.

A lecture room has a rectangular array of chairs. There are 6 boys in each row and 8 girls in each column. 15 chairs are unoccupied. Let s be the number of possible rows or columns. The value of p+q+r+s is


--------------------------------------------------------- Quant Question # 239 ---------------------------------------------------------

C and D are points on the semi-circle with diameter AB and center O such that <(AQB) = 2*(<COD). Q is the point of intersection of AC and DB inside the circle.The tangents at C and D meet at P. The circle has radius 1. The distance of P from its center is

(a) 3^1/2 (b) 2/(3^1/2) (c) 3/(2^1/2) (d) none of the foregoing

--------------------------------------------------------- Quant Question # 240 ---------------------------------------------------------

A group of new students whose total age is 341 years join a class, because of which the strength of the class goes up by 50% but the average age comes down by 2 years. Let p be the new average of the class given that the original strength of the class was greater than 35.

Let 10^q be such that it divides 98! + 99! + 101! and q is maximum.

Then p + q is



--------------------------------------------------------- Quant Question # 241 ---------------------------------------------------------

A palindrome is a positive integer which is unchanged if you reverse the order of its digits. If all palindromes are written in increasing order, how many possible prime values can the difference between successive palindromes take?


--------------------------------------------------------- Quant Question # 242 ---------------------------------------------------------

ABCD is a square with side 1. M is the midpoint of AB, and N is the midpoint of BC. The lines CM and DN meet at I. p is the area of the triangle CIN.

The altitudes of a triangle have length as 4, 5, and 10 respectively. Let q be the length of triangle's inradius.

Then p*q is

(a) 1/11 (b) 1/10 (c) can not be determined (d) none of the foregoing

--------------------------------------------------------- Quant Question # 243 ---------------------------------------------------------

I) For positive p, q, r the minimum value of 2q/r + (1+r)/2p + 2p^2/q is 4

II) x^4 > x - 1/2 for all real x

Which among the above is true?

(a) Only I (b) I && II (c) Only II (d) none of the foregoing

--------------------------------------------------------- Quant Question # 244 ---------------------------------------------------------

Bush places letter numbers 1, 2, ... , 9 into the typing tray one at a time during the day in that order. Each letter is placed on top of the pile. Every now and then Mulford takes the top letter from the pile and types it. He leaves for lunch remarking that letter 8 has already been typed. How many possible orders there are for the typing of the remaining letters. [For example, letters 1, 7 and 8 might already have been typed, and the remaining letters might be typed in the order 6, 5, 9, 4, 3, 2. So the sequence 6, 5, 9, 4, 3, 2 is one possibility. The empty sequence is another.]



--------------------------------------------------------- Quant Question # 245 ---------------------------------------------------------

A graph has 100 points. Given any four points, there is one joined to the other three. What is the smallest number possible of points that are joined to all the others?

(a) 74 (b) 99 (c) 51 (d) 97

--------------------------------------------------------- Quant Question # 246 ---------------------------------------------------------

There are 94 identical bricks, each 4 x 10 x 19. How many different heights of tower can be built (assuming each brick adds 4, 10 or 19 to the height)?

(a) 315 (b) 360 (c) 410 (d) 465

--------------------------------------------------------- Quant Question # 247 ---------------------------------------------------------

Define the sequence a(1), a(2), a(3), ... by a1 = A, a(n+1) = a(n) + d(a(n)), where d(b) is the largest factor of b less than b. For how many integers A > 1 is 2002 a member of the sequence?

(a) 0 (b) 2 (c) more than 2 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 248 ---------------------------------------------------------

An equilateral triangle of side length p has its vertices on the sides of a square of area 1. Then max(p) is

(a) (2^1/2 + 1)/2 (b) (5^1/2 + 2)/4 (c) 6^1/2 - 2^1/2 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 249 ---------------------------------------------------------

If x, y, z are positive integers such that x + [y] + {z} = 3.8, [x] + {y} + z = 3.2, {x} + y + [z] = 2.2, where [p] denotes the greatest integer less than or equal to p and {p} denotes the fractional part of p e.g. [1.23] = 1, {1.23} = 23/100. The numerical value of [x^2 + y^2 + z^2] is

(a) 7 (b) 8 (c) 9 (d) 11


--------------------------------------------------------- Quant Question # 250 ---------------------------------------------------------

A rectangular block L x 120 x H, with L ≤ 120 ≤ H is cut into two non-empty parts by a plane parallel to one of the faces, so that one of the parts is similar to the original. How many possibilities are there for (L, H)?

