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
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? (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