Number System

 Back to Questions

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 '$t$'?


13 and 52


132 and 96


18 and 126


56 and 45

 Hide Ans

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)


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