SAT Practice Book 2009 2010

TABLE of CONTENTS

2009-2010

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

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2009-2010

PROPERTIES of INTEGERS 

1. If x is an integer greater than 1 and if 1 , which of the following must be y x x true?

4. If n is any negative number, which of the following must be positive? n 2 (B) 2n (C) n + 2 (D) n – 2 (E) 2 – n

(A)

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 – x2?

5. If k is a positive even integer, then (k+1)(k+2) could equal which of the following?

(A) 2x (B) 4x (C) 2x + 2 (D) 2x + 4 (E) 4x + 4

(A) 10 (B) 20 (C) 30 (D) 40 (E) 50

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?

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) 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.

SAT Practice Book

(A) I only (B) II only (C) III only (D) I and II (E) II and III 2 11

20092009-2010 2010

PROPERTIES of INTEGERS 

7. If a, b, and c are positive integers, and if (a−c)b=0, which of the following must be true?

10. If

x 3 is an integer, then x must be 2

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

(A) a 0, what is the m value of ? k 3 16 1 (B) 3 3 (C) 4 (D) 3 16 (E) 3

(A)

1 2

(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

15. If

(A) (B) 13. If Marisa drove n miles in t hours, which of the following represents her average speed, in miles per hour? n t 1 (C) nt (E) n 2 t

(A)

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(B)

(C) (D)

t n

(E)

x y 2 9x 9 y = , then =? a b 3 10 a 10b 9 10 20 23 20 27 2 3 3 5

(D) nt

30

16.

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RATIO, PROPORTION & PERCENTS  18.

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?

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) $200 (B) $320 (C) $360 (D) $400 (E) $450

(A) 1,000 (B) 2,000 (C) 3,000 (D) 4,000 (E) 5,000

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

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EXPONENTS, SQUARES & SQUARE ROOTS

2009-2010

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



5. Positive integers x, y, and z satisfy the 1 1 equations x 2 and y z 16 . If z > y 3 what is the value of x + z?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

(A) 5 (B) 7 (C) 11 (D) 13 (E) 15

2. If 24x = 16, then x =? (A) 1 (B) 2 (C) 4 (D) 8 (E) 12

3. If t 3

6.

(3x) 2

For what value of x is the statement above FALSE? (A) –3 (B) 0 1 (C) 3 (D) 1 (E) For no value of x

351 , what is the value of 4t 3 ?

7. If x and y are positive consecutive odd integers, where y > x, which of the following is y2 – x2?

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) 2x (B) 4x (C) 2x + 2 (D) 2x + 4 (E) 4x + 4

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

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3x 2

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EXPONENTS, SQUARES & SQUARE ROOTS 

8. If m and k are positive and 10m 2 k 1 100m , what is m 1 in terms of k? (A) (B) (C) (D) (E)

11. If a and b are positive integers and 1 2

a b

k 10 k 90 k 10 1 10k 1 90k

6

432 , what is the value of ab?

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

9. If 8 + k = 15, then k = ?

12. If xy = 10, what is the value of 2

(A) 7 (B) 49 (C) 529 (D) 7 (E) 23

(A) 5 (B) 8 (C) 10 (D) 12 (E) 20

13. If x 3

10. If a, b, and c are different positive integers and 2 a 2 b 2 c 64 , then 2 a 2b 2c ?

y 9 what is x in terms of y?

(A) y (B) y2 (C) y3 (D) y6 (E) y12

(A) 14 (B) 17 (C) 21 (D) 28 (E) 34

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1 3

33 22

x 2 y ? y

20092009-2010 2010 14. x 9

EXPONENTS, SQUARES & SQUARE ROOTS  17. If 2 x of x?

x 3

2x

2x

2x

27 , what is the value

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

18. If k is a positive integer, what is the 5k least value of k for which is an 3 integer?

15. If k, n, x, and y are positive numbers satisfying x what is (xy )

4 3 2 3

k 2 and y

4 3

n2 ,

in terms of n and k?

