CAT 2003 Slot 1QA Question 49

Number TheoryEasy
Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

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

Answer & solution

  • A

    5

  • 7

  • C

    13

  • D

    14

Solution

For (n − 1)(n − 2) … 3.2.1 to not be divisible by n, n should be a prime number.

But, there are 7 prime numbers in the range 12 ≤ n ≤ 40 are 7.

The prime numbers are 13, 17, 19, 23, 29, 31, 37.

Hence, option (b).

CAT 2003 Slot 1 QA Q49: The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n − 1)(n − — Solution | TheCATExam