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Numbers - miscellaneous applications || Quantitative Aptitude || CAT 2021 || 17 April (App update required to attempt this test)

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Question 1

For an odd positive integer n, satisfying 51 ≤ n ≤ 99, the quantity n³ − n is always divisible by (TITA)

Question 2

The number of prime factors of A is seven times the number of prime factors of B . If B has a total of 64 factors, what can be the maximum possible number of prime factors of A?

Question 3

Rupali added the first n natural numbers. However, he added one of the numbers twice, by mistake, and obtained the sum as 2^3k+1(5) and k is also a natural number greater than 2 .The sum which Rupali got was a 3-digit number. Find the number that was added twice.

Question 4

If (x² + 1)/(x – 1)³ = A/(x – 1)³ + B/(x – 1)² + C/(x – 1), the value of A, B, C in this order are

Question 5

Two distinct positive odd integers m and n have their highest common factor as 2ⁿ – 1 where n is an integer and the difference of HCF and n should be smallest composite number. What is the possible highest common factor of the sum and the difference of m and n?

Question 6

A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?

Question 7

Suppose, the seed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
=seed(s(n)), otherwise,
Where s(n) indicates the sum of digits of n.
For example, Seed (7)= 7, seed(248)=seed(2+4+8)= seed(1+4)=seed (5)=5 etc.
How many positive integers n such that n<500, will have seed (n)=9?

Question 8

Direction: A manufacturing unit can produce one or more of the commodities A, B and C. If x units of A, y units of B and x units of C are produced then the cost of production is x + y + z (in rupees) while the net profit equals f(x, y, z) (in Rupees). A total amount of Rs. 30000 is available to cover the cost of production.

If f(x, y, z) = x + 2y + 3z then the maximum possible profit (in Rupees) is

Question 9

If f(x, y, z) = √(xyz) the maximum possible profit (in Rupees) is

Question 10

Let X be a two digit number such that both X and X² end with the same digit and none of the digits in X equals zero. When the digits of X are written in the reversed order, the square of the new number so obtained has last digit as 6 and is less than 3000. Then the number of distinct possibilities for X is given by

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CAT & MBA Quantitative Aptitude

Apr 17CAT & MBA