Is x^2 > y^2 ? (1) |x| > y (2) x > |y|

We can solve the question using two approaches -

Approach 1: Using the concept of absolute value

\(x^2 > y^2\)

Taking square root on both sides

\(|x| > |y|\)

Inference: Is the distance of x from 0 greater than the distance of y from 0

Statement 1

\(|x| > y\)

This statement tells us that the distance of x from 0 is greater than the value of y. However, we do not know anything about the distance of y from 0.

Case 1: ---------- 0 ----- y ---------- x -----

Is the distance of x from 0 greater than the distance of y from 0 - Yes !

Case 2: ---------- y --------------------- 0 -- x -----

Is the distance of x from 0 greater than the distance of y from 0 - No !

The statement is not sufficient. Hence we can eliminate A and D.

Statement 2

\(x > |y|\)

The value of x is greater than the distance of y from 0. As modulus (the distance) is always non negative, we can conclude that x will be positive. There can be two cases

Case 1: ---------- y ------- 0 -------------------------- x -----------

Case 2: ---------- 0 ------- y -------------------------- x -----------

In both cases, Is the distance of x from 0 greater than the distance of y from 0 - Yes !

Sufficient

Option B

Approach 2: Picking Numbers

Statement 1

\(|x| > y\)

Case 1: x = 10 ; y = 2
Is \(x^2 > y^2\) -- Yes !

Case 2: x = 10 ; y = -12
Is \(x^2 > y^2\) -- No!

The statement is not sufficient. Hence we can eliminate A and D.

Statement 2

|y| is non negative, hence x is positive.

Case 1: x = 10 ; y = 2
Is \(x^2 > y^2\) -- Yes !

Case 2: x = 10 ; y = -9
Is \(x^2 > y^2\) -- Yes !

Option B