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
WORD PROBLEMS
2009- 2010
2009-2010
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 of h+
64
2
v feet. If the object is thrown upward from a height of 6 feet with an initial velocity of 32 feet per second, what will be its maximum height, in feet?
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.)
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? (A) Two (B) Four (C) Five (D) Six (E) Ten
15. 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
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?
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?
WORD PROBLEMS
2009- 2010
2009-2010
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?
FACTORING
2009-2010 1. If a + 2(x + 1) = s, what is x + 1, in terms of s and a? (A) a s 2 (B) 2 a s (C) 2 a s (D) s a 2 (E) s a 22. If x2+y2 = 73 and xy = 24, what is the value of (x + y)2? (A) 73 (B) 97 (C) 100 (D) 121 (E) 144 3. If 2 1 2 1 ) ( ) (a b a b , which of the following must be true?
(A) b = 0 (B) a + b = 1 (C) a – b = 1 (D) a2 + b2 = 1 (E) a2 – b2 = 1 4. If x2 – y2 = 77 and x + y = 11, what is the value of x? (A) 10 (B) 9 (C) 8 (D) 7 (E) 6
5. 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
6. If (2x – 2)(2 – x) = 0, what are all the
possible values of x? (A) 0 only (B) 1 only (C) 2 only (D) 1 and 2 only (E) 0, 1, and 2
FACTORING
2009- 2010
2009-2010
7. If a and b are positive integers and
a2 – b2 = 7, what is the value of a? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7
8. If x2 – y2 = 10 and x + y = 5, what is the
value of x – y? 9. If xy = 7 and x – y = 5, then x2y – xy2 =? (A) 2 (B) 12 (C) 24 (D) 35 (E) 70 10. If 2x + z = 2y and 2x + 2y + z = 20,
what is the value of y? (A) 5
(B) 8 (C) 10 (D) 15
(E) It cannot be determined from the information given. 11. if d cx bx ax x x x3 2 3 2 90 1 30 1 10 1
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? (A) 0 (B) 2 (C) 3 (D) 7 (E) 14
FACTORING
2009- 2010 2009-2010 13. If 2x − 64 = 0, which of the following could be a value of x? (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? (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 2 2 y x ? (A) 0 (B) 9 (C) 18 (D) 81 (E) 162 16. If (x+5) y= 2
x −x+13, what is the value of y When x = 2?
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.
18. If x2+x=30, which of the following is a possible value of x2 x? (A) -30 (B) 10 (C) 20 (D) 30 (E) 870