Sat Practice Book

TABLE of CONTENTS

1. Properties of integers

2. Number Lines and Fractions

3. Elementary Number Theory(Divisibility)

4. Sequences

5. Sets

6. Ratio, Proposition, and Percents.

7. Exponents, Squares, and Square Roots

8. Word problems

9. Factoring

10.

Mean, Median, and Mode

11.

Solving Equations and Rational Equations

12.

Direct Variation and Inverse Variation

13.

Inequalities

14.

System of Linear Equations

15.

Solving Quadratic Equations

16.

Functions

17.

Made Up Operations

18.

Coordinates Geometry

19.

Parallel Lines and Angles

20.

Triangles

21.

Polygons

22.

Circles

23.

Solid Geometry

24.

Statistics, Data and Graph

25.

Probabilities

PROPERTIES of INTEGERS



1. If x is an integer greater than 1 and if

x x

y 1, which of the following must be true? I. y x II. y is an integer. III. xy > x2 (A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

2. If x and y are positive consecutive odd

integers, where y > x, which of the following is y2 _{– x}2_? (A) 2x (B) 4x (C) 2x + 2 (D) 2x + 4 (E) 4x + 4

3. If x, y, and z are positive integers such

that the value of x + y is even and the value of (x + y) 2 _{+ x + z is odd, which of} the following must be true?

(A) x is odd. (B) x is even.

(C) If z is even, then x is odd. (D) If z is even, then xy is even. (E) xy is even.

4. If n is any negative number, which of

the following must be positive? (A) 2 n (B) 2n (C) n + 2 (D) n – 2 (E) 2 – n

5. If k is a positive even integer, then

(k+1)(k+2) could equal which of the following? (A) 10 (B) 20 (C) 30 (D) 40 (E) 50

6. Which of the following must be true for

all integers a,b, and c ? I. a- 0 =a II. a-b=b-a III. (a-b)-c=a- (b-c) (A) I only (B) II only (C) III only (D) I and II

PROPERTIES of INTEGERS



2009-2010

2009-2010

7. If a, b, and c are positive integers, and if

(a−c)b=0, which of the following must be true? (A) a<b (B) b<c (C) a =b (D) a=c (E) b=c

8. If a is an odd integer and b is an even

integer, which of the following is an odd integer? (A) 3b (B) a+3 (C) 2(a+b) (D) a+2b (E) 2a+ b

9. If (p+1) (t-3) =0 and p is positive, what is

the value of t? (A) -3 (B) -1 (C) 0 (D) 1 (E) 3 10. If 2 3

x _{is an integer, then x must be}

(A) a negative integer (B) a positive integer (C) a multiple of 3 (D) an even integer (E) an odd integer

NUMBER LINES & FRACTIONS



2009-2010

1.

Which of the lettered points on the number line above could represent the result when the coordinate of point P is multiplied by the coordinate of point Q? (A) A (B) B (C) C (D) D (E) E 2.

On the number line above, there are 9 equal intervals between 0 and 1. What is the value of x?

3.

On the number line above, t, u, v, w, x, y, and z are coordinates of the

indicated points. Which of the following is closest in value to |u + v| ? (A) t (B) w (C) x (D) y (E) z 4.

On the number line above, which of the following corresponds tou w ? (A) t (B) v (C) x (D) y (E) z 2 1 7 2 3

5. What number, when used in place of

above, makes the statement true? (A) 4

(B) 5 (C) 9 (D) 12 (E) 15

6. The numerator of a certain fraction is

5 less than the denominator. If the fraction is equal to

4 3

, what is the denominator of this fraction? (A) 8

(B) 12 (C) 16 (D) 20 (E) 24

NUMBER LINES & FRACTIONS



2009-2010

2009-2010

7.

In the figure above, AC = 24 and AB = BC. Point D (not shown) is on the line between A and B such that AD = DB. What does DC equal? (A) 6 (B) 12 (C) 16 (D) 18 (E) 20 8. If x = 2

1 _{, what is the value of}

1 1 1 x x ? (A) –4 (B) 0 (C) 1 (D) 2 (E) 3

9. Which of the following numbers is

between 5 1_and 4 1_? (A) 0.14 (B) 0.15 (C) 0.19 (D) 0.21 (E) 0.26 10.

If x, x2_{, and x}3 _{lie on a number line in} the order shown above, which of the following could be the value of x? (A) –2 (B) 2 1 (C) 4 3 (D) 1 (E) 2 3 11.

On the number line above, the tick marks are equally spaced. What is the value of w – p ? (A) 3/4 (B) 2/3 (C) 1/2 (D) 1/3 (E) 1/4

NUMBER LINES & FRACTIONS



2009-2010

2009-2010

12.

On the number line above, the tick marks are equally spaced. Which of the lettered points represents y ?

(A) A (B) B (C) C (D) D (E) E 13.

Which of the following is the best

estimate of the length of segment AB on the number line above?

(A) 4 (B) 3.5 (C) 3 (D) 1.5 (E) 1 14.

In the figure above, if the coordinates of points X and Y are added together, the result will be the coordinate of a point between which two consecutive integers? (A) −3 and −2 (B) −2 and −1 (C) −1 and 0 (D) 0 and 1 (E) 2 and 3 15.

On the number line above, the tick marks are equally spaced. What is the value of b−a? (A) 4/5 (B) 3/4 (C) 2/5 (D) 1/4 (E) 1/5

NUMBER LINES & FRACTIONS



2009-2010

2009-2010

16.

If the tick marks on the number line above are equally spaced, which of the lettered points A through E is between 1/4 and 3/8? (A) A (B) B (C) C (D) D (E) E 17.

If x is the coordinate of the indicated point on the number line above, which of the lettered points has coordinate  2x ?

(A) A (B) B (C) C (D) D (E) E

18. If 3 times a number is equal to 3/2,

what is the number? (A) 1/3 (B) 1/2 (C) 2/3 (D) 2 (E) 3 19.

On the number line above, the tick marks are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest positive value? (A) a (B) b (C) c (D) d (E) e

DIVISIBILITY



1. There are 8 sections of seats in an

auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this

auditorium? (A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700

2. “All numbers that are divisible by both

2 and 6 are also divisible by 4.”

