2024 AMC 8
Complete problem set with solutions and individual problem pages
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?
- A.
- B.
- C.
- D.
- E.
Solution 1
First, figure out all pairs of numbers whose product is 6. Then, using the process of elimination, we can find the following:
is possible:
is possible:
is possible:
The only integer that cannot be the sum is .
Solution 2
First, see that in order for the two numbers to have a product of 6, it must either have 6 as a factor or have factors that have a product of 6 (Notably ).
When we look at the answer choices, we see that answers all are more than 6, so they can all be added as a sum of 6. Answer works because , so 6 is the only answer choice that doesn't work. Thus, the answer is .
