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What is the sum of two consecutive even numbers, the difference of whose squares is 84?

34
38
42
46

Correct Answer: 42

Explanation:

Let the numbers be x and x + 2.

Then, (x + 2)² - x² = 84

⟹ 4x + 4 = 84

⟹ 4x = 80

⟹ x = 20.

∴ The required sum = x + (x + 2) = 2x + 2 = 42.

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