Which of the following numbers can be used to show that the statement above is FALSE? (A) 4 (B) 8 (C) 12 (D) 18 (E) 24

3. If m is the greatest prime factor of 38

and n is the greatest prime factor of 100, what is the value of m + n ? (A) 7

(B) 12 (C) 24 (D) 29 (E) 44

4. If p is an integer and 3 is the

remainder when 2p + 7 is divided by 5, then p could be (A) 2 (B) 3 (C) 4 (D) 5 (E) 6

5. When 15 is divided by the positive

integer k, the remainder is 3. For how many different values of k is this true? (A) One

(B) Two (C) Three (D) Four (E) Five

6. How many cubical blocks, each with

edges of length 4 centimeters, are needed to fill a rectangular box that has inside dimensions 20 centimeters by 24 centimeters by 32 centimeters? (A) 38 (B) 96 (C) 192 (D) 240 (E) 384

DIVISIBILITY



2009-2010

2009-2010

7. What is the greatest three–digit

integer that has a factor of 10?

8. If there is no waste, how many square

yards of carpeting is needed to cover a rectangular floor that is 12 feet by 18 feet? (1 yard = 3 feet) (A) 8 (B) 16 (C) 24 (D) 30 (E) 216 9.

If x is divisible by 3 and y is divisible by 5, which of the following must be divisible by 15? I. xy II. 3x + 5y III. 5x + 3y (A) I only (B) III only (C) I and II only (D) I and III only (E) I, II, and III

10. How many integers greater than 20

and less than 30 are each the product of exactly two different numbers, both of which are prime?

(A) Zero (B) One (C) Two (D) Three (E) Four

11. If the integer m is divided by 6, the

remainder is 5. What is the remainder if 4m is divided by 6 ? (A) 0 (B) 1 (C) 2 (D) 4 (E) 5

12. A large solid cube is assembled by

gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the large cube?

DIVISIBILITY



2009-2010

2009-2010

13. When the positive integer n is divided

by 6, the remainder is 2. What is the remainder when 24n is divided by 36 ?

14. If k is a positive integer divisible by 7,

and if k < 90, what is the greatest possible value of k ? (A) 83 (B) 84 (C) 87 (D) 88 (E) 89

15. There are 6 bookcases in a house.

Each bookcase contains at least 125 books but not more than 160 books. Which of the following could be the total number of books in all 6 bookcases? (A) 500 (B) 625 (C) 725 (D) 925 (E) 1,000

16. Which of the following is divisible by 3

and by 5 but is not divisible by 10 ? (A) 30

(B) 35 (C) 40 (D) 45 (E) 60

17. When the positive integer m is

divided by 5, the remainder is 3. What is the remainder when 20m is divided by 25?

18. For what positive number is the

square root of the number the same as the number divided by 40?

19. The result when a number is divided

by 2 is equal to the result when that same number is divided by 4. What is that number? (A) -4 (B) -2 (C) 0 (D) 2 (E) 4

20. What is the product of the smallest

prime number that is greater than 50 and the greatest prime number that is less than 50?

SEQUENCES



1. –1, 0, 1, 2

A sequence is formed by repeating the 4 numbers above in the same order indefinitely. What is the sum of the first 28 terms of the sequence? (A) 12

(B) 13 (C) 14 (D) 15 (E) 16

2. Rita’s dog weighed 5 pounds when she

bought it. Over the next several years, the dog’s weight increased by 10 percent per year. Which of the

following functions gives the weight, w, in pounds, of the dog after n years of weight gain at this rate?

(A) w(n) = 5 + 0.1n (B) w(n) = 5(0.1)n

(C) w(n) = 5(0.9)n

(D) w(n) = 5(1.1)n

(E) w(n) = 5(n)1.1

3. Each month, a telephone service

charges a base rate of $10.00 and an additional $0.08 per call for the first 40 calls and $0.04 for every call after that. How much does the telephone service charge for a month in which 50 calls are made?

(A) $12.20 (B) $12.80 (C) $13.60 (D) $14.40 (E) $17.60 y, 2y + 7, y + 6 . . .

4. In the increasing sequence above, the

first term is y and the difference between any two consecutive terms is 3. What is the value of the fourth term in the sequence? (A) –4 (B) 2 (C) 5 (D) 13 (E) 19

5. In a sequence of numbers, the first

number is 4 and each number after the first is 1 more than 5 times the

preceding number. What is the third number in the sequence?

(A) 16 (B) 21 (C) 94 (D) 96 (E) 106

6. The first term of a sequence is 3, and

each term after the first is 2 more than the previous term. Which of the

following is an expression for the nth term of the sequence for any positive integer n? (A) 2n (B) 1+2n (C) 2+2n (D) 3+2n (E) 2+3n

SEQUENCES



2009-2010

2009-2010

7. The nth term of a sequence is defined

to be 4n + 3. The 50th term is how much greater than the 45th term? (A) 5 (B) 16 (C) 20 (D) 23 (E) 24

8. After the first term in a sequence of

positive integers, the ratio of each term to the term immediately

preceding it is 2 to 1. What is the ratio of the 8th term in this sequence to the 5th term? (A) 6 to 1 (B) 8 to 5 (C) 8 to 1 (D) 64 to 1 (E) 256 to 1 4, 11, 18, . . .

9. In the sequence above, the first term is

4 and each term after the first is 7 more than the previous term. What is the 12th term of the sequence?

(A) 77 (B) 81 (C) 84 (D) 86 (E) 92 10. 3, 5,–5...

The first term in the sequence of numbers shown above is 3. Each even– numbered term is 2 more than the previous term and each odd–numbered term, after the first, is –1 times the previous term. For example, the second term is 3 + 2, and the third term is (–1) × 5. What is the 55th term of the sequence? (A) –5 (B) –3 (C) –1 (D) 3 (E) 5

11. The sum of 5 consecutive integers is

1,000. What the value of the greatest of these integers?

12. 5.101001000100001 …

The decimal number above consists of only 1 ‘ s and 0’s to the right of the decimal point. The first 1 is followed by one 0, the second 1 is followed by two 0’ s, the third 1 is followed by three 0’ s, and so on. What is the total number of 0’s between the 98th and the 101st 1 in this decimal number? (A) 288

(B) 291 (C) 294 (D) 297 (E) 300

SEQUENCES



The first term in the sequence above is a, and each term after the first is 3 times the preceding term. If the sum of the first 5 terms is 605, what is the value of a?

14. 7, 15, 31, 63, ...

The first term in the sequence above is 7, and each term after the first is determined by multiplying the

preceding term by m and then adding p. What is the value of m?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 9 15. Z W Y X

The sequence above may be changed in either of two ways. Either two

adjacent letters may be interchanged or the entire sequence may be

reversed. What is the least number of such changes needed to put the letters into alphabetical order from left to right? (A) 2 (B) 3 (C) 4 (D) 5 (E) 6

16. After the first term, each term in a

sequence is 3 greater than

3

1 _{of the}

preceding term. If t is the first term of the sequence and t ≠ 0, what is the ratio of the second term to the first term? (A) 3 9 t (B) 3 3 t (C) t t 3 9 (D) t t 3 3 (E) 3 2 9 t 17. 8, 17, 26, 35, 44, ...

