Problem 4 · 2022 Math Kangaroo
Easy
Number Theory
factorization
The numbers 3, 4, 5, 6 and 7 are written in the five circles of the shape shown. The product of the numbers in the four outer circles is 360. Which number is in the inner circle?
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Answer: E — 7
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Hint 1 of 2
The five numbers are fixed: 3, 4, 5, 6, 7. Find their total product first.
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Hint 2 of 2
Divide the product of all five by the product of the four outer ones to isolate the inner number.
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Approach: divide the full product by the outer product
- The product of all five numbers 3,4,5,6,7 is 2520.
- The four outer numbers multiply to 360.
- The inner number is 2520 / 360 = 7, so the answer is E.
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