Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 56

EASY

CAT

IMPORTANT

Earn 100

How many numbers less than or equal to $500$ are there, each of which is the product of more than three distinct prime numbers?

50% studentsanswered this correctly

Important Questions on Numbers and Their Properties

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CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 57

How many numbers below

100

can be expressed as a difference of two perfect squares in only one way?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 58

The LCM of the two quotients obtained when two numbers a and b are divided by their HCF is

77

. LCM of another pair of quotients, when other two numbers c and d have the same HCF as that of a and b, and when divided by it is

221

. Which of the following could be the ratio of the sum of a and b to that of the difference between c and d?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 59

Let p, q, and s be integers such that

p^{2} = {sq}^{2}

. Then, it follows that:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 60

Let N be a positive integer not equal to

1

. Then, none of the numbers

2, 3, \dots ., N

is a divisor of

(N! - 1)

. Thus, we can conclude that:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 1

The product of two positive numbers is

616

. If the ratio of the difference of their cubes to the cube of their difference is

157 : 3

, then the sum of the two numbers is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 2

If m and n are integers such that

(\sqrt{2})^{19} \times 3^{4} \times 4^{2} \times 9^{m} \times 8^{n} = 3^{n} \times 16^{m} \times (\sqrt[4]{64})

then m is:

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 7

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 8

If the sum of squares of two numbers is

97

, then which one of the following cannot be their product?