(A) 3 (B) 5 (C) 15 (D) 25 (E) 60

1 (A) nk n (B) k k (C) n (D) nk (E) 1

19. If n is a positive integer, then (6 10 n ) (1 10 n ) must equal 16. If m x m 7 m 28 and (m5 ) y the value of x + y?

(A)

m15 , what is

(B)

(A) 7 (B) 12 (C) 14 (D) 24 (E) 31

(C) (D) (E)

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7 10 7 10 n 7 10 2 n 6 10 n 6 10 2 n

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20092009-2010 2010

EXPONENTS, SQUARES & SQUARE ROOTS 

20. If x and y are positive integers and 4 2 x 2 y , what is x in terms of y? (A) y – 2 (B) y – 1 (C) y (D) y + 1 (E) y + 2

21. If

16 = 2 k what is the value of k? (A) 1 (B) 2 (C) 3 (D) 4 (E) 8

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EXPONENTS, SQUARES & SQUARE ROOTS

2009-2010

1. If x = 5 y and y = z + 1, what is

x in 5

4.

terms of z ?

(A) 6 (B) 5 (C) 4 (D) 3 (E) 2

5. If x 2 − 64 = 0, which of the following could be a value of x?

2. If k is a positive integer, which of the following is equivalent to 3k + 3k ?

3. If 7 10 = 7

(A) −8 (B) −4 (C) 0 (D) 16 (E) 32

k

7 n what is the value of n?

6. If a and b are positive integers and 9(3 a ) = 3 b what is a in terms of b ?

(A) 10 (B) 9 (C) 7 (D) 5 (E) 3

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x what is the value 2

of x ?

(A) z (B) z + 1 (C) 5 z (D) 5 z +1 (E) 5 z 1

(A) 2 3 (B) 3 2 k (C) 6 k (D) 6 2 k (E) 9 2 k

If 2 y = 8 and y =



(A) b − 2 (B) b − 1 (C) b (D) b + 1 (E) b + 2

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EXPONENTS, SQUARES & SQUARE ROOTS 

7. If y is a positive integer, and 3 y − 7 = 8, what is the value of y ?

10. If x and y are integers such that x 2 = 64 and y 3 = 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

8.

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

11. If x 1 h = 1, what does h equal in terms of x ? (A) -x 1 (B) x 1 (C) 2 x (D) x (E) x 2

12. If 7 n  7 3  7 12 , what is the value of n?

9. If x - 36 = 0, which of the following could be a value of x ? 2

(A) 2 (B) 4 (C) 9 (D) 15 (E) 36

(A) -6 (B) -4 (C) 0 (D) 3 (E) 12

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EXPONENTS, SQUARES & SQUARE ROOTS 

13. If x is a positive integer satisfying x 7 = k and x 9 = m, which of the following must be equal to x 11 ?

15. If t is a number greater than 1, then t 2 is how much greater than t ? (A) 1 (B) 2 (C) t (D) t (t − 1) (E) (t − 1)(t + 1)

2

m k (B) m 2 - k (C) m 2 - 7 m (D) 2k 3 (E) k + 4

(A)

14. If n and k are positive integers and 8 n n = 2 k , what is the value of ? k

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

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

(A)

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2009-2010

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?

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

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

(A) n 12 (B) n 12 (C) n 12

2. If 4 less than 3 times a certain number is 2 more than the number, what is the number?

(D) n 12 (E) n 12

(A) –1 (B) –3 (C) 1 (D) 2 (E) 3

1 8 1 8 1 8 1 8 1 8

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?

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

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WORD PROBLEMS 

6.

Schedule Event

I Session I n Break tSession II h Lunch eSession III Break sSession IV c

Beginning Time

8. Ending Time

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?

?

4:30 P.M.

hedule above, each session is to be 1

1 2

(A) 288 (B) 291 (C) 294 (D) 297 (E) 300

1 hour 4 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?

hours long, each break is to be

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) 8:15 A.M. (B) 8:30 A.M. (C) 8:45 AM. (D) 9:00 A.M. (E) 9:15 A.M.

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

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?

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

(A) 2n – 3 (B) 2n – 1 (C) 2n + 1 (D) 2n + 3 (E) 6n + 1

SAT Practice Book

5.101001000100001 …

(A) 22 (B) 23 (C) 24 (D) 25 (E) 34 40 22

20092009-2010 2010

WORD PROBLEMS  1 of a cup of 5 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?

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?

