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# Is x > y ? (1) x^(1/2)>y (2) x^3>y

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Re: Is x > y ? [#permalink]  09 Oct 2012, 05:37
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Jp27 wrote:
Bunuel wrote:
satishreddy wrote:
hey bunnel.....can we also rewrite sq root X>M as X>M2 , by squaring both sides to make things simple,,,,,,,,,

We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality).
For example:
2<4 --> we can square both sides and write: 2^2<4^2;
0\leq{x}<{y} --> we can square both sides and write: x^2<y^2;

But if either of side is negative then raising to even power doesn't always work.
For example: 1>-2 if we square we'll get 1>4 which is not right. So if given that x>y then we can not square both sides and write x^2>y^2 if we are not certain that both x and y are non-negative.

We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).
For example:
-2<-1 --> we can raise both sides to third power and write: -2^3=-8<-1=-1^3 or -5<1 --> -5^2=-125<1=1^3;
x<y --> we can raise both sides to third power and write: x^3<y^3.

Hope it helps.

Hi few observations please correct me if Im wrong ->

\sqrt{x} > y -> cannot square this but I can always cube both sides

y > \sqrt{x} - Can i square this? Rational behind this is right hand side of the inequality is +ve so left must be to, hence this can be written as y^2>x ??

\sqrt{x} > y -> cannot square this but I can always cube both sides - YES (although it won't help much, the square root will stay)
y > \sqrt{x} - Can i square this? Rational behind this is right hand side of the inequality is +ve so left must be to, hence this can be written as y^2>x ?? YES, but the right hand side always non-negative (it can be 0)
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  05 Nov 2012, 09:00
Is x > y ?

a). x2 > y
Gives 2 conditions x > y & x < y
eg:- Consider x=2 and y=1, then x2 > y and x > y
Consider x= -4 and y = 1, then x2 > y and x < y
Insufficient.

b) sqrt x < y
ie., x < y2, again as above gives 2 conditions x > y & x < y
Insufficient.

C) Form a we have x > y & x < y, and form b we have x > y & x < y, literally both are same
Insufficient.
Ans . E
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  05 Nov 2012, 20:58
Expert's post
Maurice wrote:
Is x > y ?

a). x2 > y
Gives 2 conditions x > y & x < y
eg:- Consider x=2 and y=1, then x2 > y and x > y
Consider x= -4 and y = 1, then x2 > y and x < y
Insufficient.

b) sqrt x < y
ie., x < y2, again as above gives 2 conditions x > y & x < y
Insufficient.

C) Form a we have x > y & x < y, and form b we have x > y & x < y, literally both are same
Insufficient.
Ans . E

