Three consecutive positive integers have a product that is exactly five times their sum. What is the largest of these three integers?
5
Let the integers be n - 1, n, and n + 1. Their sum is 3n and their product is n(n - 1)(n + 1) = n(n² - 1). Setting the product equal to 5 times the sum: n(n² - 1) = 5(3n) = 15n. Dividing by n gives n² - 1 = 15, so n² = 16 and n = 4. The three integers are 3, 4, and 5, so the largest is 5.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
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