Is x^2 y^2 ? (1) x y 0 (2) x 1 y

Question

Is x^2 > y^2 ?

(1) x > y > 0
(2) x > 1 > y

cantaffordname · Answer

Value of any negative square is always bigger hence from statement 1 we know that x and y are negative so A is sufficient.

Statement two x is greater than 1 and y is lower than 1 so if we take 2 as x and -3 as y the statement is satisfied but the sqaure of both number would flip inequities. Hence statement 2 is not sufficient

Posted from my mobile device

shridhar786 · Answer

Is x^2 > y^2 ? STATEMENT 1--x > y > 0 From this we know x and y----positive and x>y so , x^2 > y^2 when x = 2 y = 1 x^2 > y^2 when x = \frac{1}{2} y = \frac{1}{3} x^2 > y^2 so , SUFFICIENT STATEMENT 2--x > 1 > y X>1 and y<1 when x =2 y = 0 then x^2 > y^2 --YES when x = 2 y = -4 then x^2 < y^2 --NO so INSUFFICIENT A is the answer

freedom128 · Answer

Is x^2>y^2 ?
--> Is (x-y)(x+y)>0 ?
--> Are both (x-y) and (x+y) of the same sign ?

(1) x > y > 0
We know from statement (1) as follows:
a. x > y --> x - y > 0 --> (x-y) is positive
b. x > 0 and y > 0 both positive --> (x+y) is positive
--> Both (x-y) and (x+y) are of the same sign. Thus, x^2>y^2 must be true
SUFFICIENT

(2) x > 1 > y
We know from statement (2) as follows:
a. x > y --> x - y > 0 --> (x-y) is positive
b. x>1 is positive. However, y<1 could be positive or negative of zero --> (x+y) could be positive or negative or zero
--> Both (x-y) and (x+y) could be of either the same sign or the opposite sign. Thus, x^2>y^2 could be either true of false.
NOT SUFFICIENT

Answer is (A)

+1 kudo if this solution is deemed good

Is x^2 > y^2 ? (1) x > y > 0 (2) x > 1 > y

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions