Problem 5 · 2014 Math Kangaroo
Easy
Number Theory
factor-pairs
The product of two natural numbers is 36, and their sum is 37. What is the (positive) difference between the two numbers?
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Answer: E — 35
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Hint 1 of 2
List the factor pairs of 36 and check which pair adds to 37.
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Hint 2 of 2
A pair multiplying to 36 and adding to 37 must be far apart, not close together.
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Approach: find the factor pair of 36 that sums to 37
- The factor pairs of 36 are 1×36, 2×18, 3×12, 4×9, 6×6.
- Their sums are 37, 20, 15, 13, 12 — only 1 and 36 give the sum 37.
- The difference is 36 − 1 = 35.
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