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1

Explanation for Correct Answer C :

Choice (C) is correct. Converting from feet to inches, the length of

the rope is inches. Therefore, the maximum number of

pieces, each inches long, that can cut from the rope is

Explanation for Incorrect Answer A :

Choice (A) is incorrect. Converting from feet to inches, the length of

the rope is inches. A total of pieces (not ), each

inches long, can be cut from the -inch-long rope.

Explanationfor IncorrectAnswer B :

Choice (B) is incorrect. Converting from feet to inches, the length of

the rope is inches. A total of pieces (not ), each

inches long, can be cut from the -inch-long rope.

Explanation for Incorrect Answer D :

Choice (D) is incorrect. Converting from feet to inches, the length of

the rope is inches. To cut a total of pieces, each

inches long, would require inches of rope.

Explanation for Incorrect Answer E :

View Answers and Explanations

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Online - Practice Test #3

A r ope is feet long . Wha t is th e m ax im um nu m ber of pieces, each inch es

long, that can be cut from the rope? ( foot inches)

(A)

(B)

(C)

(D)

(E)

ANSWERS ANDEXPLANATIONS

Test Sections

Section 1

Section 3

Section 4

Section 5

Section 6

Section 7

Section 8

Section 9

Sect ion 1 0
https://satonlinecourse.collegeboard.org/SR/quizzesaction.dohttps://satonlinecourse.collegeboard.org/SR/examsaction.dohttps://satonlinecourse.collegeboard.org/SR/professionalreportshomeaction.dohttps://satonlinecourse.collegeboard.org/SR/helpAction.dohttps://satonlinecourse.collegeboard.org/SR/studentProfileAction.dohttps://satonlinecourse.collegeboard.org/SR/viewMyOrganizer.dohttp://popup%28%27/SR/mybookmarkaction.do'%20,600%20,600)https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40E9-66B4-9F5F-9BE4-B7C62645AE24-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40E9-66B4-9F5F-9BE4-B7C646DE3384-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C6C098A518-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C6008F7F8E-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C651E87543-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C6A4FC1CB5-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C66FD69DDB-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C62C0C2B44-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/showExamAnswerExplanation.do?assessmentResultId=10846464&assessmentLocator=3CF8A603-66B4-9F5F-0099-8B08F172FC7B-1::AS&section=3CFB40D9-66B4-9F5F-9BE4-B7C68A022024-1::S&fromPage=examscorereport&resultId=https://satonlinecourse.collegeboard.org/SR/fptscorereportaction.do?whereFrom=scoreNow&assessmentResultId=10846464https://satonlinecourse.collegeboard.org/SR/professionalreportshomeaction.dohttps://satonlinecourse.collegeboard.org/SR/examsaction.dohttps://satonlinecourse.collegeboard.org/SR/quizzesaction.dohttps://satonlinecourse.collegeboard.org/SR/lessonsaction.dohttps://satonlinecourse.collegeboard.org/SR/gettingstartedaction.dohttps://satonlinecourse.collegeboard.org/SR/studenthomeaction.dohttps://satonlinecourse.collegeboard.org/SR/logoff.dohttp://popup%28%27/SR/mybookmarkaction.do'%20,600%20,600)https://satonlinecourse.collegeboard.org/SR/viewMyOrganizer.dohttps://satonlinecourse.collegeboard.org/SR/studentProfileAction.dohttps://satonlinecourse.collegeboard.org/SR/helpAction.do


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https://satonlinecourse.collegeboard.org /SR/showExamAnswerExplanation.do?fromPage=examscorereport&assessmentResultId=10846464&assessmentLocat 2

Choice (E) is incorrect. Converting from feet to inches, the length of

the rope is inches. To cut a total of pieces, each

inches long, would require inches of rope.

2


Choice (C) is correct. When two lines intersect, vertical angles areformed. Since vertical angles have equal measures and since is a

line, then Since we have

which simplifies to so


Choice (A) is not correct. If were then we would have

Solving this equation for gives

However, not Therefore, cannot be

Explanation for Incorrect Answer B :

Choice (B) is not correct. If were then we would have




Choice (D) is not correct. If were then we would have



Lines and intersect at a point as shown above. If wha t is the v alue

of

(A)

(B)

(C)

(D)

(E)



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Choice (E) is not correct. If were then we would have



3

Explanation for Correct Answer D :

