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Problem 55

Number theory Difficulty 1.1 Find the answer CEMC Pascal · Canada · 2020

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

$2$
$3$
$4$
$5$
$6$

Your answer

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

Official solution

The positive divisor pairs of 24 are:

1 and 24 and 12 and 8 and 6

Of these, the pair whose sum is 11 is 3 and 8.

The difference between these two integers is $8 - 3 = 5$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.