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Is 2x  3y < x^2 ? [#permalink]
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07 Sep 2010, 13:15
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Is 2x  3y < x^2 ? (1) 2x  3y = 2 (2) x > 2 and y > 0
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Re: Inequalities [#permalink]
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07 Sep 2010, 13:23
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Re: Inequalities [#permalink]
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07 Sep 2010, 13:32
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Thanxs Bunuel!, you rule! don't you ever think in writing a book about GMAT?
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Re: Inequalities [#permalink]
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07 Sep 2010, 13:42
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metallicafan wrote: Is \(2x  3y < x^2\) ?
(1) 2x  3y = 2 (2) x > 2 and y > 0 1. you should see you can replace the terms of 2x3y so you get 2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective)
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Re: Inequalities [#permalink]
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11 Sep 2010, 15:09
shaselai wrote: metallicafan wrote: Is \(2x  3y < x^2\) ?
(1) 2x  3y = 2 (2) x > 2 and y > 0 1. you should see you can replace the terms of 2x3y so you get 2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective) Thanks shaselai, much easier to follow.
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Re: Inequalities [#permalink]
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11 Sep 2010, 15:42
Dawgie wrote: shaselai wrote: metallicafan wrote: Is \(2x  3y < x^2\) ?
(1) 2x  3y = 2 (2) x > 2 and y > 0 1. you should see you can replace the terms of 2x3y so you get 2<x^2 ? since any number squared is positive this is SUFF 2. You can view this problem in another way: 2x will always be less than x^2 as x >2. And since y >0 that means the left side 2x3y will be even fewer than 2x so left side will always be less than x^2 SUFF (brunnel's answer is another approach so i chose this way from another pespective) Thanks shaselai, much easier to follow. Just a little correction, which makes no difference for this particular question but is very important, as GMAT likes to catch on differences like this: square of a number is nonnegative (and not positive) > \(x^2\geq{0}\), because if \(x=0\) then \(x^2=0\). Hope it helps.
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Re: Inequalities [#permalink]
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11 Sep 2010, 15:47
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In heat of solving question, I missed to notice that statement 1 is same as inquality question. I concluded with D but after spending time
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Re: Inequalities [#permalink]
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13 Sep 2010, 05:58
Bunuel,
Your explaination for why second statement alone is sufficient to answer the question proves that x(x2)+3y > o. But this does not answer whether ( 2x3y < x^2)
Can you please explain.
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Re: Inequalities [#permalink]
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13 Sep 2010, 08:21



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Re: Inequalities [#permalink]
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13 Sep 2010, 22:44
Thanks Bunuel.. Now it is clear



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Re: Is 2x  3y < x^2 ? (1) 2x  3y = 2 (2) x > 2 and y [#permalink]
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09 Apr 2013, 10:04
Dear Bunuel Need some clarification on this question, as i am getting A as an answer What i did: 2x  3y < X^2  since x^2 will be positive number i divided both sides by X^2  the equation provided became (2x3y)/x^2<0. later when i plugged in various numbers to test the validity they gave me both a Yes and a No answer. Where am i going wrong. Can you please correct me?



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Re: Is 2x  3y < x^2 ? (1) 2x  3y = 2 (2) x > 2 and y [#permalink]
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09 Apr 2013, 10:16
mbhussain, Don't divide but just subtract x2 from both sides of the equation x2 +2x  3y < 0 ==> x2  2x +3y > 0 ==> x(x2)+3y > 0 Since statement II says y > 0 then 3y is positive Also x > 2 implies x(x2) is also positive Positive + Positive will always be > 0. Hence B is sufficient. You can use numbers that meet Statement II and you'll get the same result. //kudos please, if the above explanation is good.
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Re: Inequalities [#permalink]
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04 Jul 2013, 01:43
Bunuel wrote: (2) \(x>2\) and \(y>0\) > is \(2x3y<x^2\) > is \(x(x2)+3y>0\) > as \(x>2\) then \(x(x2)\) is a positive number and as \(y>0\) then \(3y\) is also a positive number > sum of two positive numbers is more than zero, hence \(x(x2)+3y>0\) is true. Sufficient.
Answer: D.
Great Manipulation for Statement 2!
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Re: Is 2x  3y < x^2 ? [#permalink]
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Re: Is 2x  3y < x^2 ? [#permalink]
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23 Mar 2015, 10:43
I thought it was B but you are great. Posted from my mobile device
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Re: Is 2x  3y < x^2 ? [#permalink]
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23 Mar 2015, 18:28
Hi All, In this DS question, you might find that 'rewriting' the question makes it easier to answer. Either way, you'll find that a combination of logic, Number Properties and TESTing VALUES will come in handy. We're asked if 2X  3Y < X^2. You can 'rewrite' the question to ask if 2X < X^2 + 3Y. Either way, this is a YES/NO question. Fact 1: 2X  3Y = 2 Here, the 'original' version of the question is probably easier to answer, since we now have a value that we can 'substitute' in for (2X  3Y).... The question now asks..... Is 2 < X^2? X^2 can be 0 or any positive value, so with ALL possible values of X, the answer to the question is ALWAYS YES. Fact 1 is SUFFICIENT Fact 2: X > 2 and Y > 0 With this Fact, the 'rewritten' version of the question is probably easier to answer. Since we know that X > 2......2X will ALWAYS be < X^2. We also know that Y > 0, so (X^2 + 3Y) will get larger as Y gets larger. This all serves as evidence that.... 2X is ALWAYS < X^2 + 3Y. The answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT Final Answer: GMAT assassins arne't born, they're made, Rich
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Is 2x  3y < x^2 ? [#permalink]
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27 Mar 2016, 20:17
Here is a visual that should help.
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Screen Shot 20160327 at 8.17.47 PM.png [ 476.59 KiB  Viewed 1918 times ]
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Re: Is 2x  3y < x^2 ? [#permalink]
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28 Mar 2016, 05:53
metallicafan wrote: Is 2x  3y < x^2 ?
(1) 2x  3y = 2 (2) x > 2 and y > 0 Statement 1) 2x3y =2 => 3y =2x+2 The question > 2x3y<x^2 => 2xx^2<3y Comparing these e equations we get that 3y> 2xx^2 (x^2 is always positive and hence the value of 2xx^2 will always be less than 2x+2 Sufficient Statement 2)x>2, y>0 Consider, x=4 and y = 2, substituting the values of x and y in 2x3y<x^2, we get > 2<16; or x=3 and y=4 we get 2*33*4<3^2 => 612<9 or 6<9 In all the cases we get 2x3y<x^2 Sufficient. Answer D Please suggest if this approach is correct. Thanks a lot



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Re: Is 2x  3y < x^2 ? [#permalink]
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19 Oct 2016, 02:09
Hi Bunuel,
Can we not consider imaginary number such as (\sqrt{(2)}) that woud result 2 for x^2?



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Re: Is 2x  3y < x^2 ? [#permalink]
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19 Oct 2016, 02:14




Re: Is 2x  3y < x^2 ?
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