Multiples of 7:
49, 56, 63, 70, 77, 84, 91, 98
Multiples of 8:
48, 56, 64, 72, 80, 88, 96
Which of those numbers answer your question?
At first sight, the answer is the LCM (Lowest common multiple) of 7 and 8?
Looking further, there is a problem with the question ("but not any other set of single digit number"). Any number divisible by 8 is also divisible by 2 and 4, hence the two-digit number divisible by 7 and 8 will always be divisible by 7, 8, 4 and 2.
Thanks, Ms. Sue
Mathmate thanks that's what I thought just wanted to make sure maybe it was a misprint on the riddle.
I read the problem as the PAIR of numbers that can go into the two digit numbers. The numbers 7 and 8 are the only single digit PAIR of numbers that fit that description.
Ms Sue, I think your interpretation is very reasonable.
However, mathematically speaking, there is no limit on the number of members in a set. As Paul indicated, there is probably a misprint, where it read "but not any other SET of single digit numbers" it is probably supposed to read "but not any other PAIR of single digit numbers".