Who am I? Help with math riddle?

A

angel05bby

New member
I am a number with the following properties:
If I am not a multiple of 4, then I am between 60 and 69.
If I am a multiple of 3, I am between 50 and 59.
If I am not a multiple of 6, I am between 70 and 79.
What number am I?
 
(i) if not / by 4 then 61, 62, 63, 65, 66, 67, 69
(ii) if / by 3 then 51, 54, 57
(ii) if not / 6 then 71, 73, 74, 75, 76, 77, 79

- try (ii) first since there are the fewest numbers: if it was divisible by three, then it would have to also be divisible by 4 and 6 (otherwise it would have to be one of the numbers in i or iii) - BUT none of 51, 54, 57 are divisible by both 4 and 6 so the number cannot be divisible by 3

- if it is not divisible by 3, then it cannot be divisible by 6 (obviously since 6 is 2x3) so it must be one of the numbers in (iii) and must be divisible by 4 (otherwise it would have to be one of the numbers in i)

- only 76 is divisible by 4 so that is the answer to the riddle

Voila!
 
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