Choice (D) is correct. If is the average of the three numbers

and then From this it follows that


and


Choice (A) is not correct. It is given that is the average of the three

numbers and Therefore, if were equal to then

would be equal to However, is equal to not

It follows that cannot be equal to


Choice (B) is not correct. It is given that is the average of the three


would be equal to However, is equal to

not It follows that cannot be equal to

Explanation for Incorrect Answer C :

Choice (C) is not correct. It is given that is the average of the three


would be equal to However, is equal to

The av erage (arit hm etic mean ) of the num bers shown above is What is the

v alue of

(A)

(B)

(C)

(D)

(E)



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Choice (E) is not correct. It is given that is the average of the three


would be equal to However, is equal to not

It follows that cannot be equal to

4


Choice (C) is correct. The familys average daily use of electricity for

a month was less than kilowatt-hours if and only if the point

representing that month on the line graph lies below the horizontal

grid line at There are three such points: July, August, and May.


Choice (A) is not correct. T he familys average daily use of electricity

for a month was less than kilowatt-hours if and only if the point


grid line at There are three such points, not one.

The line graph above shows the av erage daily use of electricit y , in kilowat t-hours,

by a fa mily for ea ch m onth of a y ear, sta rt ing i n J uly . For how man y m onths of

the y ear was the familys av erage daily use of electricity less than kilowatt-

hours?

(A) One

(B) Two

(C) Three

(D) Fiv e

(E) Eight



5/18




Choice (B) is not correct. T he familys average daily use of electricity

for a month was less than kilowatt-hours if and only if the point


grid line at The two leftmost points on the graph lie below the

horizontal grid line at but the point for May is a third such point.


Choice (D) is not correct. There are five months for which the

familys average daily use of electricity was between and

kilowatt-hours, but this is not what the question asked.


Choice (E) is not correct. There are eight months for which the

familys average daily use of electricity was less than kilowatt-

hours, but in only three of these months was the familys average

daily use less than kilowatt-hours.

5

Explanation for Correct Answer A :

Choice (A) is correct. The equation means that is equal

to the sum of and which is equivalent to the statement is

more than


Choice (B) is not correct. The equation represents thestatement is times as great as


Choice (C) is not correct. The equation represents the

statement the sum of and is equal to


Choice (D) is not correct. The inequality represents the

statement the sum of and is greater than

Which of the following r epr esents t he sta tem ent, is m ore than ?

(A)

(B)

(C)

(D)

(E)



6/18




Choice (E) is not correct. The inequality represents the

statement the sum of and is greater than

6


Choice (D) is correct. At Middletown High School, of juniors

are members of the marching band. This means that of the

juniors are members of the band. The fraction of the number of

seniors who are members of the band is equal to the fraction of the

number of juniors who are members of the band. Therefore, since

there are seniors, the number of seniors in the band is


Choice (A) is not correct. If there were seniors in the band, then

the fraction of the number of seniors who are members of the band

would be The fraction of the number of seniors who are

members of the band is equal to the fraction of the number of juniors

who are members of the band, so of the juniors would be

members of the band. However, the fraction of the number of juniors

who are members of the band is not


Choice (B) is not correct. If there were seniors in the band, then



members of the band is e ual to the fraction of the number of uniors

At Middletown Hig h Sch ool, of ju ni ors are mem ber s of the m ar ch ing

band. T he fraction of the nu m ber of seniors who are m em ber s of the ba nd is equ alto the fraction of the n um ber of juniors who are m embers of the band. How m any

of the seniors are in the band?

(A)

(B)

(C)

(D)

(E)



7/18



who are members of the band, so of the juniors would be members

of the band. However, the fraction of the number of juniors who are

members of the band is not


Choice (C) is not correct. If there were seniors in the band, then




who are members of the band, so of the juniors would be

members of the band. However, the fraction of the number of juniors

who are members of the band is not


Choice (E) is not correct. If there were seniors in the band, then




who are members of the band, so of the juniors would be members

of the band. However, the fraction of the number of juniors who are

members of the band is not

7

Line intersects at point so tha t as shown above. If and

(not shown) are the midpoints of and respectiv ely , which of the

following mu st be true?

I. an d ar e on th e sam e side of

II. an d ar e on th e same side of

III. an d ar e on opposite sides of

(A ) I on ly

(B) II on l


8/18



Explanation for Correct Answer E :

Choice (E) is correct. Consider each one of the statementsindependently to determine whether it must be true.

Statement I concerns points and Point is the midpoint of

so both and are to the left of point on It follows

that and are on the same side of so statement I must be true.

Statement II concerns points and Point is the midpoint of

and so must lie to the right of on It follows

that and are on the same side of so statement II must be

true.

