#1 Quiz 15 Hard Quant Questions

Q #1



AB = DE, BC = CD, BE is parallel to CD, and BC is parallel to DF.

Quantity A	Quantity B
The area of triangle ABE	The area of quadrilateral BCDF

Q #2



In the semicircle above, the length of arc AC is equal to the length of arc BD, and the length of arc AB is less than the length of arc BD.

Quantity A	Quantity B
\(\frac{\text{the length of chord AB}}{\text{the length of chord CD}}\)	\(\frac{1}{2}\)

Q #3


Four people each roll a fair die once.

Quantity A	Quantity B
The probability that at least two people will roll the same number	70%

Q #4

In a group of 200 workers, 10% of the males smoke, and 49% of the females smoke.

Quantity A	Quantity B
Total number of workers who smoke	59

Q #5


Set A consists of 350 consecutive multiples of 2.

Set B consists of 200 consecutive multiples of 3.

The median of Set A is 199.5 greater than the median of Set B.

Quantity A	Quantity B
The \(30^{th}\) percentile of Set A	The \(70^{th}\) percentile of Set B

Q #6


Each of 100 balls has an integer value from 1 to 8, inclusive, painted on the surface. The number \(Nx\) of balls representing integer x is defined by the formula \(Nx = 18 –(x – 4)^2\).

What is the interquartile range of the 100 integers?

(A) 1.5

(B) 2.0

(C) 2.5

(D) 3.0

(E) 3.5





Q #7


The two lines are tangent to the circle. If \(AC = 10\) and \(AB = 10 \sqrt{3}\), what is the area of the circle?

A) \(100 \pi\)

B) \(150 \pi\)

C) \(200 \pi\)

D) \(250 \pi\)

E) \(300 \pi\)






Q #8


If 0 < y < x, then which of the following is a possible value of \(\frac{27x + 23y}{3x + 2y}\)?

I. 8.7
II. 9.2
III. 10.8

A) I only
B) II only
C) III only
D) I and II only
E) II and III only




Q #9


When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y?

I. 15.15
II. 18.16
III. 17.17

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only





Q #10

A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 5 is

A. 3

B. 7

C. 21

D. 27

E. 189





Q #11



Hannah attended some college and earns 20% more than the average person in her educational category. After she earns her degree, she’ll earn the average weekly salary for bachelor’s degree holders. Hannah will spend $ 6,000 in tuition and take a 50% pay cut for 30 weeks to earn the degree. After she gets her degree, for how many weeks will she need to work to recoup her lost wages and tuition using the extra money she will earn weekly?

weeks




Q #12


A box contains 1 blue ball, 1 green ball, 1 yellow ball, and 2 red balls.
Three balls are randomly selected (one after the other) without replacement.
What is the probability that the 2nd ball is NOT red and the 3rd ball is yellow?

Express your answer as a fraction.





Q #13


The integer a is greater than 1 and is not equal to the square of an integer. Which of the following answer choices could potentially be equal to the square of an integer?

Indicate all that apply.

❑ \(\sqrt{a}\)

❑ \(a^2\) \(- 1\)

❑ \(a^2\) \(+ 1\)

❑ \(a^2\) \(- a\)

❑ \(a^2\) \(- 2a + 1\)

❑ \(2a\)






Q #14


A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for two hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance between the two cities?

A.48

B.72

C.96

D.120

E. 192





Q #15

How many positive integers less than 10,000 are such that the product of their digits is 210?

A. 24

B. 30

C. 48

D. 54

E. 72