Let N be a positive integer not equal to 1 . Then, none of the numbers 2 , 3 , … . , N is a divisor of ( N ! - 1 ) . Thus, we can conclude that:

The smallest number between N and N ! , which is a divisor of ( N ! + 1 ) , is a prime number

At least, one of the numbers ( N + 1 ) , ( N + 2 ) , … , ( N ! - 2 ) is a divisor of ( N ! - 1 )

None of the foregoing statements is necessarily correct

E M B I B E

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

EASY

CAT

IMPORTANT

Earn 100

Let p, q, and s be integers such that $p^{2} = {sq}^{2}$ . Then, it follows that:

50% studentsanswered this correctly

Important Questions on Numbers and Their Properties

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:

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 3

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is

HARD

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 4

If

5^{x} - 3^{y} = 13438 and 5^{x - 1} + 3^{y + 1} = 9686

, then

x + y

equals

MEDIUM

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 5

How many factors of

2^{4} \times 3^{5} \times 10^{4}

are perfect squares that are greater than

1

?

EASY

CAT

IMPORTANT

Quantitative Aptitude for the CAT>Chapter 1 - Numbers and Their Properties>Practice Exercises>Q 6

While multiplying three real numbers, Ashok took one of the numbers as

73

instead of

37

. As a result, the product went up by

720

. Then the minimum possible value of the sum of squares of the other two numbers 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?