If x and y are positive, is x^3 > y? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 21:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x and y are positive, is x^3 > y?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 06 Apr 2010
Posts: 144
Followers: 3

Kudos [?]: 655 [0], given: 15

If x and y are positive, is x^3 > y? [#permalink]

### Show Tags

23 Jun 2010, 11:30
00:00

Difficulty:

55% (hard)

Question Stats:

45% (02:32) correct 55% (00:31) wrong based on 42 sessions

### HideShow timer Statistics

If x and y are positive, is x^3 > y?

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-is-x-3-y-100086.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Jun 2014, 01:22, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 03 May 2010
Posts: 88
WE 1: 2 yrs - Oilfield Service
Followers: 12

Kudos [?]: 109 [0], given: 7

Re: If x and y are positive, is x^3 > y? [#permalink]

### Show Tags

23 Jun 2010, 23:29
Statement 1 is actually "root(x) > y"

x>0 and y>0 Is x^3 > y?

From statement 1:
root(x) > y
Test cases:
x = 4 and y = 1 => root(x) = 2 > 1. x^3 = 64 > 1 ... Answer : Yes
x = 0.01 and y = 0.005 => root(x) = 0.1 > 0.05. x^3 = 0.001 < 0.005 ...Answer: No
INSUFFICIENT

From statement 2:
x > y
Test cases:
x = 2 and y = 3 => x^3 = 8 > 3. Answer -Yes
x = 0.1 and y = 0.01 => x^3 = 0.001 < 0.01. Answer - No
INSUFFICIENT

Both 1 and 2 together:
Test cases:
x = 4 and y = 1 satisfies both statements, and x^3 > y is true.
x = 0.01 and y = 0.005 satisfies both statements and x^3>y is false.
INSUFFICIENT.

Pick E.
Manager
Joined: 17 Jul 2013
Posts: 110
Followers: 0

Kudos [?]: 6 [0], given: 67

Re: If x and y are positive, is x^3 > y? [#permalink]

### Show Tags

26 Jun 2014, 23:36
Hi Bunuel,

Can we do this ques based on graphs .. I am working on a technique that could help me to hit all in equality questions.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 36548
Followers: 7077

Kudos [?]: 93125 [0], given: 10552

Re: If x and y are positive, is x^3 > y? [#permalink]

### Show Tags

27 Jun 2014, 01:27
GmatDestroyer2013 wrote:
Hi Bunuel,

Can we do this ques based on graphs .. I am working on a technique that could help me to hit all in equality questions.

Thanks

I wouldn't suggest to use graph approach for this question because x^3 and $$\sqrt{x}$$ functions are not easy to plot and compare. Below are two approaches which are good for it.

If x and y are positive, is x^3>y?

NUMBER PLUGGING:

(1) $$\sqrt{x}>y$$ --> if $$x=1$$ and $$y=\frac{1}{2}$$ then the answer will be YES but if $$x=\frac{1}{4}$$ and $$y=\frac{1}{5}$$ then the answer will be NO. Two different answers, hence not sufficient.

(2) $$x>y$$ --> if $$x=1$$ and $$y=\frac{1}{2}$$ then the answer will be YES but if $$x=\frac{1}{4}$$ and $$y=\frac{1}{5}$$ then the answer will be NO. Two different answers, hence not sufficient.

(1)+(2) Both examples are valid for combined statements, so we still have two answers. Not sufficient.

ALGEBRAIC APPROACH:

For $$1\leq{x}$$: ------$$\sqrt{x}$$----$$x$$----$$x^3$$, so $$1\leq{\sqrt{x}}\leq{x}\leq{x^3}$$ (the case $$\sqrt{x}=x=x^3$$ is when $$x=1$$). $$y$$ is somewhere in green zone (as $$y<\sqrt{x}$$ and $$y<x$$), so if we have this case answer is always YES: $$y<x^3$$.

But:

For $$0<x<1$$: $$0$$----$$x^3$$----$$x$$----$$\sqrt{x}$$----$$1$$, so $$0<x^3<x<\sqrt{x}$$. $$y$$ is somewhere in green or red zone (as $$y<\sqrt{x}$$ and $$y<x$$), so if we have this case answer is sometimes YES: $$y<x^3$$ (if $$y$$ is in green zone), and sometimes NO: $$x^3<y$$ (if $$y$$ is in red zone). In fact in this case $$y=x^3$$ is also possible, for example when $$x=\frac{1}{2}$$ and $$y=\frac{1}{8}$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-and-y-are-positive-is-x-3-y-100086.html
_________________
Re: If x and y are positive, is x^3 > y?   [#permalink] 27 Jun 2014, 01:27
Similar topics Replies Last post
Similar
Topics:
3 Is y a positive number? (1) 2x + y > 27 (2) x – 3y < 24 3 29 Sep 2015, 04:15
6 Is |x – 3| > |y – 3|? 11 15 Feb 2011, 12:28
15 If x and y are positive, is x^3 > y? 8 30 Aug 2010, 08:38
3 Is x^3 > y^2? 3 22 May 2010, 23:33
17 If x and y are positive, is x^3 > y? 15 24 Jul 2009, 08:54
Display posts from previous: Sort by