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 $6$ . Which of the following integers cannot be the sum of the two numbers?

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

Solution 1

Using the process of elimination, we can find the following: A is possible: $2*3$ C is possible: $1*6$ D is possible: $2*6$ E is possible: $3*6$ So therefore, the only integer that cannot be the sum is $(B) \boxed{6}$ . -ILoveMath31415926535

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2024 AMC 8 Problems/Problem 5

Problem

Solution 1