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