14. A measuring cup contains

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

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?

12. The numerator of a certain fraction is 5 less than the denominator. If the fraction is equal to 3 , what is the 4 denominator of this fraction?

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

(A) 8 (B) 12 (C) 16 (D) 20 (E) 24

16. How old was a person exactly 1 year ago if exactly x years ago the person was y years old?

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?

SAT Practice Book

(A) y – 1 (B) y – x – 1 (C) x – y –1 (D) y + x + 1 (E) y + x – 1

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WORD PROBLEMS 

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?

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?

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

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

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?

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20092009-2010 2010

WORD PROBLEMS 

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?

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.

I. 13 II. 26 III. 52

If each number satisfies exactly one of the conditions, which of the following could be the combination to the lock?

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

(A) 14 – 20 – 13 (B) 14 – 25 – 13 (C) 15 – 18 – 16 (D) 20 – 15 – 20 (E) 34 – 30 – 21

24. How many seconds are there in m minutes and s seconds?

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) 60m + s (B) m + 60s (C) 60(m + s) m s (D) 60 m s (E) 60

SAT Practice Book

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

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2009-2010

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?

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) 12 (C) 15 (D) 20

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”?

(E) 22

1 2

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) 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.

(A) $16 (B) $18 (C) $19 (D) $20 (E) $21

The kitten and the bunny weighed 7 pounds. The kitten and the puppy weighed 8 pounds. The bunny and the puppy weighed 9 pounds.

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?

What is the weight of the puppy? (A) 2 pounds (B) 3 pounds (C) 4 pounds (D) 5 pounds (E) 6 pounds SAT Practice Book

1 2

(A) 5 (B) 10 (C) 20 (D) 30 (E) 40 44 11

20092009-2010 2010

WORD PROBLEMS 

7. If the product of 0.3 and a number is equal to 1, what is the number?

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.

8. A company sells boxes of balloons in which the balloons are red, green, or blue. Luann purchased a box of balloons 1 in which of them were red. If there 3 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.)

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?

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?

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?

(A) $7.50 (B) $8.00 (C) $9.00 (D) $9.50 (E) $10.00

(A) –5 (B) –4 (C) –3 (D) 0 (E) 4

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WORD PROBLEMS 

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?

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) 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.

(A) 60t − 500 (B) 500 − 60t (C) 30,000 − t 60 (D) 500 − t 500 (E) 60t

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?

17. By 7:00 P.M.,

(A) (B)

1 of the junior class had 3 arrived at a school dance. By 8:00 P.M., 30 more juniors had arrived, raising 1 attendance to of the junior class. How 2 many people are in the junior class?

(A) 30 (B) 90 (C) 120 (D) 180 (E) 240

y m y m

(C)

p py

m p y (m p) (D) m py (E) m( m p )

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WORD PROBLEMS 

18. The total cost of a taxicab ride is the sum of (1) a basic fixed charge for using the taxicab, and 1 (2) an additional charge for each of a 4 mile that is traveled. 3 If the total cost to ride mile is $4.00 4 1 and the total cost to ride 1 miles is 2 $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)

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

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?

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

(A) $11 (B) $13 (C) $16 (D) $17 (E) $18

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)

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23.

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

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2009-2010

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?

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

(A)

(A) $12.20 (B) $12.80 (C) $13.60 (D) $14.40 (E) $17.60

1 -pound sticks of butter 4 together weigh as much as 25 pounds of butter?

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?

2. How many

(A) $11 (B) $12 (C) $14 (D) $16 (E) $17 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?

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) $4.50 (B) $5.00 (C) $6.50 (D) $7.50 (E) $9.50

SAT Practice Book

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

49 11

20092009-2010 2010

WORD PROBLEMS  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?

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.

(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?

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

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

11. When a certain number is multiplied by 1 and the product is then multiplied by 4 32, the result is 60. What is the number?

SAT Practice Book

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20092009-2010 2010

WORD PROBLEMS 

12. An object thrown upward from a height of h feet with an initial velocity of v feet per second will reach a maximum height v2 of h+ feet. If the object is thrown 64 upward from a height of 6 feet with an initial velocity of 32 feet per second, what will be its maximum height, in feet?

