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

( A ) 32
( B ) 42
( C ) 38
( D ) 34

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A)
Let the number be x and x+1
$Then \; \; (x + 2)^2 - x^2 = 84$
$x^2 + 4 + 4x - x^2 = 84$
$4x + 4 = 84$
$4x = 84 - 4$
$4x = 80$
$x = 20$
\begin{align*} \text {The required sum} &= x + (x + 2) \\&= 2x + 2 \\&= 2 \times 20 + 2 \\&= 42 \end {align*}

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A)

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

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