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Problem 204

Algebra Difficulty 1.7 Find the answer CEMC Pascal

When two positive integers are multiplied, the result is 24. When these two integers are added, the result is 11. What is the result when the smaller integer is subtracted from the larger integer?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

The positive divisor pairs of 24 are: 1 and 24, 2 and 12, 3 and 8, 4 and 6. Of these, the pair whose sum is 11 is 3 and 8. The difference between these two integers is 83=58 - 3 = 5.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.