Math Gold Medalist

Lor

2024 AMC 8 

Problem 5

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

$\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9$

Casework

Case 1)At lest one of the dice=6

Case 2) There is no 6(so one of them is 2 or 4 and the other one is 3)

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   Solution