I hope you got a chance to try your hand at this week’s question. Let’s start by refreshing your memory:
How many three-digit numbers contain three primes that sum to an even number?
Answer and Explanation
In order for three prime numbers to sum to an even number, either one of those three primes or all three of those primes has to be ‘2’. First, let’s count the instances that have exactly one ‘2’. Each of these instances can contain any of the single-digit prime numbers: 3, 5, and 7.
Ist case: 2 _ _
2nd case: _ 2 _
3rd case: _ _ 2
In each case, there can be three different prime numbers. Therefore, we get 3 x 3, 9 possibilities, for each case. Since there are three cases, we end up getting 27.
The final step is to account for that one instance in which all three numbers are 2, as in the number 222.
Therefore, the answer is (B) 28.
How’d you do? If you’re up for another challenge (and I know you are) check back in two weeks for our next installment of Magoosh GRE Brain Twister!