15. If Marisa drove n miles in t hours, which of the following represents her average speed, in miles per hour? n t t (B) n 1 (C) nt (D) nt (E) n2t

(A)

13. On Monday morning Mr. Smith had a certain amount of money that he planned to spend during the week. On each subsequent morning, he had one fourth the amount of the previous morning. On Saturday morning, 5 days later, he had $1. How many dollars did Mr. Smith originally start with on Monday morning? (Disregard the $ sign when gridding your answer.)

16. Morgan’s plant grew from 42 centimeters to 57 centimeters in a year. Linda’s plant, which was 59 centimeters at the beginning of the year, grew twice as many centimeters as Morgan’s plant did during the same year. How tall, in centimeters, was Linda’s plant at the end of the year?

14. Ali, Ben, and Carla made a total of 20 sandwiches. Ben made 3 times as many as Ali, and Carla made twice as many as Ben. How many sandwiches did Ali make?

17. Since the beginning of 1990, the number of squirrels in a certain wooded area has tripled during every 3-year period of time. If there were 5,400 squirrels in the wooded area at the beginning of 1999, how many squirrels were in the wooded area at the beginning of 1990?

(A) Two (B) Four (C) Five (D) Six (E) Ten

SAT Practice Book

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20092009-2010 2010

WORD PROBLEMS 

18. 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

19. All of Kay’s brothers can swim. If the statement above is true, which of the following must also be true? (A) If Fred cannot swim, then he is not Kay’s brother. (B) If Dave can swim, then he is not Kay’s brother. (C) If Walt can swim, then he is Kay’s brother. (D) If Pete is Kay’s brother, then he cannot swim. (E) If Mark is not Kay’s brother, then he cannot swim.

20. When her son’s class held its magazine drive, Dr. Nelson bought 7 one-year magazine subscriptions for the waiting room in her office. She bought 4 subscriptions that have 12 issues per year, 2 subscriptions that have 4 issues per year, and 1 subscription that has 52 issues per year. Altogether, how many magazines will her office receive from these subscriptions?

SAT Practice Book

52 44

FACTORING 

2009-2010

1. If a + 2(x + 1) = s, what is x + 1, in terms of s and a? s (A) 2a s a (B) 2 s a (C) 2 s (D) a 2 s (E) a 2

4. If x2 – y2 = 77 and x + y = 11, what is the value of x?

2. If x2+y2 = 73 and xy = 24, what is the value of (x + y)2?

5. If a, b, and c are different positive integers and 2 a 2 b 2 c 64 , then 2 a 2b 2c ?

(A) 10 (B) 9 (C) 8 (D) 7 (E) 6

(A) 73 (B) 97 (C) 100 (D) 121 (E) 144

(A) 14 (B) 17 (C) 21 (D) 28 (E) 34

1

1

6. If (2x – 2)(2 – x) = 0, what are all the possible values of x?

3. If (a b) 2 (a b) 2 , which of the following must be true?

(A) 0 only (B) 1 only (C) 2 only (D) 1 and 2 only (E) 0, 1, and 2

(A) b = 0 (B) a + b = 1 (C) a – b = 1 (D) a2 + b2 = 1 (E) a2 – b2 = 1

SAT Practice Book

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20092009-2010 2010

FACTORING 

7. If a and b are positive integers and a2 – b2 = 7, what is the value of a?

10. If 2x + z = 2y and 2x + 2y + z = 20, what is the value of y?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

(A) 5 (B) 8 (C) 10 (D) 15 (E) It cannot be determined from the information given.

8. If x2 – y2 = 10 and x + y = 5, what is the value of x – y?

11.

if 1 2 1 1 x3 x x ax 3 bx 2 cx d 10 30 90 for all values of x, where a,b,c, and d are constants, what is the value of a+b+c+d ?

12. 3(x-7)(x-2)=k In the equation above, k is a constant. If the roots of the equation are 7 and 2, what is the value of k?

