Question

Two positive numbers have their HCF as $12$ and their sum is $84$. Find the number of pairs possible.

• A. $4$
• B. $3$
• C. $2$
• D. $1$

Answer 1

The correct option is B $3$

As the HCF is $12$, the numbers can be written as $12x$ and $12y$, where x and y are co-prime to each other.
So, $12x+12y=84=>x+y=7$
The pair of numbers that are co-prime to each other and sum up to $7$ are $(2,5),(1,6),(3,4)$.
Hence, only $3$ pairs of such numbers are possible.
The numbers are $(24,60),(12,72)$ and $(36,48)$