---------------------------------------------------------------------------------------------------------------------- Q2:
If n is a positive integer and the product of all the integers from 1 to n, inclusive, is divisible by 990, what is the least possible value of n?
A.8
B.9
C.10
D.11
E.12
Answer:
---------------------------------------------------------------------------------------------------------------------- Q3:
What is the remainder when the positive integer n is divided by 2?
(1) When n is divided by 5, the remainder is an odd integer.
(2) When n is divided by 10, the remainder is an odd integer.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q4:
What is the hundreds digit of the integer z?
(1) 10z = 93,120
(2) z rounded to the nearest hundred is 9,300.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q5:
The interior of a rectangular carton is designed by a certain
manufacturer to have a volume of x cubic feet and a ratio of length to
width to height of 3:2:2. In terms of x, which of the following equals
the height of the carton, in feet?
A. 3√x
B. 3√[(2x)/3]
C. 3√[(3x)/2]
D. (2/3) 3√x
E. (3/2) 3√x
Answer:
---------------------------------------------------------------------------------------------------------------------- Q6:
Leo can buy a certain computer for p1 dollars in State A, where the sales tax is t1 percent, or he can buy the same computer for p2 dollars in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in State A than in State B?
(1) t1 > t2
(2) p1t1 > p2t2
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q7:
Last year, 36 houses in a certain development had roof repairs and 48 houses were repainted. If 20 houses in the development had roof repairs but were not repainted last year, how many houses were repainted but did not have roof repairs?
A. 12
B. 16
C. 20
D. 28
E. 32
Answer:
---------------------------------------------------------------------------------------------------------------------- Q8:
Which of the following is equal to [1/(√3-√2)]2?
A. 1
B. 5
C.√6
D. 5 - √6
E. 5 + 2√6
Answer:
---------------------------------------------------------------------------------------------------------------------- Q9:
If n and t are positive integers, is n a factor of t?
(1) n = 3n-z
(2) t = 3n
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q10:
On a certain date, Hannah invested $5,000 at x percent simple annual interest and a different amount at y percent simple annual interest. What amount did Hannah invest at y percent simple annual interest?
(1) The total amount of interest earned by Hannah’s due investments in one year was $900.
(2) Hannah invested the $5,000 at 6 percent simple annual interest.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q11:
??
???
????
?????
?????
1 2 3 4
The figure shown represents a board with 4 rows of pegs, and at the
bottom of the board are 4 cells numbered 1 to 4. Whenever the ball
shown passes through the opening between two adjacent pegs in the
same row, it will hit the peg directly beneath the opening. The ball
then has the probability 1/2 of passing through the opening
immediately to the left of that peg and probability 1/2 of passing
through the opening immediately to the right. What is the probability
that when the ball passes through the first two pegs at the top it will
end in Cell 2?
A. 1/16
B. 1/8
C. 1/4
D. 3/8
E. 1/2
Answer:
---------------------------------------------------------------------------------------------------------------------- Q12:
A can manufacturing company has 5 identical machines, each of which produces cans at the same constant rate. How many cans will all 5 machines produce running simultaneously for z hours?
(1) Running simultaneously, 3 of the machines produce 72,000 cans in 2z hours.
(2) Running simultaneously, 2 of the machines produce 24,000 cans in z hours.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q13:
What is the value of xy?
(1) 2(x+y) = 4
(2) 2(x+3y) = 16
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q14:
The function f is defined by f(x) = - 1/x for all nonzero numbers x. If f(a) = - 1/2 and f(ab) = 1/6, then b =
A. 3
B.1/3
C.- 1/3
D.-3
E.-12
Answer:
---------------------------------------------------------------------------------------------------------------------- Q15:
Is xy > x/y?
(1) xy > 0
(2) y < 0
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q16:
Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
A.75%
B.80%
C.100%
D.120%
E.125%
Answer:
---------------------------------------------------------------------------------------------------------------------- Q17:
Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
A.24
B.30
C.60
D.90
E.120
Answer:
---------------------------------------------------------------------------------------------------------------------- Q18:
If xy ≠ 0 and x2y2– xy = 6, which of the following could be y in terms of x?
I.1/(2x)
II.– 2/x
III.3/x
A. I only
B. II only
C. I and II
D. I and III
E. II and III
Answer:
---------------------------------------------------------------------------------------------------------------------- Q19:
If y is an integer and y =∣x∣ + x, is y = 0?
(1) x < 0
(2) y < 1
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q20:
y°
x°
z°
In the figure shown, what is the value of x?
(1) y = x
(2) z = x
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
----------------------------------------------------------------------------------------------------------------------
Q22:
If x is negative, is x < -3?
(1) x2 > 9
(2) x3 < -9
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q23:
If k = -1, which of the following is (are) true?
I. k k = k
II.∣k∣ = -k
III.k0 = -k
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
Answer:
---------------------------------------------------------------------------------------------------------------------- Q24:
A certain computer program generates a sequence of numbers a1, a2, … , an such that a1 = a2 = 1 and a k = a k-1 + 2a k-2 for all integers k such that 3 ≤ k ≤ n. If n > 6, then a7 = ?
A. 32
B. 43
C. 64
D. 100
E. 128
Answer:
---------------------------------------------------------------------------------------------------------------------- Q25:
If n is an integer greater than 6, which of the following must be divisible by 3?
A. n (n+1) (n-4)
B. n (n+2) (n-1)
C. n (n+3) (n-5)
D. n (n+4) (n-2)
E. n (n+5) (n-6)
Answer:
---------------------------------------------------------------------------------------------------------------------- Q26:
If n is a positive integer that is less than 10, what is the value of n?
(1) n is the tenth digit in the decimal representation of 1/n.
(2) n is the hundredth digit in the decimal representation of 1/n.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q28:
At a monthly meeting, 2/5 of the attendees were males and 7/8 of the male attendees arrived on time. If 9/10 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
A. 11/100
B. 3/25
C. 7/50
D. 3/20
E. 4/25
Answer:
---------------------------------------------------------------------------------------------------------------------- Q29:
In the coordinate plane, a circle has center (2, -3) and passes through the point (5, 0). What is the area of the circle?
A. 3π
B. 3√2 π
C. 3√3 π
D. 9π
E. 18π
Answer:
---------------------------------------------------------------------------------------------------------------------- Q34:
What is the median number of employees assigned per project for the projects at Company Z?
(1) 25 percent of the projects at Company Z have 4 or more employees assigned to each
project.
(2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each
project.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q35:
p is an integer; n is an integer; and p/n is an integer. Is p/n odd?
(1) p is divisible by 4.
(2) n is divisible by 4.
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- Q36:
What is the value of the integer N?
(1) 101 < N < 103
(2) 202 < 2N < 206
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 TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Answer:
---------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------