Is x y (2) x^2 y

Question

Is x < y ?

(1)  \sqrt{x} > y 
(2)  x^2 > y

Bunuel · Answer

Is x < y ? (1) \sqrt{x} > y If x = 4 and y = 1, the answer would be NO. However, if x = 1/4 and y = 1/3, the answer would be YES. Not sufficient. (Note here that since x is under an even root, it must be a nonnegative number.) (2) x^2 > y If x = 4 and y = 1, the answer would be NO. However, if x = -4 and y = 1, the answer would be YES. Not sufficient. (1)+(2) x , x^2 , and \sqrt{x} can only be arranged on the number line in the following two ways: If x>1 0----1----\sqrt{x}----x----x^2---- If 0 < x < 1 0----x^2----x----\sqrt{x}----1---- (If x = 1, then the values of x , x^2 , and \sqrt{x} will coincide on the number line.) In either case, since y is less than both x^2 and \sqrt{x} , it must also be less than x itself. Answer: C. Similar questions to practice: https://gmatclub.com/forum/is-x-y-1-x-1 ... 50545.html https://gmatclub.com/forum/is-x-y-1-x-2 ... 27793.html https://gmatclub.com/forum/is-x-y-1-x-2 ... 80724.html https://gmatclub.com/forum/is-x-y-1-x-1 ... -1670.html https://gmatclub.com/forum/is-x-y-1-x-1 ... 00636.html Hope it helps.

Spectre26 · Answer

since \sqrt{x} is there, x must be > 0 x can lie in two region: 0 < x < 1 or x > = 1 For the first case: x^2 < x < \sqrt{x} For the second case: \sqrt{x} < x < x^2 As per statement I, y can be in any of the mentioned regions ( 0 to 1 or > 1), Here y can be > or < x As per statement II, y must be > 1, Here y must be < x Correct Option: C

chetan2u · Answer

There are certain properties associated with where a number is placed on a numberline.

Between 0 and 1, the value of x decreases as power increases =>  \sqrt{x}>A>x>x^2>B .
If y is at A's position, the answer is Yes, but if at B, the answer is NO for statement 1. 
Greater than 1, the value of x increases as power increases =>  x^2>B>x> \sqrt{x}>A 
If y is at A's position, the answer is Yes, but if at B, the answer is NO for statement 2.

When you combine....
x is always between  \sqrt{x}  and  x^2 , so if these both are greater than y, then surely all values between  \sqrt{x}  and  x^2 , will also be greater than y or x>y
Sufficient

C

Is x < y ? (1) x^(1/2) > y (2) x^2 > 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