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How many multiples of 3 are there from 1 to 100 which are not multiples of 2?

  • A.17
  • B.21
  • C.34
  • D.22

Answer: A

There are 17 such numbers.

Multiples of 3 from 1 to 100: \(\lfloor 100/3 \rfloor = 33\). Those that are also multiples of 2 are the multiples of 6: \(\lfloor 100/6 \rfloor = 16\).

\[ 33 - 16 = 17 \]

These are the odd multiples of 3: 3, 9, 15, ..., 99. 34 is roughly double, and 21 and 22 fit no step.

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