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01

Is x less than 20 ?

(1) The sum of x and y is less than 20

(2) y is less than 20

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02

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(1) The measure of angle QPR is 30o

(2) The sum of the measures of angles PQR and PRQ is 150o



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03

Over a certain time period, did the number of shares of stock in 5XWKV�SRUWIROLR�LQFUHDVH"

(1) Over the time period, the ratio of the number of shares of stock to the total number of shares of stocks and bonds in� 5XWKV�SRUWIROLR�LQFUHDVHG�

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04

A certain list consists of several different integers. Is the product of all the integers in the list positive ?

(1) The product of the greatest and smallest of the integers in the list is positive

(2) There is an even number of integers in the list







05

The cost of each adults' ticket for a certain concert was $30, and the cost of each child's ticket for the concert was $24. If Hannah purchased tickets for this concert, what was the average (arithmetic mean) cost per ticket ?

(1) Hannah purchased twice as many children's tickets as adults' tickets

(2) Hannah purchased 4 children's tickets






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06

If n is a positive integer and r is the remainder when n2 - 1 is divided by 8, what is the value of r ?

(1) n is odd.

(2) n is not divisible by 8.







07A certain movie depicted product A in 21 scenes, product B in 7 scenes, product C in 4 scenes and product D in 3 scenes. The four product manufacturers paid amounts proportional to the number of scenes in which their product was depicted in the movie. If each manufacturer paid x dollars per scene, how much did the manufacturer of product D pay for this advertising?

(1) The manufacturers of products A and B together paid a total of $560,000 for this advertising

(2) The manufacturer of product B paid $60,000 more for this advertising than the manufacturer of product C paid






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08

If k is a line in the xy-plane, what is the slope of k?

(1) The x-intercept of k is 2

(2) The y-intercept of k is 3







09

One member of a committee of 5 men and 8 women resigned and was not replaced. What fraction of the remaining members were men?

(1) 7 of the remaining members were women 12

(2) The member who resigned was a woman






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10

If b is positive, is ab positive ?

(1) a2b > 0

(2) a2 + b = 13







11

If w and z are positive, is w < 1 ? z

(1) w < z

(2) z < 4






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12

A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5

(2) The distance between point X and point Y is 9







13

In 1984, a certain union had a total of 15,600 members. Was the percent increase in the total number of members in the union from 1984 to 1985 greater than that from 1985 to 1986 ?(1) From 1984 to 1985, the total number of members in the union increased by 781, and from 1985 to 1986, the total number of members in the union again increased by 781

(2) In 1985, the union had a total of 16,381 members and in 1986, the union had a total of 17,162 members






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14

What is the greatest integer that is less than t ?

(1) t = 9 4

(2) t = -3 2

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15

Does set S contain any even numbers

(1) There are no prime numbers in S

(2) There are no multiples of 4 in S






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16

Three thousand families live in a certain town. How many families who live in the town own neither a car nor a television set?

(1) Of the families who live in the town, 2,980 own a car

(2) Of the families who live in the town, 2,970 own both a car and a television set







17

What is the value of v3 - k3 ?

(1) vk > 0

(2) v - k = 6






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18

What is the value of 3n - 4 ?

(1) 6n - 10 = 30

(2) n = 20 3 9







19

If eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of the eleven integers?

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(2) The average of the last nine integers is 9






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20

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(1) The dealer’s cost for the coffee table was $340

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21

Is x + y negative ?

(1) x is negative

(2) y is positive






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22

In the triangle ABC above, what is the length of side BC ?

(1) Line segment AD has a length 6

(2) x = 36






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23

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24

If l and k are lines in the xy-plane, is the product of the slopes of l�DQG�N�HTXDO�WR��"

(1) Line l passes through the origin and the point (1,2).

(2) Line k has x-intercept 4 and y-intercept 2.







25

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(1) 14 and 35 are factors of N

(2) N = (25)(32)(57)(76)






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26

In the xy-plane, at what two points does the graph of y = (x + a)(x + b) intersect the x-axis?

(1) a + b = -1

(2) The graph intersects the y-axis at (0, -6)







27

A store sells milk in cartons of two sizes, one-half gallon and one-quarter gallon. If the store sold a total of 300 cartons of milk yesterday, how many gallons of milk did it sell yesterday?

(1) Yesterday the store sold 120 one-quarter gallon cartons of milk

(2) Yesterday the store sold 90 gallons of milk in one-half gallon cartons






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28

A wooden rod is cut into two pieces. What is the length of the longer piece?

(1) One of the pieces is 20 inches longer than the other piece

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29

If the product of the three digits of the positive integer k is 14, what is the value of k ?

(1) k is an odd integer

(2) k < 700






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30ANSWER KEY1. E2. D 3. C4. C5. A6. A7. D8. C9. D10. E11. A12. C13. D14. D15. E

16. E17. E18. D19. D20. C21. E22. A23. C24. C25. D26. C27. D28. C29. E

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