How old am I?
Tom is older than Jeremy.
The largest common divisor of both Tom's and Jeremy's ages is 3.
The sum of both their ages are 60.
The digital roots of both ages is 3.
What is Tom's age?
Details and assumptions
A digital root is the sum of all the digits of a number until it is only left with one digit. Example: The digital root of 129 is 1+2+9=12 and 1+2=3 Thus, the digital root is 3.
The answer is 57.
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Personally I don't think Tom is 57 and Jeremy is 3, although I solve it. This is because from the 1st statement, the ages of them consist of two digit. If you say Jeremy's age can be written as 03, then you are wrong, since 0 is not a prime number. Therefore this question will not having any answer, since to match the first 4 statement, the only combination of their ages is {(27, 33)}, but their digital roots are 9 and 6 respectively. Prime numbers are not include 0 and 1.
http://mathforum.org/library/drmath/view/57036.html