Problem 6 · 2013 AMC 8
Easy
Arithmetic & Operations
multiplication-pyramid
The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, 30 = 6 × 5. What is the missing number in the top row?
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Answer: C — 4.
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Hint 1 of 2
You can't fill the top box directly — but you can work backwards. The bottom 600 came from multiplying, so a missing factor is found by dividing. Which box can you unlock with 600 ÷ 30?
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Hint 2 of 2
In a product pyramid, multiply to go down and divide to go back up. Solve the box you have the most info about first, then chain to the unknown.
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Approach: divide your way back up the pyramid
- Bottom box 600 = (left-middle 30) × (right-middle). Reverse the multiplication: right-middle = 600 ÷ 30 = 20.
- That right-middle box came from the top: it = 5 × (top-right). Reverse again: top-right = 20 ÷ 5 = 4.
- Why this works: any "product" pyramid is just multiply-down / divide-up — always start from the box you can compute and divide back toward the gap.
- Check downward: top 6 × 5 = 30 (matches), then 30 × 20 = 600 (matches).
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