Statement III concerns points and We know that is to the

left of point on Point is the midpoint of so must lie

to the right of on It follows that and are on opposite

sides of so statement III must be true.

Therefore, all three of the statements I, II, and III must be true.


Choice (A) is not correct. Statement I must be true, but statements II

and III must also be true.


Choice (B) is not correct. Statement II must be true, but statements I

and III must also be true.


Choice (C) is not correct. Statement III must be true, but statements

I and II must also be true.


Choice (D) is not correct. Statements I and III must be true, but

statement II must also be true.

8

(C) III only

(D) I and III only

(E) I, II, and III


Georg e collected tokens worth a total of point s. If each of th e tokens has a

v alue of either point s or point s, h ow m an y -point tokens did George

collect?


9/18




Choice (E) is correct. Let be the number of -point tokens

George collected, and let be the number of -point tokens he

collected. Since George collected a total of tokens, it follows that

Since these tokens are worth a total of points, it

follows that Multiplying the first equation by

( ) and subtracting from the second gives

and so Therefore, George collected tokens of value

points.


Choice (A) is not correct. George collected tokens of value

points, but the question asked for the number of -point tokens he

collected.


Choice (B) is not correct. If George had collected only tokens of

value points, he would then have tokens of value points.

Then the total value of Georges tokens would be only

points, not points.


Choice (C) is not correct. If George had collected only tokens of

value points, he would then have tokens of value points.

Then the total value of Georges tokens would be only

points, not points.


Choice (D) is not correct. If George had collected only tokens of

value points, he would then have tokens of value points.Then the total value of Georges tokens would be only

points, not points.

9

(B)

(C)

(D)

(E)



10/18


https://satonlinecourse.collegeboard.org /SR/showExamAnswerExplanation.do?fromPage=examscorereport&assessmentResultId=10846464&assessmentLoc 10

Explanation for Correct Answer B :

Choice (B) is correct. The equation is equivalent to

From the table, only when


Choice (A) is incorrect. From the table,

not


Choice (C) is incorrect. From the table, not


Choice (D) is incorrect. From the table, not


Choice (E) is incorrect. From the table, not

10

The function is defined by the table above. For wha t v alue of does

(A)

(B)

(C)

(D)

(E)


The figure a bov e shows a tr apezoid divided into three tria ngles. What is the area of

the shaded trian gle?

(A)

(B)

(C)

(D)


11/18




Choice (D) is correct. We can find the area of the shaded triangle by

subtracting the sum of areas of two unshaded triangles from the area

of the trapezoid. The area of a trapezoid can be calculated by

multiplying the average of the lengths of the bases by the altitude ofthe trapezoid. The length of bases of the trapezoid are and and

so their average is The altitude of the trapezoid is so

the area of trapezoid is The two unshaded triangles are

congruent right triangles with legs of length and so the area of

each unshaded triangle is The sum of the areas of the

two unshaded triangles is then It follows that the area

of the unshaded triangle is


Choice (A) is not correct. If the area of the shaded triangle was

then the sum of the areas of the three triangles would be

The sum of the areas of the three triangles is

equal to the area of the trapezoid. However, the area of the trapezoid

is not Therefore, the area of the shaded triangle cannot be


Choice (B) is not correct. If the area of the shaded triangle was

then the sum of the areas of the three triangles would beThe sum of the areas of the three triangles is




Choice (C) is not correct. The sum of areas of two unshaded triangles

is However, the question is asking for the area of

shaded triangle, not the sum of the areas of the unshaded triangles.


Choice (E) is not correct. If the area of the shaded triangle was

then the sum of the areas of the three triangles would be

The sum of the areas of the three triangles is



(E)



12/18



11


Choice (E) is correct. In the -plane, the graph of

is a parabola that intersects the -axis at

and at When so

the graph of is above the -axis for values less

than below the -axis for values between and and

above the -axis for values greater than It follows that all the

values of for which are those values between

and Of these, the smallest integer value is


Choice (A) is not correct. If then

Therefore, is not a value of

for which


Choice (B) is not correct. If then


for which


Choice (C) is not correct. If then


for which


Choice (D) is not correct. If then

Therefore, is not a value of for

which

12

What is the smal lest possible int eger v alue of for w hich

(A)

(B)

(C)

(D)

(E)


In the -plane, thr ee of the v ertices of a square are and If

the square is reflected about the line which of the following is one v ertex of


13/18




Choice (A) is correct. Since three vertices of the square are

and the fourth vertex is To find the reflection of

across one can recall that the reflection of any point

about is given by Therefore, the reflection

of about the line is the point

Alternatively, since has slope any line perpendicular to

must have slope (the negative reciprocal of ). The line

with slope that passes through is Thus the

perpendicular from to intersects at

Following this perpendicular an equal distance beyond shows

that the reflection of about the line is


Choice (B) is not correct. The point lies on the line

Thus is the reflection of itself, about the line

The point is not one of the vertices of the original square and,

thus, not a vertex of the resulting square.


