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Ages & Problems on Numbers · Question 50 of 60

Question 50

MediumOriginal question

The product of two consecutive positive even integers is 168. What is their sum?

Options for question 50

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Let them be nn and n+2n + 2: n(n+2)=168n(n + 2) = 168.

  2. n2+2n−168=0n^2 + 2n - 168 = 0, so (n+14)(n−12)=0(n + 14)(n - 12) = 0.

  3. n=12n = 12: the integers are 12 and 14, so the sum is 26.

Worth noting

14 is only the larger integer. Quick check: 168 sits just below 132=16913^2 = 169, so the two evens are either side of 13.

Concept
Product of consecutive even integers
Typical time
60 s
Your time
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The rule this testsProblems on numbers
Practise this chapter →

Ten questions from Ages & Problems on Numbers, at your own pace.

Practise this chapter →

Ten questions from Ages & Problems on Numbers, at your own pace.