You might want to re-consider what happens when you take both statements together. Check out the solutions on page 1 or check this link:
http://www.veritasprep.com/blog/2011/08 ... -question/
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 19020 Followers: 3358 Kudos [?]: 24331 [0], given: 2676 Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink] 06 Nov 2012, 04:49 Expert's post Maurice wrote: Is x > y ? a). x2 > y Gives 2 conditions x > y & x < y eg:- Consider x=2 and y=1, then x2 > y and x > y Consider x= -4 and y = 1, then x2 > y and x < y Insufficient. b) sqrt x < y ie., x < y2, again as above gives 2 conditions x > y & x < y Insufficient. C) Form a we have x > y & x < y, and form b we have x > y & x < y, literally both are same Insufficient. Ans . E Answer to the question is C, not E. Check the solutions on page 1 and 2. For example: is-x-y-1-x-1-2-y-2-x-3-y-100636.html#p777179 Hope it helps. _________________ Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 14 Kudos [?]: 187 [0], given: 11 Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink] 16 Jan 2013, 04:36 It totally helped me to setup a chart to test the values out: y < x (a) increasing integer (b) increasing fraction y > x (c) decreasing fraction (d) decreasing integer Test this out on statement (1) and statement (2)... _________________ Impossible is nothing to God. Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 14 Kudos [?]: 187 [0], given: 11 Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink] 22 Jan 2013, 00:35 shrouded1 wrote: I thought this was a really tough question ! Is x > y ? (1) \sqrt{x} > y (2) x^3 > y I notice usually these types test the fractions... if x and y are swapping signs... 1. \sqrt{x} > y==>x > y^2 Let x>y: 2 > 1 (It works!) Let x<y: 1/3 > (1/4)^2 (It works!) Let x<y: -1/3 ? 1/16 (It doesn't work) INSUFFICIENT! 2. x^3 > y Let x>y: (2)^3 > 1 (It works!) Let x<y: 1/27 ? 1/4 (It doesn't work!) Let x<y: -1/27 > -1/4 (It works) INSUFFICIENT! Combine: eq in Statement 1 and 2 works for x>y Answer: C _________________ Impossible is nothing to God. Verbal Forum Moderator Status: Preparing for the another shot...! Joined: 03 Feb 2011 Posts: 1425 Location: India Concentration: Finance, Marketing GPA: 3.75 Followers: 127 Kudos [?]: 589 [0], given: 62 Re: DS Inequality [#permalink] 05 Jun 2013, 07:48 Expert's post Manhnip wrote: Is x > y? (1) √ x > y (2) x^3 > y Please provide an easy method to solve this problem in less than 2 mins The number properties change when the numbers move beyond the range of 0 and 1. Draw a number line and try to check the values of \sqrt{x} and x^3. Both the statements explain only about one range, but as soon as one combines both the statements, the range becomes quite clear and hence C becomes the answer. _________________ SVP Joined: 06 Sep 2013 Posts: 1628 Location: United States Concentration: Finance GMAT 1: 710 Q48 V39 WE: Corporate Finance (Investment Banking) Followers: 11 Kudos [?]: 152 [0], given: 254 Re: Is x > y ? [#permalink] 27 Dec 2013, 08:42 gurpreetsingh wrote: Statement 1: \sqrt{x} > y ....take x = 4, y = 1 (yes); take x = 1/4 and y = 1/3 (no) hence not sufficient. Statement 2: x^3 > y take x = 2 and y = 3 (no) , take x = 2, y = 1 (yes) hence not sufficient. take statement 1 and 2 together. Now the answer could be either C or E. Either y is -ve or postive. If y is -ve then x >y always holds true. If y is +ve then x>y^2 and x^3>y => x^6 > y^2 divide both the inequalities: x^5 >1 => x >1. Since square root of x (> 1) is greater than y => x>y. Hence C. The graphical approach is good, but its essential to understand that how the inequalities behaves in different domains. Yeah kinda tough indeed Hey gupreet or anyone how did you get to this? If y is +ve then x>y^2 and x^3>y => x^6 > y^2 Like from both statements to the x^6 > y^2? Thanks Cheers! J Kudos rain! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4664 Location: Pune, India Followers: 1069 Kudos [?]: 4771 [0], given: 163 Re: Is x > y ? [#permalink] 01 Jan 2014, 22:24 Expert's post jlgdr wrote: gurpreetsingh wrote: Statement 1: \sqrt{x} > y ....take x = 4, y = 1 (yes); take x = 1/4 and y = 1/3 (no) hence not sufficient. Statement 2: x^3 > y take x = 2 and y = 3 (no) , take x = 2, y = 1 (yes) hence not sufficient. take statement 1 and 2 together. Now the answer could be either C or E. Either y is -ve or postive. If y is -ve then x >y always holds true. If y is +ve then x>y^2 and x^3>y => x^6 > y^2 divide both the inequalities: x^5 >1 => x >1. Since square root of x (> 1) is greater than y => x>y. Hence C. The graphical approach is good, but its essential to understand that how the inequalities behaves in different domains. Yeah kinda tough indeed Hey gupreet or anyone how did you get to this? If y is +ve then x>y^2 and x^3>y => x^6 > y^2 Like from both statements to the x^6 > y^2? Thanks Cheers! J Kudos rain! If y is positive and x^3>y, it means x^3 is also positive (since it is greater than y which is positive). If both sides of an inequality are positive, you can square the inequality. x^3>y (x^3)^2>y^2 x^6 > y^2 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  18 Apr 2014, 03:04
shrouded1 wrote:
I thought this was a really tough question !