Choice (C) is not correct. The point is the reflection of

about the line The point is not one of the vertices of

the original square, and so is not a vertex of the resulting

square.


Choice (D) is not correct. The point lies on the line

Thus is the reflection of itself, about the line

The point is not one of the vertices of the original

square and, thus, not a vertex of the resulting square.


Choice (E) is not correct. The point is the reflection of

about the line The point is not one of the vertices of

the resulting square?

(A)

(B)

(C)

(D)

(E)



14/18



the original square, and so is not a vertex of the resulting

square.

13

Explanation for Correct Answer B :

Choice (B) is correct. Since of the campers could swim, then

there were swimmers among the campers and who couldnt

swim; and since of the campers took climbing lessons, there were

campers who took climbing lessons.

Each of the campers who took climbing lessons either could swim

or couldnt swim. Since a total of campers at the summer camp

couldnt swim, at most of the campers who took climbing

lessons couldnt swim. Therefore, the least possible number ofcampers taking climbing lessons who could swim is


Choice (A) is not correct. If were the least possible number of

campers taking climbing lessons who could swim, then there could be

campers who couldnt swim and also took climbing lessons. But

there are only campers at the summer camp who couldnt swim.


Choice (C) is not correct. There were campers who took climbing

lessons, but it need not be true that all of these campers could swim.


Choice (D) is incorrect. Since only campers took climbing

lessons, there cannot be campers who took climbing lessons and

also could swim.


Of the cam pers at a summ er cam p, could swim. If of the cam pers took

climbing lessons, wha t w as the least possible num ber of cam pers taking clim bing

lessons who could swim ?

(A)

(B)

(C)

(D)

(E)



15/18



Choice (E) is incorrect. There were swimmers among the

campers, but the question asks for the least possible number of

campers taking climbing lessons who could swim. Since only

campers took climbing lessons, there cannot be campers who

took climbing lessons and also could swim.

14


Choice (E) is correct. Let be the point on for which

Then triangle and triangle are both righttriangles. Since the measure of is and the hypotenuse of

triangle has length the length of the side opposite is

of so By the Pythagorean Theorem, it follows that

The measure of is so

triangle is an isosceles right triangle. We have so

is also The length of segment is then


Choice (A) is not correct. Let be the point on for which

We have and If the length

of was then the length of would be

However, the length of must be less than because is one

leg of a right triangle with hypotenuse Therefore, the length of

cannot be


Choice (B) is not correct. Let be the point on for which

In above, the measur e of is and the measure of is

What is the len gt h of seg ment

(A)

(B)

(C)

(D)

(E)



16/18



We have Also

so

Therefore, the length of cannot be


Choice (C) is not correct. Let be the point on for which

We have and so

Therefore, the length of cannot be


Choice (D) is not correct. Let be the point on for which

The length of is but the length of is

15


Choice (A) is correct. Taking the power of each side of

gives This simplifies to


Choice (B) is not correct. equals not


Choice (C) is not correct. equals not


If an d wh at does equal in term s of

(A)

(B)

(C)

(D)

(E)



17/18



Choice (D) is not correct. equals not


Choice (E) is not correct. equals not

16


Choice (A) is correct. In each equation, is expressed in terms of

two other variables; in all, a total in three variables appear in the

right-hand sides of the three equations: and However, each

variable appears in exactly two of the equations, once with acoefficient of and once with a coefficient of Hence if all three

equations are added, all the variables on the right will cancel:

It follows that and so the value of is


Choice (B) is not correct. Adding the three given equations yields

which simplifies to

not Therefore, the value of is not


Choice (C) is not correct. Adding the three given equations yields

Based on th e system of equations abov e, wh at is th e v alue of

(A)

(B)

(C)

(D)

(E)



18/18


which simplifies to

not Therefore, the value of is not


Choice (D) is not correct. Adding the three given equations yields

that the value of is but the value of is

Explanation for Incorrect Answer E :Choice (E) is not correct. Adding the three given equations yields

which simplifies to

Therefore, the value of is not

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