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CAT 2005 — QA Question 25

Number TheoryEasy

Let S be a set of positive integers such that every element n of S satisfies the conditions   

a. 1000 ≤ n ≤ 1200
b. every digit in n is odd

Then how many elements of S are divisible by 3?

Answer & solution

Correct answer: 9

  • 9

  • B

    10

  • C

    11

  • D

    12

Solution

n will be of the form 11ab, where a and b are odd numbers.

We are looking for all n’s divisible by 3.

∴ 1 + 1 + a + b = 3 or 6 or 9 or 12 or 15 or 18

∴ a + b = 1 or 4 or 7 or 10 or 13 or 16

∴ a + b = 1 or 7 or 13 is not possible as the sum of two odd numbers cannot be odd.

∴ (a, b) = (1, 3), (3, 1), (1, 9), (3, 7), (5, 5), (7, 3), (9, 1), (7, 9), (9, 7)

∴ 9 elements of S are divisible by 3.

Hence, option (a).

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CAT 2005 QA Q25: Let S be a set of positive integers such that every element n of S satisfies the conditions a. 1000 ≤ n &le — Solution | TheCATExam