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A positive integer $X$ is 2 more than a multiple of 3. Its units digit is the same as the units digit of a number that is 4 more than a multiple of 5. What is the smallest possible value of $X$?

Guest Dec 23, 2018

#1**0 **

The units digit of a number that is 4 more than a multiple of 5 must be 4 or 9. We can just try a few numbers starting from 4. We can try 4, 9, 14, 19, 24, etc.

4 doesn't work because 4 = multiple of 3 +1.

9 doesn't work because 9 is multiple of 3

14 does work because 14 = multiple of 3 + 2. 14 = 12 + 2.

The smallest value of X is \(\boxed{14}\).

- PM

PartialMathematician Dec 23, 2018