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

The Correct Option is D

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