Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
Each integer is chosen independently and at random from the set of integers {1, 2, 3, …, 100}. You ultimately care about evens & odds, so you should go ahead and note that each integer has a 50% chance of being even (and a 50% chance of being odd). The operation between the two integers could be addition or multiplication, with an equal chance of either. Nicely, the “equal chances” throughout this problem allow you to list the individual outcomes and assign equal weight to each.
Addition:
E + E = E
E + O = O
O + E = O
O + O = E
Multiplication:
E × E = E
E × O = E
O × E = E
O × O = O
The key is to notice that you have to separately count E + O and O + E (likewise for multiplication). Out of eight outcomes with equal probability, five produce an even result. Thus, the probability you want is 5/8.
The correct answer is C.