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?
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
- 1
- 3
- 2
- 6
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The Correct Option is D
Solution and Explanation
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
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