Is x > y ?

(1) \sqrt{x} > y
(2) x^3 > y

Statement I is insufficient:

x = 4 and y = 3 then x is greater than y
x = 1/4 and y = 1/3 then x is not greater than y

Statement II is insufficient:
x = 4 and y = 2 then x is greater than y
x = -1/4 and y = -1/2 then x is not greater than y

Combining both we can clearly see that:
x^1/2 > y
x^3 > y

If we plug in positive fractions or positive numbers each time x is greater than y. Hence answer is C.
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  22 Jun 2014, 18:18
Wow...I was totally stumped by this question. I wonder if this is solvable in two minutes? Its not for me ..at least not as of now...
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Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  06 Jul 2014, 23:10
Bunuel wrote:
shrouded1 wrote:
I thought this was a really tough question !

Is x > y ?

(1) \sqrt{x} > y
(2) x^3 > y

Is x>y?

(1) \sqrt{x}>y --> if x=4 and y=1 then the answer will be YES but if x=\frac{1}{4} and y=\frac{1}{3} then the answer will be NO. Two different answers, hence not sufficient.

Note that from this statement we can derive that x\geq{0} because an expression under the square root cannot be negative.

(2) x^3>y --> if x=4 and y=1 then the answer will be YES but if x=2 and y=3 then the answer will be NO. Two different answers, hence not sufficient.

(1)+(2) From (1) we have that x\geq{0}. Now, \sqrt{x}, x, x^3 can be positioned on a number line only in 2 ways:

1. 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^3), so if we have this case answer is always YES: y<x.

2. For 0\leq{x}<1: 0----x^3----x----\sqrt{x}----1, so 0\leq{x^3}\leq{x}\leq{\sqrt{x}}. y is somewhere in green zone (as y<\sqrt{x} and y<x^3), so if we have this case answer is always YES: y<x.

So in both cases y<x. Sufficient.

Hope it's clear.

when if x=1/4 and y=1/3 then \sqrt{X} = 1/2, and 1/2 > 1/3. You have chosen wrong plugin data here.
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y [#permalink]  07 Jul 2014, 00:19
Expert's post
honchos wrote:
Bunuel wrote:
shrouded1 wrote:
I thought this was a really tough question !

Is x > y ?

(1) \sqrt{x} > y
(2) x^3 > y

Is x>y?

(1) \sqrt{x}>y --> if x=4 and y=1 then the answer will be YES but if x=\frac{1}{4} and y=\frac{1}{3} then the answer will be NO. Two different answers, hence not sufficient.

Note that from this statement we can derive that x\geq{0} because an expression under the square root cannot be negative.

(2) x^3>y --> if x=4 and y=1 then the answer will be YES but if x=2 and y=3 then the answer will be NO. Two different answers, hence not sufficient.

(1)+(2) From (1) we have that x\geq{0}. Now, \sqrt{x}, x, x^3 can be positioned on a number line only in 2 ways:

1. 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^3), so if we have this case answer is always YES: y<x.

2. For 0\leq{x}<1: 0----x^3----x----\sqrt{x}----1, so 0\leq{x^3}\leq{x}\leq{\sqrt{x}}. y is somewhere in green zone (as y<\sqrt{x} and y<x^3), so if we have this case answer is always YES: y<x.

So in both cases y<x. Sufficient.

Hope it's clear.

when if x=1/4 and y=1/3 then \sqrt{X} = 1/2, and 1/2 > 1/3. You have chosen wrong plugin data here.

Nope.

If x=\frac{1}{4} and y=\frac{1}{3}, then (\sqrt{x}=\frac{1}{2})>(y=\frac{1}{4}) (statement is satisfied) but (x=\frac{1}{4})<(y=\frac{1}{3}) giving a NO answer to the question.
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Re: Is x > y ? (1) x^(1/2)>y (2) x^3>y   [#permalink] 07 Jul 2014, 00:19
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