The first 5 terms in a sequence are shown above. Each term after the first is found by adding 9 to the term

immediately preceding it. Which term in this sequence is equal to 8 + (26 – 1)9? (A) The 8th (B) The 9th (C) The 25th (D) The 26th (E) The 27th

SEQUENCES



2009-2010

2009-2010

18. What is the greatest of 5 consecutive

integers if the sum of these integers equals 185?

19. 2, 6, 14, 30, ...

In the sequence above, the first term is 2. Each number after the first is obtained by adding 1 to the

preceding number and then doubling the result. What is the sixth number in the sequence? (A) 122 (B) 123 (C) 124 (D) 125 (E) 126

20. “The sum of three consecutive odd

integers is 111. “

If n represents the least of the three integers, which of the following equations represents the statement above? (A) 3n = 111 (B) 3n + 2 = 111 (C) 3n + 4 = 111 (D) 3n + 6 = 111 (E) 3n + 9 = 111

21. The first term of a sequence is 20 and

the second term is 8. The third term and each term thereafter is the average (arithmetic mean) of the two terms immediately preceding it. What is the value of the first term in the sequence that is not an integer?

22. The nth term of a sequence is given by

the formula n2 2n.How much larger

is the 10th term of the sequence than the 9th term?

23. 150, 30, 6,…

In the sequence above, each term after the 1st term is

5

1_{of the term preceding}

it. What is the 5th term of this sequence?

SETS



1. How many positive four-digit integers

have 1 as their first digit and 2 or 5 as their last digit?

(A) 144 (B) 180 (C) 200 (D) 300 (E) 720

2. In the figure above, circular region P

represents shirts with pockets, circular region Q represents shirts with buttons, and circular region R represents shirts with collars. What is represented by the shaded region? (A)Shirts with pockets, buttons, and collars

(B) Shirts with pockets and buttons, but without collars

(C) Shirts with pockets and buttons (some possibly with collars)

(D) Shirts with pockets and collars (some possibly with buttons)

(E) Shirts with buttons and collars (some possibly with pockets)

3. P = 1,3,5,6

Q = 2,4,6,7,9

Sets P and Q are shown above. If x is a member of set P and y is a member of set Q, which of the following CANNOT be equal to the product xy ?

(A) 16 (B) 18 (C) 20 (D) 21 (E) 24

4. How many positive integers less than

1,000 are multiples of 5 and are equal to 3 times an even integer?

SETS



2009-2010

2009-2010

5. The Lyndhurst High School twelfth

graders are represented in the circle graph in Figure 1. Figure 2 is another way to illustrate the use of computers by these twelfth graders. If the same 200 twelfth graders are represented in both figures, what is the total number of twelfth graders represented by the shaded circle in Figure 2 ?

6. A set has property X if t2 t is in the set whenever t is in the set. Which of the following sets has property X ? (A) 2, 1,0

(B) 1,0

(C) 1,0,1

(D) 0,1

(E) 1,2

7. Which of the following is an element of

both the set of positive odd integers and the set of prime numbers? (A) 2

(B) 5 (C) 9 (D) 12 (E) 21

SETS



8. Students at Northern High School are

represented in Figure 1 above. Figure 2 above is another way to show which pets these students have. If the same 500 students are represented in both figures, what is the total number of students represented by the shaded circle in Figure 2 ?

9. Some integers in set X are even.

If the statement above is true, which of the following must also be true? (A) If an integer is even, it is in set X. (B) If an integer is odd, it is in set X. (C) All integers in set X are even. (D) All integers in set X are odd. (E) Not all integers in set X are odd. 7 , 2 11 , 4 , 2 5 , 1 , 7 4 A , ,4,7 4 7 , 7 4 B

10. If n is a member of both set A and set

B above, which of the following must be true? I. n is an integer. II. 4n is an integer. III. n = 4 (A) None (B) II only (C) I and II only (D) I and III only (E) I, II, and III

SETS



2009-2010

2009-2010

11. If A is the set of prime numbers and B

is the set of two-digit positive integers whose units digit is 5, how many numbers are common to both sets? (A) None

(B) One (C) Two (D) Five (E) Nine

12. There are 25 trays on a table in the

cafeteria. Each tray contains a cup only, a plate only, or both a cup and a plate. If 15 of the trays contain cups and 21 of the trays contain plates, how many contain both a cup and a plate?

13. The least integer of a set of

consecutive integers is –25. If the sum of these integers is 26, how many integers are in this set?

(A) 25 (B) 26 (C) 50 (D) 51 (E) 52

14. Set X has x members and set Y has y

members. Set Z consists of all

members that are in either set X or set Y with the exception of the k common members (k > 0). Which of the

following represents the number of members in set Z? (A) x + y + k (B) x + y – k (C) x + y + 2k (D) x + y – 2k (E) 2x + 2y – 2k

15. If E is the set of even integers, P is the

set of positive integers, and F is the set of integers less than 5, which of the following integers will be in all three sets? (A) 6 (B) 4 (C) 1 (D) 0 (E)–2 16. If 0 x 8 and 1 y 3, which of the following gives the set of all possible values of xy?

(A) xy = 4 (B) 0 xy 24 (C) 1 xy 11 (D) 1 xy 24 (E) 8 xy 24

SETS



2009-2010

2009-2010

17. How many integers in the set of all

integers from 1 to 100, inclusive, are not the square of an integer?

(A) 19 (B) 50 (C) 81 (D) 89 (E) 90

18. In a set of eleven different numbers,

which of the following CANNOT affect the value of the median?

(A) Doubling each number

(B) Increasing each number by 10 (C) Increasing the smallest number only

(D) Decreasing the largest number only

(E) Increasing the largest number only .

19. Set X = {30, 31, 32, 33} Set Y = {32, 33, 34, 35, 36} Sets X and Y are shown above. How many numbers in set X are also in set Y ? (A) Two (B) Three (C) Four (D) Seven (E) Nine

20. If k is a positive integer, let be defined as the set of all multiples of k. All of the numbers in which of the following sets are also in all three of the sets , and ?

(A) (B) (C) (D) (E)

RATIO, PROPORTION & PERCENTS



1. Which of the following tables shows a

relationship in which w is directly proportional to x?

