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# Is |x^2|<|x^4|?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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21 Sep 2017, 00:56
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Difficulty:

55% (hard)

Question Stats:

63% (01:49) correct 37% (01:44) wrong based on 173 sessions

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Is $$|x^2|<|x^4|$$?

1) $$x<-1$$
2) $$|x|<|x^3|$$

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Current Student Joined: 02 Jul 2017 Posts: 290 Concentration: Entrepreneurship, Technology GMAT 1: 730 Q50 V38 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 10:46 2 2 Is $$|x^2|<|x^4|$$ ? As $$x^2$$ and $$x^4$$ will always be positive , so we have to find if $$x^2 < x^4$$ Also above case will always be true except when -1<x<1 1. as for fractions we know $$(\frac{1}{2})^4 < (\frac{1}{2})^3 <(\frac{1}{2})^2<(\frac{1}{2})$$ that is, for x between -1 and 1 and x => $$x^4 <x^2 <x$$ 2. and for x=1 => $$x =x^2 =x^4$$ So here we have to find if -1<x<1 or not. 1) x<−1 Directly tells us equation that we are looking for : that is value of x is not in between -1 and 1. So this makes above statement true. Sufficient 2) |x|<|x^3| Here we get magnitude of x is less than magnitude of $$x^3$$. Here magnitude of x cannot be in between 0 and 1 as for x between 0 and 1 $$x^3 < x$$ => $$(1/2)^3 < x$$ And as we are given magnitude comparison we can say x doesn't lie between -1 and 1. So this makes given question true Sufficient Answer: D Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 11:36 MathRevolution wrote: Is $$|x^2|<|x^4|$$? 1) $$x<-1$$ 2) $$|x|<|x^3|$$ Hi Bunuel I have a doubt here, Statement 1 specifically mentions that $$x<-1$$ but as per statement 2 either $$x<-1$$ or $$x>1$$. IN either case we will get a definite Yes for the question stem hence answer will be D But ideally both statements should provide same information. What am I missing here? Math Expert Joined: 02 Sep 2009 Posts: 58381 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 11:53 niks18 wrote: MathRevolution wrote: Is $$|x^2|<|x^4|$$? 1) $$x<-1$$ 2) $$|x|<|x^3|$$ Hi Bunuel I have a doubt here, Statement 1 specifically mentions that $$x<-1$$ but as per statement 2 either $$x<-1$$ or $$x>1$$. IN either case we will get a definite Yes for the question stem hence answer will be D But ideally both statements should provide same information. What am I missing here? What contradiction do you see between these two? _________________ Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 11:57 1 Bunuel wrote: niks18 wrote: MathRevolution wrote: Is $$|x^2|<|x^4|$$? 1) $$x<-1$$ 2) $$|x|<|x^3|$$ Hi Bunuel I have a doubt here, Statement 1 specifically mentions that $$x<-1$$ but as per statement 2 either $$x<-1$$ or $$x>1$$. IN either case we will get a definite Yes for the question stem hence answer will be D But ideally both statements should provide same information. What am I missing here? What contradiction do you see between these two? Hi, My point is that statement 1 says that x<-1 i.e x is negative But from statement 2 x>1 is also possible and will satisfy the inequality. Need clarity whether such scenario is possible in a DS question Math Expert Joined: 02 Sep 2009 Posts: 58381 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 12:02 niks18 wrote: Bunuel wrote: niks18 wrote: Hi Bunuel I have a doubt here, Statement 1 specifically mentions that $$x<-1$$ but as per statement 2 either $$x<-1$$ or $$x>1$$. IN either case we will get a definite Yes for the question stem hence answer will be D But ideally both statements should provide same information. What am I missing here? What contradiction do you see between these two? Hi, My point is that statement 1 says that x<-1 i.e x is negative But from statement 2 x>1 is also possible and will satisfy the inequality. Need clarity whether such scenario is possible in a DS question On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem. Here statement do not contradict. (1) says x < -1. (2) gives x < -1 or x > 1. Statements do NOT contradict: together they give x < -1. _________________ Retired Moderator Joined: 25 Feb 2013 Posts: 1178 Location: India GPA: 3.82 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 21 Sep 2017, 12:37 1 Thanks Bunuel for the clarification To end the confusion I guess we can directly solve the question as - Given $$|x^2|<|x^4|$$ or $$\frac{|x^4|}{|x^2|}>1$$ Hence the question stem becomes Is $$|x^2|>1$$ Statement 1: $$x<-1$$, squaring both sides we get $$x^2>1$$ (sign of inequality will reverse because $$|x|>|-1|$$) or $$|x^2|>1$$. So we get a Yes for our question stem. Hence Sufficient Statement 2: $$|x|<|x^3|$$ or $$\frac{|x^3|}{|x|}>1$$ Hence $$|x^2|>1$$. Sufficient Option D Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Is |x^2|<|x^4|? [#permalink] ### Show Tags 24 Sep 2017, 19:21 => |x^2|<|x^4| ⇔ |x^4| - |x^2| > 0 ⇔ |x^2| ( |x^2| - 1 ) >0 ⇔ |x^2| < 0 or |x^2| > 1 ⇔ |x| > 1 ⇔ x < -1 or x > 1 Condition 1) x<-1 is sufficient clearly. Condition 2) |x|<|x^3| ⇔ |x^3| - |x| > 0 ⇔ |x|( |x^2| - 1 ) > 0 ⇔ |x|( |x| + 1 ) ( |x| - 1 ) > 0 ⇔ -1 < |x| < 0 or |x| > 1 ⇔ |x| > 1 ⇔ x < -1 or x > 1 This is sufficient too. Ans: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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01 Jun 2019, 00:11
MathRevolution wrote:
Is $$|x^2|<|x^4|$$?

1) $$x<-1$$
2) $$|x|<|x^3|$$

1. Put any value of x<-1 it'll always be |x^2|<|x^4|. Satisfied.
Exception range [-1,1] avoided.

2. So, x can't be zero. Any +ve or -ve value will satisfy |x|<|x^3|

Exception range [-1,1] avoided.
So, |x^2|<|x^4| True. Put any +ve or -ve value to check. It'll satisfy.

D. Independently sufficient.

Lots of good GMAT sums exploit the anomaly of [-1,1] range.
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01 Jun 2019, 00:51
MathRevolution wrote:
Is $$|x^2|<|x^4|$$?

1) $$x<-1$$
2) $$|x|<|x^3|$$

The question asks whether x^4 > x^2

If at all it happens in -infinity to -1 and 1 to infinity.
We need to check if any of 2 gives any clue on x range.

A. Says x < -1. Perfect the equation is valid in this range.

B.says Mod(x) < mod (x3)
This equation is also valid when x< -1 and x > 1 which matches with our required range. Hence answer D is correct

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Re: Is |x^2|<|x^4|?   [#permalink] 01 Jun 2019, 00:51
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