(a) 24 (b) 28 (c) 40 (d) 44

--------------------------------------------------------- Quant Question # 251 ---------------------------------------------------------

9 judges each award 20 contestants of Miss PaGalGuy 2007 a rank from 1 to 20. The contestants's score is the sum of the ranks from the 9 judges, and the winner of the first round is the contestant with the lowest score. For each contestant the difference between the highest and lowest ranking (from different judges) is at most 3. What is the highest score the winner could have obtained?

(a) 23 (b) 24 (c) 27 (d) 28

--------------------------------------------------------- Quant Question # 252 ---------------------------------------------------------

ABC is an acute-angled triangle. The angle bisector AD, the median BM and the altitude CH are concurrent. Then <A in degrees (is)

(a) < 45 (b) = 45 (c) > 45 (d) can not be determined

--------------------------------------------------------- Quant Question # 253 ---------------------------------------------------------

I) A committee has met 40 times, with 10 members at every meeting. No two people have met more than once at committee meetings => There are more than 60 people on the committee.

II) One cannot make more than 30 subcommittees of 5 members from a committee of 25 members with no two subcommittees having more than one common member.

Which of the above is not true?

(a) only I (b) only II (c) I && II (d) none of the foregoing

--------------------------------------------------------- Quant Question # 254 ---------------------------------------------------------


A wooden unit cube rests on a horizontal surface. A point light source a distance x above an upper vertex casts a shadow of the cube on the surface. The area of the shadow (excluding the part under the cube) is 35.

Let ABCD be a square. P, Q, R, S are on AB, BC, CD, DA extended respectively. A, B, C, D are the midpoints of DS, AP, BQ, CR respectively. Area(ABCD)/area(PQRS) = y.

Which among the following is true about x and y?

(a) x > y (b) 1/x = y (c) x < 1/y (d) x = y

--------------------------------------------------------- Quant Question # 255 ---------------------------------------------------------

Let -2 < x < 3, 0 < y < 4, 2 < z < 5. If (3-x)(4-y)(5-z)(3x+4y+5z) achieves the maximum possible value then which among the following is not true?

(a) 3x+4y = 0 (b) |x| < |y| (c) z = 5/2 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 256 ---------------------------------------------------------

P lies inside the triangle ABC. �BAC = 50 . �PAB = 10 , �PCA = 30 , �PBA = 20 . o o o o

�PBC is

(a) 20 (b) 40 (c) 50 (d) 60o o o o

--------------------------------------------------------- Quant Question # 257 ---------------------------------------------------------

Two different infinite geometric progressions both have sum 1 and the same second term. One has third term 1/8. Its second term(upto 2 places of decimal) is

(a) 0.25 (b) 0.20 (c) 0.15 (d) none of the foregoing

--------------------------------------------------------- Quant Question # 258 ---------------------------------------------------------

How many (x, y, z) satisfy log(2xy) = logx*logy, log(yz) = logy*logz, log(2zx) = logz*logx ?


--------------------------------------------------------- Quant Question # 259 ---------------------------------------------------------


The positive integer n is such that if the first digit is moved to become the last digit, then the new number is 7n/2. The number of digits in smallest n are

(a) 4 (b) 5 (c) 6 (d) 7

--------------------------------------------------------- Quant Question # 260 ---------------------------------------------------------

How many equilateral triangles of side 2/3^1/2 are formed by the lines y = k, y = x(3^1/2) + 2k, y = -x(3^1/2) + 2k for |k| <= 10 where k is an integer?

(a) 600 (b) 660 (c) 720 (d) 780

--------------------------------------------------------- Quant Question # 261 ---------------------------------------------------------

The numerical value of [(1^4 + 1/4)*(3^4 + 1/4)*...*(19^4 + 1/4)]/[(2^4 + 1/4)*(4^4 + 1/4)*...*(20^4 + 1/4)] is


--------------------------------------------------------- Quant Question # 262 ---------------------------------------------------------

Problems 261, 262 and 263 were posed in QQAD. 25 users solved at least one of the three. Amongst those who did not solve 261, twice as many solved 262 as 263. The number solving only 261 was one more than the number solving 261 and at least one other. The number solving just 261 equalled the number solving just 262 plus the number solving just 263. How many solved just 262?


--------------------------------------------------------- Quant Question # 263 ---------------------------------------------------------

A tangent to the inscribed circle of a triangle drawn parallel to one of the sides meets the other two sides at A and B. What is the maximum length AB, if the triangle has perimeter p? (vx is the positive square root of x)

(a) p/v24 (b) p/6 (c) p/v48 (d) p/8

qqad in 2006

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