cat 2024 Question 20

Question

If x and y satisfy the equations $\mid x \mid + x + y = 15$ and $x + \mid y \mid - y = 20$, then $(x - y)$ equals

Accepted Answer

We can consider the quadrants of a graph:

First quadrant: Both x and y are positive

This would change the equation to 2x+y=15 and x=20, giving a negative value of y; hence, this is not the case.

Second quadrant: x is negative, but y is positive

This would change the equations to y=15 and x=20, giving a positive value of x, which hence can not be the case.

Third quadrant: Both x and y are negative

This would change the equation to y=15 and x-2y=20; this gives a positive value of y and hence can not be the case.

Fourth quadrant: x is positive, but y is negative

This would change the equations to 2x+y=15 and x-2y=20; this gives the value of x as 10 and y as -5, which would lie in the fourth quadrant.

The value of x-y would be 10-(-5)=15

Therefore, Option B is the correct answer.

Question 20.