How many two digit prime numbers are there in which both digits are prime numbers? (For
example, 23 is one of these numbers but 31 is not, since 1 is not a prime number.)
Pick:
A) 3  B) 4  C) 5  D) 8  E) 15

Rationale: the second digit can only be 3 or 7 , so the choice quickly narrows down to 23 , 27 , 33 , 37 , 53 , 57 , 73 , and 77 . of these , 27 , 33 , and 57 are divisible by 3 , and 77 by 7 , leaving 23 , 37 , 53 , and 73 . it is easy to see that none of these is divisible by 2 , 3 , 5 , or 7 , and there is no need to look at greater prime divisors since root 77 < 11 . correct answer b
Answer: B