CAT 2023 Slot 2 Solved Paper

It is given that ‌

x

y

<‌

x+3

y−3

, which can be written as ‌

x

y

−‌

x+3

y−3

<0
‌⇒‌

x(y−3)−y(x+3)

y(y−3)

<0
‌⇒‌

xy−3x−xy−3y

y(y−3)

<0
‌⇒‌

−3(x+y)

y(y−3)

<0
‌⇒‌

3(x+y)

y(y−3)

>0
From this inequality, we can say that, when y<0⇒y(y−3)>0. Now to satisfy the given equation ‌

3(x+y)

y(y−3)

>0,
(x+y) must be greater than zero Hence, x>0 and |x|>|y|
Therefore, the magnitude of x is greater than the magnitude of y.
Hence, x>y, and |x|>|y|⇒−x<y (Since the magnitude of x is greater than the magnitude of y.)
The correct option is B.