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Quantitative
Section 18 (20 Minutes, 16 Questions)
Directions: You have 20 minutes to answer the following
16 questions. Solve each problem and decide which is the best of the choices
given. Fill in the corresponding circle on the answer sheet. You may use
any available space for scratch work.
Notes:
1. The use of a calculator is permitted.
2. All numbers used are real numbers.
3. Figures that accompany problems in this test are intended to provide
valuable information useful in solving the problems. They are drawn as
accurately as possible EXCEPT when it is stated in a specific problem
that the figure is not drawn to scale. All figures lie in a plane unless
otherwise indicated.
4. Unless otherwise specified, the domain of any function f is assumed
to be the set of all real numbers x for which f (x) is a real number.
Reference Information:
1. Circles. Area = r2, Circumference = 2 r
2. Rectangles: Area = Length X Width
3. Right Triangles: Area = ½ (Base) (Height)
4. Cubes: Volume = Length x Width x Height
5. Cylinders: Volume = r2 h
6. Pythagorean Theorem: for right triangles c2 = a2 + b2
1. The Ice View Highway, which links City A and City B, provides two rest
areas every twelve miles. How many rest areas would a car pass if it traveled
one-half of the 4,356 miles of Ice View Highway, starting at the origin
of the highway?
a. 182
b. 356
c. 363
d. 726
e. 789
2. Seventy-five freshmen have signed up for extracurricular activities.
Fifty sign up for cheerleading. Thirty sign up for the yearbook staff.
Eleven sign up for both cheerleading and the yearbook staff. How many
of the seventy-five freshman have signed up for NEITHER cheerleading nor
the yearbook staff?
a. 3
b. 6
c. 8
d. 16
e. 18
3. Dan brought his car to the mechanic to have his engine fixed. The mechanic
quoted him the following prices for parts: $350 for a new alternator,
$150 for the battery and $25 for miscellaneous parts. Assuming that the
minimal charge for labor is $45 per hour (rounded to the nearest half-hour)
and that the shop can complete all repairs in 3.5 hours, what is the minimum
amount that Dan will have to pay to have his car fixed?
a. $157.50
b. $525.00
c. $682.50
d. $705.00
e. $727.50
4. In a large lecture hall containing 540 female students, 27 were on
birth control pills, 110 were taking antibiotics, and 220 were taking
antihistamines. The remaining 183 students were not taking any medication.
In simplest terms, what is the ratio of female students taking birth control
pills to the total number of students in the lecture hall?
a. 1: 100
b. 1 : 193
c. 1: 27
d. 1 : 20
e. 1 : 5
5. Triangles with equal angles and equal sides are called
a. Similar triangles
b. Congruent triangles
c. Scalene triangles
d. Isosceles triangles
e. Equilateral triangles
6. If the length of a square is increased by 3 inches, but 3 inches are
subtracted from its width, what is the overall effect on the area of the
new rectangle?
a. It is 9 square
inches smaller than the square
b. It is 33% smaller than the square
c. It is the same area as the square
d. It is 33% larger than the square
e. It cannot be determined from the information given.
7. In the xy-plane, a circle is centered at the origin and passes through
the point (-7,0). What is the area of the circle?
a. 49/
b. 3.5
c. 7
d. 49
e. 81
8. If f (a) = a2 - 4a + 3, what is f(-1) ?
a. -2
b. 0
c. 7
d. 8
e. 9
9. What is the mean of the following set of numbers? 44, 33, 58, 22, 16,
66
a. 35.8
b. 38.5
c. 38.9
d. 39.8
e. 39.9
10. If it takes 12 people to serve 500 meals at the soup kitchen, how
many people will be required to serve 14,280 meals?
a. 29
b. 290
c. 343
d. 1190
e. 11,900
11. 23/42 - 35/84 =
a. -12/84
b. -11/84
c. 11/84
d. 12/84
e. 12/42
12. For the repeating decimal 0.04321043210432104321….., what is
the 49th digit to the right of the decimal point?
a. 0
b. 1
c. 2
d. 3
e. 4
13. For a graduation gift, Sally's mother offered to buy her three CDs
from her list of seven favorites. How many different combinations does
Sally have to choose from?
a. 21
b. 42
c. 840
d. 1764
e. 2520
14. If p =3 and q is 2, what is (9p)(27q) =
a. 39
b. 314
c. (729)2
d. 6561 x 2
e. 95
15. If m (8)(10)(12)(14)= (4)(5)(6)(7), what is the value of m?
a. 1/16
b. 1/8
c. ½
d. 8
e. 16
16. Which of the following are the solutions to the following equation?
x2 + 3x - 18= 0
a. -2, 9
b. 2, -9
c. -3, 6
d. 3, -6
e. 3, -9
STOP
The
answers to these questions are presented in Section
QA18
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