Problem:
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following number could be obtained?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are five prime numbers between and , and . Hence the product of any two of these is odd and the sum is even. Because increases as either or increases (since both and are bigger than ), the answer must be an odd number that is no smaller than and no larger than . The only possibility among the options is , and indeed .
The problems on this page are the property of the MAA's American Mathematics Competitions