Count of Numbers Satisfying Conditions

CAT 2000 Slot 1 · QA · Medium · Number Systems

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Let SS be the set of integers xx such that: I. 100≤x≤200100 \le x \le 200, II. xx is odd and III. xx is divisible by 3 but not by 7.

How many elements does SS contain?

  1. A.

    16

  2. B.

    12

  3. C.

    11

  4. D.

    13

Answer

D

Explanation

Integers between 100 and 200 divisible by 3 are 33 numbers. Odd numbers divisible by 3 in this range: 105,111,…,195105, 111, \dots, 195. This forms an AP with a=105,d=6,Tn=195  ⟹  n=16a = 105, d = 6, T_n = 195 \implies n = 16. Among these, odd multiples of 21 (3×73 \times 7) in the range are 105,147,189105, 147, 189 (3 numbers). Subtracting these gives 16−3=1316 - 3 = 13 elements.

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