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# (x+2)(x-2)

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Founder
Joined: 18 Apr 2015
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(x+2)(x-2) [#permalink]  03 Oct 2018, 23:21
2
KUDOS
Expert's post
00:00

Question Stats:

58% (01:06) correct 41% (01:13) wrong based on 53 sessions
 Quantity A Quantity B $$(x+2)(x-2)$$ $$\frac{-5(x^2-25)(x-1)}{(x+5)(x^2-6x+5)}$$

Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Intern
Joined: 20 Mar 2018
Posts: 34
GRE 1: Q164 V150
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Kudos [?]: 24 [1] , given: 2

Re: (x+2)(x-2) [#permalink]  04 Oct 2018, 01:00
1
KUDOS
On simplifying quantity B, it reduces to only -5.

Quantity A: x^2 - 4
As x^2 will always be greater than or equal to 0, the minimum value of quantity A is -4.

Hence A
Manager
Joined: 23 Oct 2018
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Re: (x+2)(x-2) [#permalink]  24 Oct 2018, 06:15
it was too complicated.
Supreme Moderator
Joined: 01 Nov 2017
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Kudos [?]: 111 [1] , given: 4

Re: (x+2)(x-2) [#permalink]  24 Oct 2018, 08:33
1
KUDOS
Expert's post
Carcass wrote:
 Quantity A Quantity B $$(x+2)(x-2)$$ $$\frac{-5(x^2-25)(x-1)}{(x+5)(x^2-6x+5)}$$

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

A=($$(x+2)(x-2)=x^2-4$$).. min value will be -4 as $$x^2\geq{0}$$
B=$$\frac{-5(x^2-25)(x-1)}{(x+5)(x^2-6x+5)}=\frac{-5(x-5)(x+5)(x-1)}{(x+5)(x^2-5x-x-5)}=\frac{-5(x+5)(x-1)(x-5)}{(x+5)(x-1)(x-5)}=-5$$

So A>B

A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: (x+2)(x-2) [#permalink]  28 Nov 2018, 12:47
We just try to simplify them:

A= (x+2)(x-2) = x^2-4

B= -5 * (x^2 - 25)(x-1) / (x+5)(x^2-6x+5) =
-5 * (x-5)(x+5)(x-1) / (x+5)(x-5)(x-1) =
-5

A= x^2 -4 and B=-5, as x^2 is something positive, it can at least be zero, so x^2-4 is definitely more than -4, So A is bigger than B.
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Re: (x+2)(x-2)   [#permalink] 28 Nov 2018, 12:47
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