CAT 2023 Number System Question (Hard)

Question

Let x and y be two positive integers and p be a prime number. If x x-p -y y p 7p, what will be the minimum value of x-y?

Optima Learn · Accepted Answer

Expand the given equation x x-p -y y p 7p Rightarrow x 2-px-y 2-py 7p. Rearrange terms x 2-y 2-p x y 7p. Since x 2-y 2 x-y x y , we get x-y x y -p x y 7p. Factor out x y x y big x-y -p big 7p. Let S x y and D x-y. Then S D-p 7p. Because x and y are positive integers, both S and D are integers and S

CAT 2023 Number System — Previous Year Question

CAT 2023

Quantitative

Number System

Hard

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