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

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Is |x^2|<|x^4|?  [#permalink]

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New post 20 Sep 2017, 23:56
00:00
A
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D
E

Difficulty:

  55% (hard)

Question Stats:

61% (01:44) correct 39% (01:43) wrong based on 159 sessions

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Is \(|x^2|<|x^4|\)?

1) \(x<-1\)
2) \(|x|<|x^3|\)

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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 09:46
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
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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 10:36
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?
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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 10:53
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?
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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 10:57
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
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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 11:02
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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 21 Sep 2017, 11:37
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
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Re: Is |x^2|<|x^4|?  [#permalink]

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New post 24 Sep 2017, 18:21
=>

|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
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Re: Is |x^2|<|x^4|?  [#permalink]

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Re: Is |x^2|<|x^4|?   [#permalink] 09 Oct 2018, 22:45
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