Question

The difference between two positive integers is $13$ and their product is $140$. Find the two integers.

• A. $7$ and $13$
• B. $12$ and $13$
• C. $20$ and $3$
• D. $7$ and $20$

Answer 1

The correct option is D $7$ and $20$

Let $x$ be the positive integer and $x+13$ be the larger integer
So, $x(x+13)=140$
$x^2+13x-140=0$
On factoring, we get,
$(x-7)(x+20)=0$
$x=-20$ or $x=7$
The smallest integer $=x+13=7+13=20$
Therefore, the two numbers are $20$ and $7$.