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Question 158

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?

Solution

Let numbers be $$22x$$ and $$22y$$, where $$x$$ and $$y$$ are co-prime numbers.

=> $$22x+22y=462$$

=> $$(x+y)=\frac{462}{22}=21$$

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.

=> Ans - (D)

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