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TAGS: Founder  Joined: 18 Apr 2015
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4 - x^2 [#permalink]
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Expert's post 00:00

Question Stats: 67% (00:30) correct 32% (00:22) wrong based on 34 sessions

 Quantity A Quantity B $$4 - x^2$$ $$5$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for right answer and explanation
[Reveal] Spoiler: OA

_________________ Manager Joined: 02 Jan 2018
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Re: 4 - x^2 [#permalink]
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Quantity B is greater. As x=+2 or -2, which are anyways smaller than 5 Intern Joined: 18 May 2016
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Re: 4 - x^2 [#permalink]
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Note that x² will always be a positive number (or 0) and thus in the equation 4 - x² always subtracted from four.
As 4 < 5, there is no number that can be subtracted from 4 to yield a number equal to or bigger than 5.
Correct answer is B.
Intern Joined: 24 Jan 2018
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Re: 4 - x^2 [#permalink]
B
Intern Joined: 17 Feb 2018
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Re: 4 - x^2 [#permalink]
if x=i i^2=-1 4-(-1)=5
why the answer isn't D
Founder  Joined: 18 Apr 2015
Posts: 6647
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Kudos [?]: 1275 , given: 6017

Re: 4 - x^2 [#permalink]
Expert's post
It is impossible.

$$x^2 - 4 = (x-2)(x+2)$$.

The roots are ONLY $$x=2$$ and $$x=-2$$

B is always bigger than A.

Hope this helps.

regards
_________________ GRE Instructor Joined: 10 Apr 2015
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Re: 4 - x^2 [#permalink]
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Expert's post
Carcass wrote:

 Quantity A Quantity B $$4 - x^2$$ $$5$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for right answer and explanation

We can solve this question using matching operations

Given:
Quantity A: 4 - x²
Quantity B: 5

Add x² to both quantities to get:
Quantity A: 4
Quantity B: 5 + x²

Subtract 5 from both quantities to get:
Quantity A: -1
Quantity B: x²

IMPORTANT: x² is greater than or equal to zero for all values of x
So, Quantity B is definitely greater than -1

Answer: B

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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails GRE Instructor Joined: 10 Apr 2015
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Re: 4 - x^2 [#permalink]
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Expert's post
hugebigmac wrote:
if x=i i^2=-1 4-(-1)=5
why the answer isn't D

ASIDE (for others wondering how i^2 = -1): i represents a complex number (aka imaginary number) such that i^2 = -1)

Good idea, hugebigmac, but all questions on the GRE are restricted to real numbers.

Cheers,
Brent
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Intern Joined: 24 Feb 2018
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Re: 4 - x^2 [#permalink]
B
Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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Kudos [?]: 79 , given: 99

Re: 4 - x^2 [#permalink]
Carcass wrote:
It is impossible.

$$x^2 - 4 = (x-2)(x+2)$$.

The roots are ONLY $$x=2$$ and $$x=-2$$

B is always bigger than A.

Hope this helps.

regards

Dear Carcass, how do we know x has + and - 2 as roots. I need more clarity of topic of roots.
Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 79 , given: 99

Re: 4 - x^2 [#permalink]
I have tried plugging in the values of x = 0,1,2,-2 and 1/5 all in all B is greater in every case..

Hence answer is B
Founder  Joined: 18 Apr 2015
Posts: 6647
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Kudos [?]: 1275 , given: 6017

Re: 4 - x^2 [#permalink]
Expert's post
IshanGre wrote:
Carcass wrote:
It is impossible.

$$x^2 - 4 = (x-2)(x+2)$$.

The roots are ONLY $$x=2$$ and $$x=-2$$

B is always bigger than A.

Hope this helps.

regards

Dear Carcass, how do we know x has + and - 2 as roots. I need more clarity of topic of roots.

Hope this helps.

Regards
_________________ Re: 4 - x^2   [#permalink] 18 May 2018, 11:37
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