(A) (B)

(C) (D)

(E)

2. Dwayne has a newspaper route for

which he collects k dollars each day. From this amount he pays out

3

k dollars per day for the cost of the papers, and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1,000? (A) 500 1, k _(B) 000 1, k (C) k 000 1, _(D) k 500 1, (E) 1,500k 3. If 3 2 y

x _{, what is the value of} y x 2 3 _? (A) 3 1 (B) 3 2 (C) 1 (D) 2 3 (E) 4 9

4. If 30 percent of 40 percent of a positive

number is equal to 20 percent of w percent of the same number, what is the value of w? (A) 80 (B) 60 (C) 50 (D) 15 (E) 10

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

5. There are 75 more women than men

enrolled in Linden College. If there are n men enrolled, then, in terms of n, what percent of those enrolled are men? (A) 75 n n _% (B) 75 2n n _% (C) ) (2 75 100 n n _% (D) 75 100 n n _% (E) 75 2 100 n n _%

6. The eggs in a certain basket are either

white or brown. If the ratio of the number of white eggs to the number of brown eggs is

3

2 _{, each of the following}

could be the number of eggs in the basket EXCEPT (A) 10 (B) 12 (C) 15 (D) 30 (E) 60

7. The price of a telephone was first

increased by 10 percent and then the new price was decreased by 25

percent. The final price was what percent of the initial price?

(A) 78% (B) 80% (C) 82.5% (D) 85% (E) 87.5%

8. The force required to stretch a spring

beyond its natural length is

proportional to how far the spring is being stretched. If a force of 15 pounds stretches a spring 8 centimeters

beyond its natural length, what force, in pounds, is needed to stretch this spring 20 centimeters beyond its natural length? (A) 23 (B) 27 (C) 30.5 (D) 35 (E) 37.5

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

9. A measuring cup contains

5

1_{of a cup of}

orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is orange juice?

10. If a + 2b is equal to 125 percent of 4b,

what is the value of b a _?

11. In a poll, 35 people were in favor of

building a new library, 14 people were against it, and 1 person had no

opinion. What fraction of those polled were in favor of building a new

library? (A) 10 7 (B) 3 2 (C) 7 3 (D) 3 1 (E) 10 3

12. If 20 percent of x equals 80 percent of

y, which of the following expresses y in terms of x? (A) y = 16% of x (B) y = 25% of x (C) y = 60% of x (D) y = l00% of x (E) y = 400% of x

13. If a, b, c and f are four nonzero

numbers, then all of the following proportions are equivalent EXCEPT

(A) c b f a (B) a b c f (C) b f a c (D) f b c a (E) 1 1 bc af

14. When the positive even integer n is

increased by 50 percent of itself, the result is between 10 and 20. What is one possible value of n?

RATIO, PROPORTION & PERCENTS



2009-2010 2009-2010 15. If a x x 2

4 and x ≠ 0, what is the value

of a? (A) 8 (B) 4 (C) 2 (D) 2 1 (E) 4 1

16. One circle has a radius of

2 1_and

another circle has a radius of 1. What is the ratio of the area of the larger circle to the area of the smaller circle?

(A) 2 : 1 (B) 3 : 1 (C) 3 : 2 (D) 4 : 1 (E) 5 : 2

17. The ratio 1.2 to 1 is equal to which of

the following ratios? (A) 1 to 2 (B) l2 to l (C) 5 to 6 (D) 6 to 5 (E) 6 to 50 18. If 30 percent of m is 40, what is 15 percent of m? (A) 15 (B) 20 (C) 25 (D) 30 (E) 35

RATIO, PROPORTION & PERCENTS



1. If

12

10 b

a , what is the value of ab?

2. The price of ground coffee beans is d

dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee? (A) c d 8 (B) 8 cd (C) d c 8 _(D) c d 8 (E) 8cd 3.

The circle graph above represents all the jeans that were sold by a retail store in 2001, according to

their brands. If the store sold 900 pairs of jeans other than brands J, K, L, M, and N, how many pairs of jeans did it sell altogether?

(A) 1,500 (B) 2,250 (C) 3,000 (D) 3,600

4. The Smith Metal Company’s old

machine makes 300 bolts per hour. Its new machine makes 450 bolts per hour. If both machines begin running at the same time, how many minutes will it take the two machines to make a total of 900 bolts? (A) 36 (B) 72 (C) 120 (D) 144 (E) 180 5. If y = z x3

5 _{, what happens to the value}

of y when both x and z are doubled? (A) y is not changed.

(B) y is halved. (C) y is doubled. (D) y is tripled.

(E) y is multiplied by 4.

6. If n is a positive integer and

2 1 2 1 n n _, then n =? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

7. If y is directly proportional to x2 _and 8

1

y when

2 1

x what is the positive value of x when 2 9 y ? (A) 4 3 (B) 2 3 (C) 4 9 (D) 3 (E) 9 8.

If the five line segments in the figure above are all congruent, what is the ratio of the length of AC (not shown) to the length ofBD? (A) 2to 1 (B) 3 to1 (C) 2 to 2 (D) 3 to 2 (E) 3 to 2 9.

The chart above shows the results when 1,000 people were asked, “How old are you?” The age they gave is represented by x. How many people said that their age was less than 40?

(A) 200 (B) 300 (C) 450 (D) 500 (E) 550 10. 37 39 2 x x _{, then x = ?} (A) 37 (B) 39 (C) 41 (D) 74 (E) 78

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

11. From 1979 to 1989, the total elephant

population in the four regions of Africa decreased by approximately what percent? (A) 10% (B) 30% (C) 50% (D) 70% (E) 90% 12. If n 1 ₌ 5

2_{, what is the value of n ?}

13.

In a survey, 3,400 people responded to the following question: “How many weeks of vacation did you take last year?” Their

responses to the question are summarized in the chart above, where n equals the number of vacation weeks indicated. How many respondents took more than 2 weeks of vacation last year?

14. A box contains 2,900 solid-colored

marbles that are either orange, blue, or green. If 29 percent of the marbles are orange and 29 percent of the marbles are blue, what percent are green? (A) 29% (B) 42% (C) 52% (D) 58% (E) 71%

15. What is the ratio of the radius r of a

circle to the circumference of the circle? (A) 1: 2 (B) 1: (C) 1: r (D) :1 (E) 2 :1

16. Fifty percent of the songs played on a

certain radio station are 3 minutes long, 30 percent are 5 minutes long, and 20 percent are 2 minutes long. What is the average (arithmetic mean) number of minutes per song played on this radio station

RATIO, PROPORTION & PERCENTS



2009-2010 2009-2010 17. If t r t r ₌ 2

5 _{what is the value of}

t r _? (A) - 3 7 (B) - 1 (C) 7 3 (D) 1 (E) 3 7

18. If q and r are positive numbers, what

percent of (q + 1) is r ? (A) ) 1 ( 100 1 q r % (B) r q 100 1 _% (C) r q 1) ( 100 _% (D) ( q r 100 _{+ 1 ) %} (E) 1 100 q r _%

RATIO, PROPORTION & PERCENTS



( m _{= 6 what is the value of} m ?

