Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
This problem can be solved quickly by first listing the target numbers: primes that could be generated as the sum of two dice rolls.
Since the target numbers must be between 2 and 12 (inclusive), we have 2, 3, 5, 7, and 11.
Now go target by target, listing the possible rolls.
2: Roll 1, then 1. One way.
3: Roll 1, then 2.
Roll 2, then 1. Two more ways.
Realize that you have to separately count rolling a 1, then a 2 and rolling a 2, then a 1. Those are two separate ways to roll a 3.
5: 1, then 4.
2, then 3.
3, then 2.
4, then 1. Four ways.
7: 1, then 6.
2, then 5.
3, then 4.
4, then 3.
5, then 2.
6, then 1. Six ways.
11: 5, then 6.
6, then 5. Only two ways.
These ways sum up: 1+ 2 + 4 + 6 + 2 = 15. Divide by 36 (= 6 × 6) to get 15/36.
The correct answer is C.
quickly listing the first roll, then the successful second rolls:
First roll = 1: second roll = 1, 2, 4, 6