M4maths Previous Puzzles

24 Jan 2018 Divisibility

How many numbers between 1 and 100 (inclusive) are divisible by 5 or 3?

OPtion

1) 53
2) 54
3) 51
4) 52
5) 48
6) 50
7) 49
8) 47
9) 46
10) None of these

Solution

There are 20 numbers divisible by 5 between 1 and 100, and 33 numbers divisible by 3 between 1 and 100.

So there are 20 + 33 = 53, so 53 numbers divisible by one or the other, but this also includes every number which is divisible by both 5 and 3 twice.
Such numbers are 15, 30 and so on multiples of 15 between 1 to 100
There are 6 numbers divisible by 15 between 1 and 100 (i.e divisible by both 3 and 5)


So answer is 20+33-6 = 47

Correct Option: 8 Best Solution (0)