2. If r is directly proportional to s and if

S =

3

2 _{when r =} 5

4_{, what is the value}

of r when s = 9 4_? 3. If 7.5 is x percent of 75, what is x percent of 10 ? (A) 10 (B) 1 (C) 0.75 (D) 0.1 (E) 0.075 4. If 1 1 x = 2

1 _{what is the value of x ?}

(A) 2 (B) 1 (C) 0 (D) - 1 (E) - 2

5. A box of staples contains 4,600

staples that are either silver, black, or red. If 46 percent of the staples are silver and 46 percent are black, what percent are red?

(A) 8% (B) 18% (C) 46% (D) 54% (E) 92%

6. The original price of a book was b

dollars. This price was discounted x percent during a sale. James used a coupon to buy the book for t percent off the sale price. Which of the following represents the price, in dollars, that James paid for the book? (A) b 100 1 x 100 1 t (B) b 100 ) 1 )( 1 ( x t (C) b 100 1 x t (D) b 100 1 xt (E) b 100 x 100 t

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

7.

Students at Northern High School are represented in Figure 1 above. Figure 2 above is another way to show which pets these students have. If the same 500 students are represented in both figures, what is the total number of students represented by the shaded circle in Figure 2 ?

8. If the value of

-t

1 _{is twice the value}

of

t

1 _{, what is the value of t ?}

9. What is the ratio of the diameter d of

a circle to half the circumference of the circle? (A) 1 : 2 (B) 1 : (C) 2 : (D) : 1 (E) 2 : 1

10. If y is directly proportional to x and if

y = 20 when x = 6, what is the value of y when x = 9 ? (A) 3 10 (B) 3 40 (C) 23 (D) 27 (E) 30

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

11. Flour, water, and salt are mixed by

weight in the ratio of 5:4:1,

respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required? (A) 4 1 _(B) 2 1 (C) 4 3 _{(D) 1} (E) 2 12. If 0.03 percent of n is 3, what is 3 percent of n ? (A) 900 (B) 600 (C) 300 (D) 0.006 (E) 0.003

13. If Marisa drove n miles in t hours,

which of the following represents her average speed, in miles per hour? (A) t n _(B) n t (C) nt 1 _{(D) nt} (E) n2t 14. If 75 percent of m is equal to k

percent of 25, where k > 0, what is the value of k m _? (A) 16 3 (B) 3 1 (C) 4 3 (D) 3 (E) 3 16 15. If b a y x ₌ 3 2_{, then} b a y x 10 10 9 9 _{= ?} (A) 10 9 (B) 23 20 (C) 27 20 (D) 3 2 (E) 5 3

RATIO, PROPORTION & PERCENTS



2009-2010

2009-2010

The circle graph above shows how David’s monthly expenses are divided. If David spends $450 per month for food, how much does he spend per month on his car? (A) $200 (B) $320 (C) $360 (D) $400 (E) $450

17. In a certain store, the regular price of

a refrigerator is $600. How much money is saved by buying this refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price?

(A) $6 (B) $12 (C) $24 (D) $54 (E) $60 18.

According to the graph above, if there are 6,000 registered voters aged 60 and over in Washington County, how many

registered voters are under the age of 30 ? (A) 1,000

(B) 2,000 (C) 3,000 (D) 4,000 (E) 5,000

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

1. 22x _{= 8}x–1_{, what is the value of x?}

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6 2. If 24x _{= 16, then x =?} (A) 1 (B) 2 (C) 4 (D) 8 (E) 12 3. If 3 351

t , what is the value of 4t3?

4. If 18 18 r t, where r and t are

positive integers and r > t, which of the following could be the value of rt?

(A) 18 (B) 36 (C) 108 (D) 162 (B) 324

5. Positive integers x, y, and z satisfy the

equations 3 1 2 1 x andyz 16. If z > y what is the value of x + z?

(A) 5 (B) 7 (C) 11 (D) 13 (E) 15 6. ₃ 2 ₃ 2 ) ( x x

For what value of x is the statement above FALSE? (A) –3 (B) 0 (C) 3 1 (D) 1

(E) For no value of x

7. If x and y are positive consecutive odd

integers, where y > x, which of the following is y2 _{– x}2_? (A) 2x (B) 4x (C) 2x + 2 (D) 2x + 4 (E) 4x + 4

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

2009-2010

8. If m and k are positive and

m k m 100 10 2 1 _{, what is} 1 m in terms of k? (A) 10 k (B) 90 k (C) 10 k (D) k 10 1 (E) k 90 1 9. If 8 + k = 15, then k = ? (A) 7 (B) 49 (C) 529 (D) 7 (E) 23

10. If a, b, and c are different positive

integers and 2a 2b 2c 64, then ? c b a 2 2 2 (A) 14 (B) 17 (C) 21 (D) 28 (E) 34

11. If a and b are positive integers and

432 6 3 1 2 1 b

a , what is the value of ab?

(A) 6 (B) 12 (C) 18 (D) 24 (E) 36

12. If xy = 10, what is the value of ₂ 2 y y x _? (A) 5 (B) 8 (C) 10 (D) 12 (E) 20 13. If 3 9 y x what is x in terms of y? (A) y (B) y2 (C) y3 (D) y6 (E) y12

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

2009-2010

14. x 9 x 3

For all values of x greater than 3, the equation above is equivalent to which of the following? (A) x = x2 (B) x = x2 _{+ 18} (C) x = x2 _{– 6x} (D) x = x2 _{– 6x + 9} (E) x = x2 _{– 6x + 18}

15. If k, n, x, and y are positive numbers

satisfying 3 2 4 k x and 3 2 4 n y , what is 3 2 )

(xy in terms of n and k? (A) nk 1 (B) k n (C) n k (D) nk (E) 1 16. If 7 28 m m mx and(m5)y m15, what is the value of x + y? (A) 7 (B) 12 (C) 14 (D) 24 (E) 31

17. If ₂x ₂x ₂x ₂x ₂7, what is the value of x?

18. If k is a positive integer, what is the

least value of k for which

3 5k _{is an} integer? (A) 3 (B) 5 (C) 15 (D) 25 (E) 60

19. If n is a positive integer, then

) ( ) (6 10 n 1 10 n must equal (A) 10 7 (B) _n 10 7 (C) _2n 10 7 (D) _n 10 6 6

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

2009-2010

20. If x and y are positive integers and

y x ₂ 2 4 , what is x in terms of y? (A) y – 2 (B) y – 1 (C) y (D) y + 1 (E) y + 2

