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4 - x^2

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Carcass
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4 - x^2 [#permalink] New post   23 Jan 2018, 14:46
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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.

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B
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sharmaapeksha960
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Re: 4 - x^2 [#permalink] New post   24 Jan 2018, 02:48
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Quantity B is greater. As x=+2 or -2, which are anyways smaller than 5
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Re: 4 - x^2 [#permalink] New post   25 Jan 2018, 01:48
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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.
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Re: 4 - x^2 [#permalink] New post   26 Jan 2018, 11:59
B
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Re: 4 - x^2 [#permalink] New post   24 Feb 2018, 10:43
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if x=i i^2=-1 4-(-1)=5
why the answer isn't D
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Re: 4 - x^2 [#permalink] New post   24 Feb 2018, 11:55
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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
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Re: 4 - x^2 [#permalink] New post   24 Feb 2018, 13:38
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Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project




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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Re: 4 - x^2 [#permalink] New post   24 Feb 2018, 13:40
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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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PrachiR
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Re: 4 - x^2 [#permalink] New post   24 Feb 2018, 16:30
B
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Re: 4 - x^2 [#permalink] New post   17 May 2018, 23:35
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.
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IshanGre
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Re: 4 - x^2 [#permalink] New post   17 May 2018, 23:36
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
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Re: 4 - x^2 [#permalink] New post   18 May 2018, 11:37
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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
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Kimberly99
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Re: 4 - x^2 [#permalink] New post   14 Feb 2023, 00:26
Hi Brent GreenlightTestPrep, If I subtract 4 from both sides, I ended up A: -x^2 B: 1 . Depends on x vaule, A can be the same (if x=1) or bigger than B (if x=2). Therefore is D. Where is my understanding going wrong here? Thanks Brent
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