What’s My Number

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?
Source: CMC Communicator Volume 29, No. 3 March 2005

SOLUTION
Not a multiple of 4 between 60 and 69:
61, 62, 63, 65, 66, 67 \qquad\left (1\right )
Multiples of 3 between 50 and 59:
54, 57 \qquad\qquad\qquad\qquad\left (2\right )
Not a multiple of 6 between 70 and 79:
71, 73, 74, 75, 76, 77 \qquad\left (3\right )
We now examine each candidate number and look for those that pass all three conditions. When a number passes/fails a condition we mark it by a P/F in the following table


Of the candidate numbers only 76 passes all three conditions.

Answer: 76.

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About mvtrinh

Retired high school math teacher.
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