If 96 and 120 have remainders 5 and 3 respectively when divided by a positive integer m, find the value of m.

If the division of 96 by m leaves the remainder 5, then 91 must be divisible by m without remainder.  Similarly, if the division of 120 by m leaves the remainder 3, then 117 must be divisible by m without  remainder. So, m must be a divisor of both 91 and 117. Among the choices, it is only 13 which satisfies this  condition.