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(x+2)(x-2)

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(x+2)(x-2) [#permalink] New post 03 Oct 2018, 23:21
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Question Stats:

56% (00:47) correct 43% (01:04) wrong based on 41 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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Re: (x+2)(x-2) [#permalink] New post 04 Oct 2018, 01:00
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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
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Re: (x+2)(x-2) [#permalink] New post 24 Oct 2018, 06:15
it was too complicated.
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Re: (x+2)(x-2) [#permalink] New post 24 Oct 2018, 08:33
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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] New post 28 Nov 2018, 12:47
Answer: A
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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