XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 22 : 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?

Video Explanation

Explanatory Answer

\( x ( x - p ) - y ( y + p ) = 7 p \)
\( x ^ { 2 } - p x - y ^ { 2 } - p y = 7 p \)
\( x ^ { 2 } - y ^ { 2 } - p x - p y = 7 p \)
\( x ^ { 2 } - y ^ { 2 } - p ( x + y ) = 7 p \)
\( ( x + y ) ( x - y ) - p ( x + y ) = 7 p \)
\( ( x + y ) ( x - y ) = p ( 7 + x + y ) \)
Let x + y = s and x - y = d
\( ( s ) ( d ) = p ( 7 + s ) \)
For x and y to be integers, s and d should both be even or should both be odd. Think Why??

The question is " 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? "

Hence, the answer is 'None of the above'

Choice E is the correct answer.

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