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?

Updated On: Oct 4, 2024
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The Correct Option is D

Solution and Explanation

Let numbers be 22xx and 22yy, where xx and yy are co-prime numbers.
22x+22y=462\rightarrow 22x+22y=462
(x+y)=4622\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)(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

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