Question

The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions?

• A. 1
• B. 3
• C. 2
• D. 6

Answer 1

Answer: (D)

6

Answer 2

Let numbers be 22$x$ and 22$y$, where $x$ and $y$ are co-prime numbers.
$\rightarrow 22x+22y=462$
$\rightarrow (x+y)=\frac{462}{2}$=21
Now, number of possible values of $(x,y) = (1,20)(2,19)(4,17)(5,16)(8,13)(10,11)$
Therefore, There are 6 such pairs.
The correct answer is (D) : 6