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1. The sum of two numbers is 25 and their difference is 13. Find their product :

A. 104

B. 114

C. 315

D. 325

Solution:

Let the numbers be x and y
Then,
x + y = 25 and x - y = 13

\begin{aligned} \Leftrightarrow 4 x y = {(x + y)}^{2} - {(x - y)}^{2} \\ \Leftrightarrow 4 x y = {(25)}^{2} - {(13)}^{2} \\ \Leftrightarrow 4 x y = 625 - 169 \\ \Leftrightarrow 4 x y = 456 \\ \Leftrightarrow x y = 114 \end{aligned}

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