# Moderate Number System Solved QuestionAptitude Discussion

 Q. The two positive integers '$p$' and '$q$' satisfy: $dfrac{(p+q)}{t} = text{HCF}(p,q)$. Which of the following two numbers sum up to '$t$'?
 ✖ A. 13 and 52 ✖ B. 132 and 96 ✖ C. 18 and 126 ✔ D. 56 and 45

Solution:
Option(D) is correct

Let $\text{HCF(p, q)} = H$

For two numbers $A$ and $B$, which are co-primes to each other.

We can represent $p$ and $q$ as
$p = H×A \text{ and } q= H×B$

So that $\dfrac{(p+q)}{t} =\text{ HCF(p, q)} = H$
⇒ $t = (A+B)$

Hence $t$ cab be represented as the sum of any two numbers which are co prime to each other.

Hence option(D) is correct choice.

## (1) Comment(s)

Ravi
()

Where and how did we get that $t=a+b$?