16Hit1600
Advanced MathVery hardConsecutive reciprocals summing to a fraction

Advanced Math practice question

The reciprocals of two consecutive positive integers have a sum of 5/6. What is the product of the two integers?

Answer: 6

1/n + 1/(n + 1) = 5/6 gives 6(2n + 1) = 5n(n + 1), so 5n² − 7n − 6 = (5n + 3)(n − 2) = 0 and n = 2; the integers are 2 and 3, with product 6.

Common wrong answers

If you answered 2
2 is the smaller integer.
If you answered 5
5 is the sum of the integers.
If you answered 12
12 uses 3 and 4.

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