If x < y, is x^2 < y^2 ?

APPROACH 1:

If x < y, is x^2 < y^2 ?

(1) y > 0

We are given that y is positive but we don't know the sign of x. If x = 0 and y = 1, then x^2 < y^2. However, if x = -100 and y = 1, then x^2 > y^2. Not sufficient.

(2) x > 0

Combining the above with x < y, we get 0 < x < y. Now, since both sides of the inequality x < y are non-negative, then we can safely square and get x^2 < y^2. Sufficient.

Answer: B.


APPROACH 2:

If x < y, is x^2 < y^2 ?

Taking the square root of x^2 < y^2, we get |x| < |y|. Hence, the question essentially asks whether y is further from 0 than x on the number line.

(1) y > 0 --> y is positive but we don't know the sign of x. If x=0 and y=1, then x^2 < y^2 but if x=-100 and y=1, then x^2 > y^2. Not sufficient.

If x is between -y and y on the number line, the answer will be YES:
--------(-y)--------0--------y--------

However, if x is to the left of -y (or is equal to it), on the number line, the answer will be NO:
--------(-y)--------0--------y--------

Not sufficient.

(2) x > 0

Combining the above with x < y, we get 0 < x < y. This implies that y is indeed further from 0 than x on the number line. Sufficient.

Sufficient.

Answer: B.

Hope it helps.