21. If 16 = 2k what is the value of k?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 8

EXPONENTS, SQUARES & SQUARE ROOTS



2. If k is a positive integer, which of the

following is equivalent to 3k+ 3k? (A) 2 3k (B) 32k (C) 6k (D) 62k (E) 92k

3. If 710 = 7 7n what is the value of n?

(A) 10 (B) 9 (C) 7 (D) 5 (E) 3 4. If 2y = 8 and y = 2

x _{what is the value} of x ? (A) 6 (B) 5 (C) 4 (D) 3 (E) 2

5. If x2 − 64 = 0, which of the following could be a value of x? (A) −8 (B) −4 (C) 0 (D) 16 (E) 32

6. If a and b are positive integers and

9(3a _{) = 3}b _{what is a in terms of b ?} (A) b − 2 (B) b − 1 (C) b (D) b + 1 (E) b + 2

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

2009-2010

7. If y is a positive integer, and

3 y − 7 = 8, what is the value of y ?

8. If a 2= 4, which of the following could be the value of a ? (A) −2 (B) − 4 1 (C) 0 (D) 4 1 (E) 2 1

9. If x2 _{- 36 = 0, which of the following} could be a value of x ? (A) -6 (B) -4 (C) 0 (D) 3 (E) 12

10. If x and y are integers such that x2 = 64 and y3 = 64 , which of the following could be true? I. x = 8 II. y = -4 III. x + y = -4 (A) I only (B) II only

(C) I and III only (D) II and III only (E) I, II, and III

11. If x 1_{h = 1, what does h equal in terms} of x ? (A) -x (B) x 1 (C) 1₂ x (D) x (E) x2

12. If 7n  73  712 , what is the value of n ? (A) 2 (B) 4 (C) 9 (D) 15 (E) 36

EXPONENTS, SQUARES & SQUARE ROOTS



2009-2010

2009-2010

13. If x is a positive integer satisfying

x7 _{= k and x}9_{= m, which of the following} must be equal to x11 ? (A) k m2 (B) m2_{- k} - (C) m2_{- 7} (D) 2k - 3 m (E) k + 4

14. If n and k are positive integers and 8n

= 2k , what is the value of

k n _? (A) 4 1 (B) 3 1 (C) 2 1 (D) 3 (E) 4

15. If t is a number greater than 1, then t2 is how much greater than t ?

(A) 1 (B) 2 (C) t (D) t (t − 1) (E) (t − 1)(t + 1) 16. If (x – 2)2 = 49, then x could be (A) -9 (B) -7 (C) 2 (D) 5 (E) 9

WORD PROBLEMS



1. There are 8 sections of seats in an

auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this

auditorium? (A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700

2. If 4 less than 3 times a certain number

is 2 more than the number, what is the number? (A) –1 (B) –3 (C) 1 (D) 2 (E) 3

3. During a game, the blue team scored

one–sixth of its points in the first quarter, one–fourth in the second quarter, one–third in the third

quarter, and the remaining points in the fourth quarter. If its total score was 36, how many points did the blue team score in the fourth quarter? (A) 6

(B) 8 (C) 9 (D) 12 (E) 25

4. At a bottling company, machine A fills

a bottle with spring water and machine B accepts the bottle only if the number of fluid ounces is between

8 7 11 and 8 1 12 . If machine B accepts a bottle containing n fluid ounces, which of the following describes all possible values of n? (A) 8 1 12 n (B) 8 1 12 n (C) 8 1 12 n (D) 8 1 12 n (E) 8 1 12 n

5. Esther drove to work in the morning

at an average speed of 45 miles per hour. She returned home in the evening along the same route and averaged 30 miles per hour. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?

WORD PROBLEMS



hedule above, each session is to be

2 1 1

hours long, each break is to be

4

1 _hour

long, and lunch is to be 1 hour long. If session IV is to end at 4:30 P.M., at

what time should session I begin? (A) 8:15 A.M.

(B) 8:30 A.M.

(C) 8:45 AM.

(D) 9:00 A.M.

(E) 9:15 A.M.

7. Carlos delivered n packages on

Monday, 4 times as many packages on Tuesday as on Monday, and 3 more packages on Wednesday than on Monday. What is the average

(arithmetic mean) number of packages he delivered per day over the three days? (A) 2n – 3 (B) 2n – 1 (C) 2n + 1 (D) 2n + 3 (E) 6n + 1 8. 5.101001000100001 …

The decimal number above consists of only 1 ‘ s and 0’s to the right of the decimal point. The first 1 is followed by one 0, the second 1 is followed by two 0’ s, the third 1 is followed by three 0’ s, and so on. What is the total number of 0’s between the 98th and the 101st 1 in this decimal number? (A) 288

(B) 291 (C) 294 (D) 297 (E) 300

9. There is the same number of boys and

girls on a school bus when it departs from school. At the first stop, 4 boys get off the bus and nobody gets on. After the first stop, there are twice as many girls as boys on the bus. How many girls are on the bus?

(A) 4 (B) 6 (C) 8 (D) 12 (E) 16

10. Stacy noted that she is both the12th _{tallest and the 12}th _shortest students in her class. If everyone in the class is of the different height, how many students are in the class?

(A) 22 (B) 23 (C) 24 (D) 25 Event Beginning _Time Ending _Time

Session I ? Break Session II Lunch Session III Break Session IV 4:30 P.M.

WORD PROBLEMS



2009-2010

2009-2010

11. A total of k passengers went on a

bus trip. Each of the n buses that were used to transport the passengers could seat a maximum of x passengers. If one bus had 3 empty seats and the remaining buses were filled, which of the following expresses the

relationship among n, x, and k? (A) nx – 3 = k

(B) nx + 3 = k (C) n + x + 3 = k (D) nk = x + 3 (E) nk = x – 3

12. The numerator of a certain

fraction is 5 less than the

denominator. If the fraction is equal to

4

3_{, what is the}

denominator of this fraction? (A) 8

(B) 12 (C) 16 (D) 20 (E) 24

13. A family of 5 is planning a 4–day

camping trip. Each person will need to bring 1 bottle of water for each day of the trip. If the water is sold only in 3– bottle packages, how many packages must the family buy for the trip?

14. A measuring cup contains

5

1 _{of a cup of}

orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is orange juice?

