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Advanced MathHardConsecutive even integers from a product

Advanced Math practice question

The product of two consecutive even integers is 48. If both integers are positive, what is the smaller one?

Answer: 6

Let the integers be n and n + 2: n(n + 2) = 48, so n² + 2n − 48 = 0, which factors as (n + 8)(n − 6) = 0. The positive solution is n = 6. Check: 6 × 8 = 48.

Common wrong answers

If you answered 7
7 × 9 = 63, and 7 isn't even; the pair is 6 and 8.
If you answered 8
8 is the LARGER integer; the question asks for the smaller.
If you answered -8
−8 is the other solution of the quadratic, but the integers are positive.

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