I am a number with the following properties:

1. If I am not a multiple of 4, then I am between 60 and 69.

2. If I am a multiple of 3, I am between 50 and 59.

3. If I am not a multiple of 6, I am between 70 and 79.

What number am I?

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76 -

ReplyDeleteIs a multiple of 4

Is not a multiple of 3

Is not a multiple of 6

consider possible multiples of 3: 51, 54, 57. But none of these are multiples of 4, so they must be between 60 and 69. Since they are not, we were wrong to consider multiples of 3. I am not a multiple of 3.

ReplyDeleteSince I am not a multiple of 3, I am not a multiple of 6 (right?).

Since I am not a multiple of 6, I must be between 70 and 79.

Since I am not between 60 and 69, I must be a mulitple of 4.

Multiples of 4 between 70 and 79 are 72 and 76, but 72 is a multiple of 3.

I am 76.

Very nicely explained Jonathan. 76 is the answer.

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