Quantitative Aptitude Test

Result

Quantitative Aptitude Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n −1)(n − 2)...3.2.1 is not divisible by n is

A
5

B
7

C
13

D
14

Solution

From 12 to 40 there are 7 prime numbers i.e., 13,17,19,23,29,31 and 37 such that (n - 1) is not divisible by any of them.
Question 2
1 / -0

The 288th term of the series a,b,b,c,c,c,d,d,d,d,e,e,e,e,e,f,f,f,f,f,f is

A
U

B
V

C
W

D
X

Solution
Question 3
1 / -0

In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90° . If AB : CD = 3 : 1, the ratio of CD : PQ is

A
1 : 0.69

B
1 : 0.75

C
1 : 0.72

D
1 : 0.88

Solution
Question 4
1 / -0

If three positive real numbers x, y and z satisfy y ⁄ x = z ⁄ y and x y z = 4, then what is the minimum possible value of y?

A
2^1/3

B
2^2/3

C
2^1/4

D
2^3/4

Solution
Question 5
1 / -0

Let A and B be two solid spheres such that the surface area of B is 300% higher than the surface area of A. The volume of A is found to be k% lower than the volume of B. The value of k must be

A
85.5

B
92.5

C
90.5

D
87.5

Solution
Question 6
1 / -0

Let T be the set of integers {3, 11, 19, 27, 451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

A
32

B
28

C
29

D
30
Question 7
1 / -0

What is the remainder when \(4^{96}\) is divided by \(6 ?\)

A
\(0\)

B
\(2\)

C
\(3\)

D
\(4\)

Solution

\(\frac{4^{96}}{6},\) we can write it in this form

\(\frac{(6-2)^{96}}{6}\)

Now, remainder will depend only the powers of \(-2 .\) So,

\(\frac{(-2)^{96}}{6},\) it is same as

\(\frac{\left([-2]^{4}\right)^{24}}{6},\) it is same as

\(\frac{(16)^{24}}{6}\)

Now, \(\frac{(16 \times 16 \times 16 \times 16 \ldots \ldots 24 \text { times })}{6}\)

On dividing individually 16 we always get a remainder \(4 .\) \(\frac{(4 \times 4 \times 4 \times 4 \ldots \ldots 24 \text { times })}{6}\)

Hence, required remainder \(=4\)

NOTE: When \(4\) has an even number of powers, it will always give remainder \(4\) on dividing by \(6 .\)
Question 8
1 / -0

There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required?

A
72

B
90

C
96

D
144

Solution
Question 9
1 / -0

A test has 50 questions. A student scores 1 mark for a correct answer, 1/3 for a wrong answer, and 1/6 for not attempting a question. If the net score of a student is 32, the number of questions answered wrongly by that student cannot be less than

A
6

B
12

C
3

D
9

Solution
Question 10
1 / -0

Students of two different sections of a school appeared for a test. The average score of the students of the 1 st section is 65 and the average score of boys and girls of the 1st section are 68 and 64 respectively. For the 2 nd section: the average score of the section is 71;the average scores of the boys and girls are also 80 and 65 respectively. It number of girls in 2 nd section is half the number of boys in the 1 stsection then the average score of the students of the two sections together is

A
67.7

B
66.6

C
69.2

D
66