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# If x and y are positive, is x > y^2?

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Intern
Joined: 18 Oct 2009
Posts: 48
Schools: Kellogg
If x and y are positive, is x > y^2?  [#permalink]

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31 Oct 2009, 21:07
1
2
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:03) correct 33% (01:53) wrong based on 132 sessions

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If x and y are positive, is x > y^2?

(1) y > x^2
(2) y = x + 1

M17-32

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GMAT Strategies: http://gmatclub.com/forum/slingfox-s-gmat-strategies-condensed-96483.html

Math Expert
Joined: 02 Sep 2009
Posts: 52285

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31 Oct 2009, 21:30
If x and y are positive, is x > y^2?

(1) y>x2. If $$x=1$$ and $$y=4$$, then the answer is NO but if $$x=y=\frac{1}{2}$$, then the answer is YES. Not sufficient.

(2) y=x+1. The question becomes: is $$x>(x+1)^2$$? Which cannot be true for ANY value of x. So, the answer to the question is NO. Sufficient.

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Joined: 25 Oct 2009
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Schools: Wharton, HBS, Stanford

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31 Oct 2009, 21:36
1
These type of quastions works try to confuse test takers with fractions in power. The best approach is Picking Numbers strategy.

Is $$x>y^2$$ given that $$x$$ and $$y$$ are positive?

(1) $$y>x^2$$

Pick $$x=\frac{8}{10}$$ and $$y=\frac{7}{10}$$, $$\frac{7}{10}>\frac{64}{100}$$, and $$\frac{8}{10}>\frac{49}{100}$$. But if we try $$x=\frac{8}{10}$$ and $$y=1$$, $$x$$ will be lower than $$y^2$$. So, (1) alone is NOT SUFFICIENT.

(2) $$y=x+1$$
given that $$x>0$$, therefore $$y>1$$. There is $$y^k>y^1$$ for all $$y>1$$, $$k>1$$. So, (2) alone is SUFFICIENT.

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Intern
Joined: 18 Oct 2009
Posts: 48
Schools: Kellogg

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01 Nov 2009, 00:42
Thanks for the explanation guys. I totally missed the "if x and y are positive" language in the question stem
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Intern
Joined: 28 Apr 2009
Posts: 32

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07 Nov 2009, 21:47
I ignored the fraction possibility..

Nice solution..

slingfox wrote:
Thanks for the explanation guys. I totally missed the "if x and y are positive" language in the question stem
Senior Manager
Joined: 13 Aug 2012
Posts: 426
Concentration: Marketing, Finance
GPA: 3.23
Re: If x and y are positive, is X > y^2?  [#permalink]

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17 Jan 2013, 02:43
1
slingfox wrote:
How would you guys approach this question:
If x and y are positive, is X > y^2?
1. y > x^2
2. y = x + 1

It is important to note that all you have to test are positive whole numbers and fractions

1.
let x=2, y=5
y > x^2 => 5 > 4 ----- x > y^2 => 2 > 25 NO!

let x=1/2, y=1/2
y > x^2 => 1/2 > 1/4 ----- x > y^2 => 1/2 > 1/4 YES!

The information given in statement 1 is insufficient.

2.
let x = 2, y = x + 1 = 3
x > y^2 ==> 2 > 9 NO!

let x = 1/2, y = 5/2
x > y^2 ==> 1/2 > 25/4 NO!

The information given in statement 2 is sufficient.

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Senior Manager
Joined: 06 Aug 2011
Posts: 336
If x and y are positive, is x>y2? (1) y>x2 (2) y=x+1  [#permalink]

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27 Feb 2014, 06:27
If x and y are positive, is x>y^2?

(1) y>x^2

(2) y=x+1
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Senior Manager
Joined: 06 Aug 2011
Posts: 336
Re: If x and y are positive, is x>y2? (1) y>x2 (2) y=x+1  [#permalink]

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27 Feb 2014, 06:30
i got that statement 2 is sufficient..

But, I tuk around more than 2 minutes to chek whether statement 1 is sufficient or not..

confused when i see x>y^2 or x2>y3 .. these kind of question most of the time i do it correct, bt i tuk long time to prove whether its sufficient or not
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Math Expert
Joined: 02 Sep 2009
Posts: 52285
Re: If x and y are positive, is x>y2? (1) y>x2 (2) y=x+1  [#permalink]

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27 Feb 2014, 07:23
sanjoo wrote:
If x and y are positive, is x>y^2?

(1) y>x^2

(2) y=x+1

Merging similar topics.
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Re: If x and y are positive, is x > y^2?  [#permalink]

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13 Mar 2018, 05:56
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive, is x > y^2? &nbs [#permalink] 13 Mar 2018, 05:56
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