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CAT 2003 Slot 1 — QA Question 18

Number TheoryEasy

How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine?

Answer & solution

Correct answer: 39

  • A

    40

  • B

    37

  • 39

  • D

    38

Solution

Number of even integers satisfying inequality i.e. 100 ≤ n ≤ 200 = 51

Total even integers divisible by 7 = 112, 126, 140, 154, 168, 182, 196 = 7

Total even integers divisible by 9 = 108, 126, 144, 162, 180, 198 = 6

The number 126 is repeated in both the sets.

∴ Total number of positive even numbers between 100 and 200 which are either divisible by 7 or 9 = 7 + 6 − 1 = 12

∴ Total number of positive even numbers between 100 and 200 which are divisible neither by 7 nor by 9 = 51 − 12 = 39

Hence, option (c).

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CAT 2003 Slot 1 QA Q18: How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine? — Solution | TheCATExam