CAT Exam 2021 Slot 2 Solved Paper

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Question : 63 of 66

Marks: +1, -0

Consider the pair of equations:

\x^2 - \xy - x = 22

and

\y^2 - \xy + \y = 34

. If

\x > \y

, then

\x - \y

equals

6
4
7
8

Solution:

We have :

x2 - xy -x = 22

...(1)

and

\y^2 -\xy + \y = 34

...(2)

Adding ( 1 ) and ( 2 )
We get :

\x^2 - 2\xy + \y^2 - \x +\y = 56

We get :

(\x - \y )^2 - (\x - \y ) = 56

Let

(\x-\y) = \t

We get

\t^2 - \t = 56

\t^2 - \t - 56 = 0

(\t - 8) (\t+7) = 0

So

\t=8

So

\x-\y =8

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