How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?

Options:

A . 61

B . 56

C . 52

D . 65

E . 9

Answer: Option A : A List all multiples of perfect squares (without repeating any number) and subtract this from 99. 4 - there are 24 multiples of 4 (4,8,12,.....96) 9 - there are 11 multiples, 2 common with 4 (36 and 72) so, add 9 multiples 16 - 0 new multiples 25 - 3 new multiples (25,50,75) 36 - 0 new ones 49 - 2 {49,98} 64 - 0 81 - 0 Total multiples of perfect squares are 38. There are 99 numbers in total. So, there are 61 numbers that are not multiples of perfect squares.

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