Question

There are two numbers such that their difference is 3 and the difference of their squares is 69.

Find the sum of the numbers.

• A. 32
• B. 23
• C. 31
• D. 22

Answer 1

The correct option is B

23

Let the two numbers be x and y.

It is given that their difference is 3. Therefore,$x-y=3$-----(1)

Also, the difference of their squares is 69. Therefore, $x^2-y^2=69$ -----(2)

$\Rightarrow (x^2-y^2)=(x-y)(x+y)$

$\Rightarrow 69=3(x+y)$

$\Rightarrow (x+y)=\frac{69}{3}=23$