2024 AMC 8 Problems/Problem 5

Problem

Aaliyah rolls two standard 6-sided dice. She notices that the product of the two numbers rolled is a multiple of . Which of the following integers cannot be the sum of the two numbers?

Solution 1

Trial and Error:

We know that 7 = 6 + 1, 8 = 6 + 2, and 9 = 6 + 3 meaning that they are not the solutions because 6 x 1 = 6, 6 x 2 = 12, and 6 x 3 = 18

Next, we know that 5 = 2 + 3 and 2 x 3 = 6 meaning that with process of elimination the answer must be 6

You can check by seeing all the numbers that add to 6, 1 + 5, 2 + 4, and 3 + 3.