Question

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

• A. 61
• B. 56
• C. 52
• D. 65

Answer 1

The correct option is A

61

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.