15. When Ms. Yun arrived at the grocery

store, there were 5 packages of hot dog rolls left on the shelf. One package contained 12 rolls, and each of the others

contained 8 rolls. If Ms. Yun bought all 5 packages, how many hot dog rolls did she purchase at the store?

(A) 32 (B) 36 (C) 44 (D) 48 (E) 52

16. How old was a person exactly 1 year ago

if exactly x years ago the person was y years old? (A) y – 1 (B) y – x – 1 (C) x – y –1 (D) y + x + 1 (E) y + x – 1

WORD PROBLEMS



2009-2010

2009-2010

17. When it is noon eastern standard

time (EST) in New York City, it is 9:00

AM. Pacific standard time (PST) in San

Francisco. A plane took off from New York City at noon EST and arrived in San Francisco at 4:00 P.M. PST on the

same day. If a second plane left San Francisco at noon PST and took exactly the same amount of time for the trip, what was the plane’s arrival time (EST) in New York City?

(A) 10:00 P.M.EST

(B) 9:00 P.M. EST

(C) 7:00 P.M. EST

(D) 6:00 P.M. EST

(E) 4:00 P.M. EST

18. Todd is older than Marta but

younger than Susan. If t, m, and s represent the ages, in years, of Todd, Marta, and Susan, respectively, which of the following is true?

(A) m < t < s (B) s < m < t (C) s < t < m (D) t < m < s (E) t < s < m

19. A school ordered $600 worth of light

bulbs. Some of the light bulbs cost $1 each and the others cost $2 each. If twice as many $1 bulbs as $2 bulbs were ordered, how many light bulbs were ordered altogether?

20. When twice a number is decreased

by 3, the result is

253. What is the number?

21. h(t) = c – (d – 4t)2

At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the

function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5, what was the height, in feet, of the ball at time t = 1?

22. Bobby receives $2 for each chore he

does during the week, plus a weekly allowance of $10. If Bobby receives no other money, which of the following expressions represents the total dollar amount Bobby receives for a week in which he has done n chores?

(A) 10 + n (B) (10 + 2)n (C) 10n + 2 (D) 10 + 2n (E) (10 + n)2

WORD PROBLEMS



2009-2010

2009-2010

23. A computer program randomly

selects a positive two–digit integer. If the integer selected is odd, twice that integer is printed. If the integer selected is even, the integer itself is printed. If the integer printed is 26, which of the following could have been the integer selected? I. 13 II. 26 III. 52 (A) I only (B) II only (C) I and II only (D) I and III only (E) I, II and III

24. How many seconds are there in m

minutes and s seconds? (A) 60m + s (B) m + 60s (C) 60(m + s) (D) 60 s m (E) m s 60

25. Kyle’s lock combination consists of 3

two–digit numbers. The combination satisfies the three conditions below.

One number is odd.

One number is a multiple of 5. One number is the day of the

month of Kyle’s birthday.

If each number satisfies exactly one of the conditions, which of the

following could be the combination to the lock? (A) 14 – 20 – 13 (B) 14 – 25 – 13 (C) 15 – 18 – 16 (D) 20 – 15 – 20 (E) 34 – 30 – 21

26. Phillip used four pieces of masking

tape, each 6 inches long, to put up each of his posters. Phillip had a 300–foot roll of masking tape when he started. If no tape was wasted, which of the following

represents the number feet of masking tape that was left on the roll after he put up n posters? (12 inches = 1 foot)

(A) 300 – 6n (B) 300 – 2n (C) 300 – n (D) 300 – n 2 1 (E) 300 – n 4 1

WORD PROBLEMS



1. A number n is increased by 5 and the

result is multiplied by 5. This result is decreased by 5. Finally, that result is divided by 5. In terms of n, what is the final result?

2. In a certain game, points are assigned to

every word. Each q, x, and z in a word is worth 5 points, and all other letters are worth 1 point each. What is the sum of the points assigned to the word “exquisite”?

(A) 21 (B) 17 (C) 16 (D) 13 (E) 9

3. A certain scale only registers weights

that are greater than 6 pounds. A person who wanted to know the weights of a puppy, a kitten, and a bunny weighed them in pairs and got the following results.

The kitten and the bunny weighed 7 pounds. The kitten and the puppy weighed 8 pounds. The bunny and the puppy weighed 9 pounds. What is the weight of the puppy?

(A) 2 pounds (B) 3 pounds (C) 4 pounds (D) 5 pounds

4. The scenic route from Mia’s home to her

office is 5 kilometers longer than the direct route. When she goes by the scenic route and returns by the direct route, the round trip is 35 kilometers. How many kilometers is the direct route? (A) 5 (B) 2 1 12 (C) 15 (D) 20 (E) 2 1 22

5. For a certain hot–water heater, the

increase in heating expenses is directly proportional to the increase in water– temperature setting. If heating expenses increase by $24 when the water–

temperature setting is increased by 20 degrees Fahrenheit, by how much will heating expenses increase when the water–temperature setting is increased by 15 degrees Fahrenheit? (A) $16 (B) $18 (C) $19 (D) $20 (E) $21

6. If Peg traveled 10 miles in 2 hours and

Linda traveled twice as far in half the time, what was Linda’ s average speed, in miles per hour?

(A) 5 (B) 10 (C) 20 (D) 30

WORD PROBLEMS



2009-2010

2009-2010

7. If the product of 0.3 and a number is

equal to 1, what is the number?

8. A company sells boxes of balloons in

which the balloons are red, green, or blue. Luann purchased a box of balloons in which

3

1_{of them were red. If there}

were half as many green balloons in the box as red ones and 18 balloons were blue, how many balloons were in the box?

9. Alice and Corinne stand back-to-back.

They each take 10 steps in opposite directions away from each other and stop. Alice then turns around, walks toward Corinne, and reaches her in 17 steps. The length of one of Alice’s steps is how many times the length of one of Corinne’s steps? (All of Alice’s steps are the same length and all of Corinne’s steps are the same length.)

10. If 3 more than n is a negative number

and if 5 more than n is a positive

number, which of the following could be the value of n? (A) –5 (B) –4 (C) –3 (D) 0 (E) 4

11. If all men in the Williams family are over

six feet tall, which of the following statements must be true?

(A) No man under six feet tall is a member of the Williams family. (B) All men over six feet tall are members of the Williams family.

(C) All men who are not members of the Williams, family are under six feet tall. (D) Every member of the Williams family over six feet tall is a man.

(E) There is one man in the Williams family under six feet tall.