9. If xy = 7 and x – y = 5, then x2y – xy2 =? (A) 2 (B) 12 (C) 24 (D) 35 (E) 70

SAT Practice Book

(A) 0 (B) 2 (C) 3 (D) 7 (E) 14

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20092009-2010 2010

FACTORING 

13. If x 2 − 64 = 0, which of the following could be a value of x?

16. If (x+5) y= x 2 −x+13, what is the value of y When x = 2?

(A) −8 (B) −4 (C) 0 (D) 16 (E) 32

14. If n is a positive odd integer, then (n+1)(n+2) could equal which of the following?

17. If (w−2) 2 =0, what is the value of (w+3)(w+4)=? (A) 30 (B) 12 (C) 7 (D) −1 (E) It cannot be determined from the information given.

(A) 10 (B) 15 (C) 20 (D) 25 (E) 30

15. If x and y are numbers such that (x+9)(y−9)=0, what is the smallest possible value of x 2 y 2 ?

18. If x 2 +x=30, which of the following is a possible value of x 2 x? (A) -30 (B) 10 (C) 20 (D) 30 (E) 870

(A) 0 (B) 9 (C) 18 (D) 81 (E) 162

SAT Practice Book

55 33

MEAN, MEDIAN & MODE 

2009-2010

1. 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?

4.

(A) 2n – 3 (B) 2n – 1 (C) 2n + 1 (D) 2n + 3 (E) 6n + 1

What was the average (arithmetic mean) of the scores of the 5 students on test II? (A) 60 (B) 65 (C) 68 (D) 70 (E) 72

2. If the average (arithmetic mean) of x and y is k, which of the following is the average of x, y, and z? (A) (B) (C) (D) (E)

2k z 3 2k z 2 k z 3 k z 2 2(k z ) 3

5. If the areas of two regions are equal and the sum of the areas of the regions is 5, what is the average (arithmetic mean) of the areas of the two regions? (A) 0 5 (B) 2 5 (C) 4 (D) 5 (E) 10

3. The median of a set of 9 consecutive integers is 42. What is the greatest of these 9 integers?

SAT Practice Book

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20092009-2010 2010

MEAN, MEDIAN & MODE 

6. When the sum of a list of prices is divided by the average (arithmetic mean) of the prices, the result is k. What does k represent?

8. Each of 5 people had a blank card on which they wrote a positive integer. If the average (arithmetic mean) of these integers is 15, what is the greatest possible integer that could be on one of the cards?

(A) The sum of the prices (B) Half of the sum of the prices (C) The average of the prices (D) The number of prices (E) Half of the number of prices

9. 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?

7. Number of Siblings per Student in a Preschool Class Number Number of Siblings of Students 0 3 I 6 2 2 3 1 The table above shows how many students in a class of 12 preschoolers had 0, 1, 2, or 3 siblings. Later, a new student joined the class, and the average (arithmetic mean) number of siblings per student became equal to the median number of siblings per student. How many siblings did the new student have?

10. If the average (arithmetic mean) of x and 3x is 12, what is the value of x? (A) 2 (B) 4 (C) 6 (D) 12 (E) 24

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

SAT Practice Book

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20092009-2010 2010

MEAN, MEDIAN & MODE 

11. The average (arithmetic mean) of a, b, and c is equal to the median of a, b, and c. If 0 < a < b < c, which of the following must be equal to b ? (A) (B) (C) (D) (E)

14.

a, 2a, b

If the average (arithmetic mean) of the 3 numbers above is 2a, what is b in terms of a ?

a c 2 a c 3 c-a 2 c-a 3 ac

(A) a 3 (B) a 2 (C) 2a 5 (D) a 2 (E) 3a

12. 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?

15. For which of the following lists of 7 numbers is the average (arithmetic mean) less than the median? (A) 1, 2, 3, 8, 9, 10, 11 (B) 3, 4, 5, 8, 11, 12, 13 (C) 5, 5, 5, 8, 11, 11, 11 (D) 5, 6, 7, 8, 9, 10, 11 (E) 5, 6, 7, 8, 9, 10, 20

13. If the average (arithmetic mean) of 5 and r is 7 and the average of 3 and s is 3, what is the average of r and s ? (A) 3 (B) 5 (C) 6 (D) 9 (E) 12

SAT Practice Book

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20092009-2010 2010

MEAN, MEDIAN & MODE  17.

