Question

The sum of two numbers is $629$ and their $HCF$ is $37$. The number of pairs satisfying the above condition is

• A. $5$
• B. $6$
• C. $10$
• D. $8$

Answer 1

The correct option is D $8$

H.C.F$=37$

So, two numbers are $37x$ and $37y$, where $x$ and $y$ are co-prime numbers.

So,$37x+37y=629$

$\Rightarrow x+y=17$

So, possible values are

$(1,16)$,$(2,15)$,$(3,14)$,$(4,13)$,$(5,12)$,$(6,11)$,$(7,10)$,$(8,9)$

Now, we will not write $(9,8)$ or $(10,7)$ as it will form the same number formed by above pair.

$\therefore 8$ pairs are satisfied by the above condition.