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# Which is greater: (x-2)^2 or x^2-4

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Senior Manager
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Which is greater: (x-2)^2 or x^2-4 [#permalink]  01 Oct 2017, 22:27
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Question Stats:

69% (00:30) correct 30% (00:34) wrong based on 13 sessions
 Quantity A Quantity B $$(x-2)^2$$ $$x^2-4$$

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

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[Reveal] Spoiler: OA
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Re: Which is greater: (x-2)^2 or x^2-4 [#permalink]  01 Oct 2017, 23:40
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Bunuel wrote:
 Quantity A Quantity B (x-2)^2 x^2-4

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

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Since no information is given for x, so x can be any value

LEt consider x=2

then QTYA A =$$(2-2)^2 = 0$$

QTY B=$$2^2 - 4 = 0$$ . QTY A = QTY b

Let consider x= 5

QTY A = $$3^2 = 9$$

QTY B =$$25-4 = 21$$

SO QTY A< QTY B

Hence the option is D.
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Re: Which is greater: (x-2)^2 or x^2-4 [#permalink]  02 Mar 2018, 12:30
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After simplification of Quantity A
$$(x-2)^2$$ = $$x^2$$ + 4 - 4x

We can subtract $$x^2$$ from both Quantity A and Quantity B, because it will not have any impact i.e the greater quantity will remain greater and by same margin.

So we'll get:

Quantity A: 4 - 4x
Quantity B: 4x

Similarly, we can add 4x on both Quantities, because it will not impact or change the greater quantity to less quantity.

Thus, we'll get

Quantity A: 4
Quantity B: 8x

As we don't know whether x is positive, 0 or negative. So Choice D is correct.
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Last edited by GREMasterBlaster on 03 Mar 2018, 03:47, edited 1 time in total.
Manager
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Re: Which is greater: (x-2)^2 or x^2-4 [#permalink]  02 Mar 2018, 19:11
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(x-2)^2 = x^2 -4x + 4
x^2 -4 ? x^2 -4x + 4
-4 ? 4 - 4x
for x=2 these are equal.
for x < 2, -4 is less.
for x > 2, -4 is more.
so we can not recognize their relationship and D is correct.
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Re: Which is greater: (x-2)^2 or x^2-4 [#permalink]  04 Mar 2018, 01:10
x^2-4x+4 and x^2-4
add +4 to both sides yields: x^2-4x+8 and x^2
then, subtract x^2 from both sides
-4x+4 and 0
then if x=0, then QA equals 4, QB 0
if x=1, then the quantities are equal.
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Re: Which is greater: (x-2)^2 or x^2-4   [#permalink] 04 Mar 2018, 01:10
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