16. For 12 bottles of shampoo of various brands, the cost and volume of each are displayed in the scatterplot above, and the line of best fit for the data is shown. Of the following, which is closest to the average (arithmetic mean) cost per ounce for the 12 bottles?

The table above shows the number of items 100 customers purchased from a hardware store over a 4 -hour period. Which of the following can be determined from the information in the table? I. The average (arithmetic mean) number of items purchased per customer

(A) $0.06 (B) $0.09 (C) $0.12 (D) $0.15 (E) $0.18

II. The median number of items purchased per customer III. The mode of the number of items purchased per customer (A) None (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III

SAT Practice Book

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20092009-2010 2010

MEAN, MEDIAN & MODE 

18. The median of a list of 99 consecutive integers is 60. What is the greatest integer in the list?

21.

The bar graph above shows the number of tons of beans produced on a large farm for the years 1985 through 1991. For which of the following two-year periods was the average (arithmetic mean) bean production closest to the bean production in 1985?

19. The average (arithmetic mean) of 6, 19, and x is 19. What is the value of x ? (A) 19 (B) 25 (C) 31 (D) 32 (E) 57

(A) 1986-1987 (B) 1987-1988 (C) 1988-1989 (D) 1989-1990 (E) 1990-1991

22. The average (arithmetic mean) of t and y is 15, and the average of w and x is 15. What is the average of t, w, x, and y ?

20. If the average (arithmetic mean) of t and t   2 is x and if the average of t and t   2 is y, what is the average of x and y ?

(A) 7.5 (B) 15 (C) 22.5 (D) 30 (E) 60

(A) 1 t (B) 2 (C) t (D) t  

1 2

(E) 2t

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20092009-2010 2010

MEAN, MEDIAN & MODE 

23. 10, 18, 4, 15, 3, 21, x If x is the median of the 7 numbers listed above, which of the following could be the value of x ? (A) 5 (B) 8 (C) 9 (D) 14 (E) 16

24. If 2x – 5, x + 1, and 3x – 8 are all integers and x + 1 is the median of these integers, which of the following could be a value for x? (A) 5 (B) 7 (C) 9 (D) 10 (E) 11

SAT Practice Book

61 66

EQUATIONS 

2009-2010

1. If 2x + 3 = 9, what is the value of 4x – 3?

4. If

(A) 5 (B) 9 (C) 15 (D) 18 (E) 21

2. If

x y

x y

2 3x , what is the value of ? 3 2y

1 3 2 (B) 3 (C) 1 3 (D) 2 9 (E) 4

(A)

2 3x , what is the value of ? 3 2y

5. If 3x + 9 = 5x + 1, what is the value of x?

1 3 2 (B) 3 (C) 1 3 (D) 2 9 (E) 4

(A)

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

3. If 5t = 45 and tk = 1, what is the value of k?

6. If 2(x – 3) = 8, what does

x 3 equal? x 3

1 45 1 (B) 9 1 (C) 5 (D) 5 (E) 9

(A)

SAT Practice Book

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20092009-2010 2010

EQUATIONS 

7. If 6,565 = 65(x + 1), then x = ?

11. If 40,404+x=44,444, then 40,404-10x = ?

(A) 10 (B) 11 (C) 100 (D) 101 (E) 1001

(A) - 4.04 (B) 0.004 (C) 4 (D) 4.04 (E) 40.4

12. If 0.0002 x

8. If 2x – 10 = 20, then x – 5 = ?

(A) 0.0001 (B) 0.1 1 (C) 2 (D) 1 (E) 1,000

(A) 5 (B) 10 (C) 15 (D) 20 (E) 30

13. If n is 3 less than w and w is 1 more than z, what is the value of n when z =1 ?

9. If x = k(k – 2), then x + 1 = ? (A) k2 – k (B) k2 – 3k (C) k2 – 2k + 1 (D) k2 + 2k + 1 (E) k2 – 1

10.

x x 2

(A) 1 (B) 0 (C) 1 (D) 2 (E) 3

39 , then x = 37

14. If 3x x 2x x 20, then x (A) 20 (B) 10 (C) 5 (D) 10 (E) 20

(A) 37 (B) 39 (C) 41 (D) 74 (E) 78 SAT Practice Book

0.0002, then x

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20092009-2010 2010

EQUATIONS 

15. 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.)

