I am a number with the following properties: * If I am not a multiple of 4, then I am ........... What number am I?

Question

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?

Answer 1

76

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(50-59)- must be multiple of 3, 4 & 6, i.e multiple of 12- no such a number, excluded
(60-69)- must be multiple of 6 but not multiple of 3 or 4, it is not possible as any multiple of 6 will also be multiple of 3, excluded
970-79)- must be multiple of 4 nut not multiple of 3 or 6. Multiples of 4 are 72 and 76 but 72 is also multiple of 3&6 so is excluded. The only number left is 76.