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# Quantitative Aptitude || Super Quiz 19 || 2018-19 (App update required to attempt this test)

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Question 1

The sum of the cubes of the digits of the 3-digit positive number is 1136. The sum of the two in the unit’s and the ten’s place of the number is four times the digit in the hundred’s place. Further, when the digit of the number is written in the reverse order, the new number thus formed is 297 more than the original number. Find the number.

Question 2

(p, q, r, s) is a set of positive integers satisfying all 3 equations:

p

r

r-p = 64

What is the value of p+r?

p

^{3}= q^{2}r

^{3}= s^{2}r-p = 64

What is the value of p+r?

Question 3

The population of Wasseypur doubles in 50 years. In how many years would it become three-times if the rate of increase is proportional to the number of inhabitants?

Question 4

For a real number p, let [p] denote the greatest integer less than or equal to p. The number of solutions of |2p-[p]| = 4 is

Question 5

What can be the maximum value of |x-1| if |x

^{2}-4| ≤ 5?Question 6

The number of solution/s for the inequalities. ω, x, y,z all are real.

ω-x

x-y

y-z

z- ω

ω-x

^{2}≥ 1/4,x-y

^{2}≥ 1/4,y-z

^{2}≥ 1/4,z- ω

^{2}≥ 1/4 isQuestion 7

What can be the maximum number of points in a circle of radius 1 unit such that the distance between any two of these points is at least 1?

Question 8

If a,b,c be real numbers such that a + b + c < 0 and the equation ax

^{2}+ bx + c = 0 has imaginary roots, thenQuestion 9

The area of a regular polygon of 12 sides that can be inscribed in the circle x

^{2}+ y^{2}-6x + 5 = 0 isQuestion 10

The number of triples (x,y,z) of positive integers satisfying 2

^{x}-5^{y}7^{z}= 1 isQuestion 11

Consider the sequence x

_{1}= 24^{1/3}, x_{2}= (24^{1/3}+24)^{1/3}and x_{n+1}= (x_{n}+24)^{1/3}, where n≥1. Then the integer part of x_{50}equalsQuestion 12

Consider a sequence of 10 Xs and 8 Ys placed in a row. By a run we mean one or more letters of the same type placed side by side. E.g., an arrangement of 10 Xs and 8 Ys which contains 4 runs of Xs 3 runs of Ys is given below:

XXXYYYXXXXYYYXXYYX

In how many ways can 10 Xs and 8 Ys be arranged in a row such that there are 4 runs of Xs and 4 runs of Ys ?

XXXYYYXXXXYYYXXYYX

In how many ways can 10 Xs and 8 Ys be arranged in a row such that there are 4 runs of Xs and 4 runs of Ys ?

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Oct 13CAT & MBA

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Vijay JhaMember since Sep 2018

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