(5 2)m 3 4

19. if

6 What is the value of m?

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

16. If tx 5 t 1 x, which of the following must be true? (A) x (B) x (C) t (D) t (E) t

20. if 2 x 4 x 6 x A) -288 B) -2 1 C) 2 1 D) 2 E) 2

4 5 4 5 5x

17. If x = 5 y and y=z+1, what is

x in terms of z ? 5

21. if

(A) z (B) z + 1 (C) 5 z (D) 5 z +1 (E) 5 z 1

18. If x 3 (A) z 4 (B) z 4 (C) z 3 (D) 7z (E) 12z

24, then x=?

1 x 1

1 , What is the value of x? 2

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

3y and y

SAT Practice Book

22.

4z, what is x in terms of z ?

if ( x 5) y x 2 x 13 what is the value of y when x=2?

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20092009-2010 2010

23. if

A) B) C) D) E)

EQUATIONS  x y a b

2 9x 9 y , then 3 10 a 10b

26. If a positive integer n is picked at random from the positive integers less than or equal to 10, what is the probability that 5n+3≤14 ?

?

9 10 20 23 20 27 2 3 3 5

A) 0 1 B) 10 1 C) 5 3 D) 10 2 E) 5

27. If (x -2) 2 =49, then x could be?

24. If 10 + x is 5 more than 10, what is the value of 2x?

(A) -9 (B) -7 (C) 2 (D) 5 (E) 9

(A) -5 (B) 5 (C) 10 (D) 25 (E) 50

28. If (2m)k =6, then mk =?

25. 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) 3 (B) 4 (C) 5 (D) 6 (E) 12

(A) -4 (B) -2 (C) 0 (D) 2 (E) 4

SAT Practice Book

65 44

VARIATIONS 

2009-2010

1. Which of the following tables shows a relationship in which w is directly proportional to x?

3. If xr = v, v = kr, and rv following is equal to k?

0, which of the

(A) 1 1 (B) x (C) x – 1 (D) x (E) x + 1

(A)

(B)

(C)

(D)

(E) 4. If y is directly proportional to x2 and y when x

2. If 5t = 45 and tk = 1, what is the value of k?

when y

1 45 1 (B) 9 1 (C) 5 (D) 5 (E) 9

(A)

SAT Practice Book

1 what is the positive value of x 2 9 ? 2

3 4 3 (B) 2 9 (C) 4 (D) 3 (E) 9

(A)

66 11

1 8

20092009-2010 2010

VARIATIONS 

5. If y is inversely proportional to x and y = 15 when x = 5, what is the value of y when x = 25?

7. If y is directly proportional to x and if y = 20 when x = 6, what is the value of y when x = 9?

1 5 1 (B) 3 (C) 3 (D) 5 (E) 75

10 3 40 (B) 3 (C) 23 (D) 27 (E) 30

(A)

(A)

6. If r is directly proportional to s and if s = when r = s=

what is the value of r when

4 ? 9

SAT Practice Book

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2009-2010

INEQUALITIES & ABSOLUTE VALUE

1. If rstv = 1 and stuv = 0, which of the following must be true?

4. If x is an integer greater than 1 and if 1 , which of the following must y x x be true?

(A) r < 1 (B) s < 1 1 (C) t > 2 (D) u = 0 (E) v = 0

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 2x < y < 0, which of the following is greatest? 5. 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 7 1 11 and 12 If machine B accepts a 8 8 bottle containing n fluid ounces, which of the following describes all possible values of n ?

(A) –2x (B) –(2x + y) (C) 2x (D) 0 (E) –y

(A) n 12 (B) n 12

3. If 3b + 1 < 10, which of the following CANNOT be the value of b?

(C) n 12

(A) –1 (B) 0 (C) 1 (D) 2 (E) 3

SAT Practice Book

(D) n 12 (E) n 12

1 8 1 8 1 8 1 8 1 8

68 11

20092009-2010 2010 6.

INEQUALITIES & ABSOLUTE VALUE  3x 2

(3x) 2

9.

For what value of x is the statement above FALSE?

10 k

3

k 5

8

What is the value of k that satisfies both equations above?

