2009-2010
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? 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
8 117 and
8
121. If machine B accepts a bottle containing n fluid ounces, which of the following describes all possible values of 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?
hedule above, each session is to be 2 11 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?
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 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 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
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?
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 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?
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?
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?
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?
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? minutes and s seconds?
(A) 60m + s
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?
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
WORD PROBLEMS
2009-2010
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?
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 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
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
1of 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?
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?
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?
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 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 the product 35xy is the square of an integer, which of the following could be equal to xy?
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
2009-2010 2009-2010
23. 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
2009-2010
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?
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 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
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)
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?
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 32, the result is 60. What is the number?
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
v2 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?
15. If Marisa drove n miles in t hours, which of the following represents her average speed, in miles per hour?
(A) t
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 following must be true?
(A) b = 0
(E) It cannot be determined from the information given.
11. if 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
FACTORING
2009-2010 2009-2010
13. If x2− 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 x2 y2?
(A) 0 (B) 9 (C) 18 (D) 81 (E) 162
16. If (x+5) y=x2−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