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?


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 such pairs.

=> Ans - (D)

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