Maths Olympiad Prep

Library / /51 of 168

Algebra Difficulty 1.7 Junior Find the answer

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. Spacing and $ signs are ignored.

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.

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: Omni-MATH, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.