12. The total cost of 3 equally priced

mechanical pencils is $4.50. If the cost per pencil is increased by $0.50, how much will 5 of these pencils cost at the new rate? (A) $7.50 (B) $8.00 (C) $9.00 (D) $9.50 (E) $10.00

13. Car A traveled 60 miles and averaged 20

miles per gallon of gasoline. If car B traveled 15 miles

for each gallon of gasoline it used, how many miles had car B traveled

when it had used the same amount of gasoline that car A used to travel 60 miles?

WORD PROBLEMS



2009-2010

2009-2010

14. At Maple Creek High School, some

members of the chess club are on the swim team and no members of the swim team are tenth graders. Which of the following must also be true?

(A) No members of the chess club are tenth graders.

(B) Some members of the chess club are tenth graders.

(C) Some members of the chess club are not tenth graders.

(D) More tenth graders are on the swim team than are in the chess club.

(E) More tenth graders are in the chess club than are on the swim team.

15. To celebrate a colleague’s graduation, the

m coworkers in an office agreed to

contribute equally to a catered lunch that costs a total of y dollars. If p of the

coworkers fail to contribute, which of the following represents the additional amount, in dollars, that each of the remaining coworkers must contribute to pay for the lunch?

(A) m y (B) p m y (C) p m py (D) m p m y( ) (E) ) (m p m py

16. While driving on a 500-mile trip, Mr.

Smith averages 60 miles per hour for the first t hours. In terms of t, where

t < 8, how many miles remain to be traveled? (A) 60t − 500 (B) 500 − 60t (C) 30,000 − t (D) 500 − t 60 (E) t 60 500 17. By 7:00 P.M., 3

1 _{of the junior class had}

arrived at a school dance. By 8:00 P.M., 30 more juniors had arrived, raising attendance to

2

1 _{of the junior class. How}

many people are in the junior class? (A) 30

(B) 90 (C) 120 (D) 180 (E) 240

WORD PROBLEMS



2009-2010

2009-2010

18. The total cost of a taxicab ride is the sum

of

(1) a basic fixed charge for using the taxicab, and

(2) an additional charge for each

4 1 _{of a}

mile that is traveled. If the total cost to ride

4

3 _{mile is $4.00}

and the total cost to ride 1

2

1 _{miles is}

$5.50, what is the total cost, in dollars, of a 3-mile ride?

(Disregard the $ sign when gridding your answer. If, for example, your answer is $1.37, grid 1.37)

19. Classified ads cost $2.50 per 30 words at

CityNewspaper. What is the least number of words that must be deleted from the text of a 75-word classified ad to reduce the cost to $5.00 or less?

(A) 5 (B) 15 (C) 20 (D) 30 (E) 60

20. Which of the following represents the total

cost, in dollars, of k compact discs at $15 each and p compact disc cases at $25 each? (Disregard sales tax.)

(A) 15k + 25p (B) 25k + 15p (C) 40(k + p) (D) 0.40(k + p) (E) (15 + k)(25 + p)

21. If x and y are two different integers and

the product 35xy is the square of an integer, which of the following could be equal to xy? (A) 5 (B) 70 (C) 105 (D) 140 (E) 350

22. An amusement park charges $7 more for

an adult’s admission than for a child’s admission. If a group of 4 adults and 3 children spent $119 on admission, what is the price of admission for one child? (A) $11

(B) $13 (C) $16 (D) $17 (E) $18

WORD PROBLEMS



The figure above shows four apartments in a building. In this building, each apartment is occupied by only one

person. Alice lives next to Sam, and Paul lives next to Alice and Dara. In which apartment could Alice live?

(A) 1 only (B) 2 only (C) 3 only (D) 2 or 3 (E) 1 or 4

24. A community college charges an activity

fee of $4.00 per student and has a student body of 8,200 students. If every student pays the fee, what is the total amount in activity fees collected from the students? (A) $32.80 (B) $328.00 (C) $3,280.00 (D) $32,800.00 (E) $328,000.00

WORD PROBLEMS



1. Each month, a telephone service charges

a base rate of $10.00 and an additional $0.08 per call for the first 40 calls and $0.04 for every call after that. How much does the telephone service charge for a month in which 50 calls are made? (A) $12.20 (B) $12.80 (C) $13.60 (D) $14.40 (E) $17.60 2. How many 4

1_{-pound sticks of butter}

together weigh as much as 25 pounds of butter?

3. The total cost of 5 equally priced

notebooks is $12.50. If the cost per

notebook is reduced by $1, how much will 3 of these notebooks cost at the new rate? (A) $4.50

(B) $5.00 (C) $6.50 (D) $7.50 (E) $9.50

4. When the number k is multiplied by 5,

the result is the same as when 5 is added to k. What is the value of 4k?

(A) 5 4 (B) 1 (C) 4 5 (D) 4 (E) 5

5. The bus fare from city A to city B is $5

more for adults than for children. If a group of 5 adults and 6 children pay a total of $124 to travel by bus from city A to city B, what is the cost of the ticket for one adult? (A) $11 (B) $12 (C) $14 (D) $16 (E) $17

6. Which of the following represents the

total cost, in dollars, of x rolls of

wrapping paper that cost $6 each and y greeting cards that cost $2 each?

(A) 2x + 6y (B) 6x + 2y (C) 8(x + y) (D) 0.8(x + y) (E) (2 + x) (6 + y)

WORD PROBLEMS



2009-2010

2009-2010

7. Jamal has some coins in his pocket.

Some of these coins are quarters, and none of the quarters in his pocket are dated earlier than 2000. Which of the following must be true?

(A) None of the coins in Jamal’s pocket are dated earlier than 2000.

(B) Some of the coins in Jamal’s pocket are dated earlier than 2000.

(C) Some of the coins in Jamal’s pocket are dated 2000 or later.

(D) Most of the coins in Jamal’s pocket are either quarters or dated earlier than 2000.

(E) Most of the coins in Jamal’s pocket are not quarters.

8. There are 6 bookcases in a house. Each

bookcase contains at least 125 books but not more than 160 books. Which of the following could be the total number of books in all 6 bookcases?

(A) 500 (B) 625 (C) 725 (D) 925 (E) 1,000

9. The city library donated some children’s

books to Mr. Clark’s first-grade class. If each student takes 4 books, there will be 20 books left. If 3 students do not take a book and the rest of the students take 5 books each, there will be no books left. How many books were donated to the class? (A) 120 (B) 140 (C) 160 (D) 175 (E) 185

10. Bernardo drives to work at an average

speed of 50 miles per hour and returns along the same route at

an average speed of 25 miles per hour. If his total travel time is 3 hours, what is the total number of

miles in the round-trip? (A) 225

(B) 112.5 (C) 100 (D) 62.5 (E) 50

11. When a certain number is multiplied by

4

1 _{and the product is then multiplied by}