Number Properties Puzzle – Challenge 6

Challenge:

In a children’s game, students count from 1 to 100 and applaud every time that they find either a multiple of 3 or a number ending with 3. How many times are they supposed to applaud?

A- 30

B- 33

C- 36

D- 39

E- 40

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The correct answer is D.

There are 33 numbers that are multiple of 3 less than 100 (3, 6, 9, 12, 15, …) and there are 10 numbers that are ending with 3 (3, 13, 23, 33, 43, …). From those numbers, 4 numbers (3, 33, 63, 93) are also the multiple of 3. Therefore, there are 39 numbers that are either a multiple of 3 or ending with 3:
33 + 10 to 4 = 39

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