(A) –3 (B) 0 1 (C) 3 (D) 1 (E) For no value of x

7. For how many ordered pairs of positive integers (x, y) is 2x + 3y < 6?

10. A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. Which of the following inequalities can be used to determine whether or not a child’s height h satisfies the regulation for this ride?

(A) One (B) Two (C) Three (D) Five (E) Seven

8. If x and y are positive consecutive odd integers, where y > x, which of the following is y2 – x2?

(A) h 10

50

(B) h 20

40

(C) h 30

20

(D) h 40

10

(E) h 45

5

(A) 2x (B) 4x (C) 2x + 2 (D) 2x + 4 (E) 4x + 4

SAT Practice Book

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20092009-2010 2010

INEQUALITIES & ABSOLUTE VALUE 

11. If 0 < x < 1, which of the following statements must be true?

13. If 0 < n < 1, which of the following gives the correct ordering of n , n, and n2 ?

I. x2 > x3 x II. x > 2 III. x> x3

(A) n < n < n2 (B) n < n2 < n (C) n < n < n2 (D) n < n2 < n (E) n2 < n < n

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

14. 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 12.

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| ?

15. If x + y = 30 and x > 8, then which of the following must be true? (A) y > 0 (B) y < 22 (C) y = 22 (D) y > 22 (E) x < 30

(A) t (B) w (C) x (D) y (E) z

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INEQUALITIES & ABSOLUTE VALUE 

16.

19. If 4x = 6u = 5v = 7w > 0, which of the following is true? (A) x < v < u < w (B) x < u < v < w (C) x < v < w < u (D) w < u < v < x (E) u < v < w < x

On the number line above, which of the following corresponds to u w ? (A) t (B) v (C) x (D) y (E) z

17.

m 3

5

k 7

15

20. If x = –1 and k > 0, which of the following has the greatest value? (A) 2kx (B) 4kx2 (C) 6kx3 (D) 8kx4 (E) l0kx5

In the equations above, m < 0 and k < 0. What is the value of m – k? (A) –24 (B) –14 (C) 8 (D) 16 (E) 20

18. If k(2x + 3)(x – 1) = 0 and x > 1, what is the value of k? (A)

3 2

(B) 0 2 (C) 3 (D) 1 (E) 2

SAT Practice Book

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INEQUALITIES & ABSOLUTE VALUE

2009-2010

1. If 2 x

3 , which of the following is a

1 1 1 1 1 1 then x could be 6 7 8 x 7 8 which of the following?

4. If

possible value of x? (A) 4 (B) 5 {C) 6 (D) 7 (E) 8

(A) 3 (B) 4 {C) 5 (D) 6 (E) 7

2. If a>b>0, which of the following is greater a than ? b (A) 1 b (B) a 1 (C) a b a (D) 2b 2a (E) b

5. If m>0, then m 2

3. If -9 < x 9 (C) x < 9 (D) x

2 >7

(E) x

9 0 (B) b < 25 (C) b = 25 (D) b > 25 (E) b < 40

8.

if x>0, then x

(A) a 5 II. p > 5

(A) 0 (B) 1 {C) x (D) x 2 (E) x 1

III. p 3 > 5 (A) II only (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III

9. If k is a positive integer divisible by 7, and if k < 90, what is the greatest possible value of k ?

12. t 3 =4

(A) 83 (B) 84 (C) 87 (D) 88 (E) 89

(A) None (B) One (C) Two (D) Four (E) More than four

SAT Practice Book

For how many values of t is the equation above true?

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20092009-2010 2010

INEQUALITIES & ABSOLUTE VALUE  14.

13. Which of the following inequalities is true about the lengths a and b of the sides of the triangle above? (A) 0≤(a+b) 2 0, what is the value of ? k 3 16 1 (B) 3 3 (C) 4 (D) 3 16 (E) 3

(A)

SAT Practice Book

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INEQUALITIES & ABSOLUTE VALUE 

16. Marcus can spend no more than $120 on jeans and shirts for school. He buys 3 pairs of jeans at $32 each. If x represents the dollar amount he can spend on shirts, which of the following inequalities could be used to determine the possible values for x ? (A) (3) (B) (3) (C) (3) (D) (3) (E) x

19 . If x and y are integers, 7