TIME —25 MINUTES 20 QUESTIONS DIRECTIONS
SECTION 4
Time —25 minutes
20 Questions
Directions: Each of the data sufficiency problems below consists of a question and two statements, labeled (1) and (2), in which certain
data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data
given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of
counterclockwise), you are to fill in oval
A if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question
asked;
B if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question
C if BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER
statement ALONE is sufficient;
D if EACH statement ALONE is sufficient to answer the question asked;
E if statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional
data specific to the problem are needed.
Numbers: All numbers used are real numbers.
Figures: A figure in a data sufficiency problem will conform to the information given in
the question, but will not necessarily conform to the additional information given
in statements (1) and (2).
You may assume that lines shown as straight are straight and that angle measures are greater than zero.
You may assume that the positions of points, angles, regions, etc., exist in the order shown.
All figures lie in a plane unless otherwise indicated.
Note: In questions that ask for the value of a quantity, the data given in the statements are
sufficient only when it is possible to determine exactly one numerical value for
the quantity.
Example:
In ∆PQR, what is the value of x?
P
x◦
Q y◦ z◦ R
(1)
PQ = PR
(2)
y = 40
Explanation: According to statement (1), PQ = PR; therefore, PQR is isosceles and y = z. Since x + y + z = 180, it follows that x + 2y
= 180. Since statement (1) does not give a value for y, you cannot answer the question using statement (1) alone. According to
statement (2), y = 40; therefore, x + z = 140. Since statement (2) does not give a value for z, you cannot answer the question using
statement (2) alone. Using both statements together, since x + 2y = 180 and the value of y is given, you can find the value of x.
Therefore, the answer is C.
GO ON TO THE NEXT PAGE.
A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are NOT sufficient.
7.
Does x = y?
1.
What is the capacity, in liters, of a certain aquarium?
(1) Three liters is
1
2
of the capacity of the aquarium.
(1)
|
x
|
=
|
y
|
(2) One-half liter is
12
1
of the capacity of the
(2)
x
2
=
y
2
aquarium.
8.
Dan took a 20-question multiple-choice test in
2.
What is the value of n?
psychology. If Dan answered every question, did he
answer at least 12 questions correctly?
(1)
n
=
2
(2)
4
n
=
4
(1) Dan answered fewer than 40 percent of the
questions incorrectly.
(2) Dan answered at least 25 percent of the questions
3. In
∆PQR, what is the measure of angle P?
incorrectly.
(1) Angle Q is a right angle.
(2) The measure of R is 17
˚.
4.
What amount did Jean earn from the commission on
r
her sales in the first half of 1988?
(1) In 1988 Jean’s commission was 5 percent of the
total amount of her sales.
t
(2) The amount of Jean’s sales in the second half of
1988 averaged $10,000 per month more than in
the first half.
9.
The figure above shows the circular cross section of a
5.
A certain car traveled from one town to another
concrete water pipe. If the inside radius of the pipe is
without stopping. What was the car’s average speed
r feet and the outside radius of the pipe is t feet, what
for the trip?
is the value of r?
(1) The car traveled the 90-mile trip in 2 hours.
(1) The ratio of t – r to r is 0.15 and t-r is equal to
(2) The car traveled the first 40 miles of the trip in 1
0.3 foot.
hour.
(2) The area of the concrete in the cross section is
1.29
Π
square feet.
6.
What is the value of x?
15.
If Mark saved an average (arithmetic mean) of $80
11.
Is
3
x
x
+
+
2
8
an integer?
per week for 3 consecutive weeks, how much did he
save the second week?
(1) x is an integer.
(1) The average amount that Mark saved per week
(2) x = 0
for the first 2 weeks was $60.
(2) The amount that Mark saved the first week was
12.
How many people did Apex Company employ in
1
the amount he saved the second week and
2
1990?
1
the amount he saved the third week.
3
(1) The company employed 538 more people in 1991
16. If
p and q are positive integers, what is the value of
than in 1990.
q?
(2) The company employed 20 percent more people
(1)
q
p
−
1
=
1
in 1991 than in 1990.
(2) p = 1
17.
If
x
≠
−
1
, which is greater,
x
1
+
1
or
2
x
?
(1)
x
≥
0
q r s t
(2) x < 3
13.
Of the four numbers represented on the number line
above, is r closest to zero?
18.
In a certain two-digit integer, the ratio of the units
digit to the tens digit is 2 to 3. What is the integer?
(1) q = -s
(2) –t < q
(1) The tens digit is 3 more than the units digit.
(2) The product of the two digits is 54.
14.
Is the integer n divisible by 20?
19.
If Carmen had 12 more tapes, she would have twice
(1) n is divisible by 5
as many tapes as Rafael. Does Carmen have fewer
(2) n is divisible by 6
tapes than Rafael?
(1) Rafael has more than 5 tapes.
(2) Carmen has fewer than 12 tapes.
20.
What is the value of
2
t
t
+
−
t
x
−
x
?
(1)
t
2
−x
t
=
3
(2) t – x = 5
S T O P
IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ON THIS SECTION ONLY.
DO NOT TURN TO ANY OTHER SECTION IN THE TEST.