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GRE Math Challenge #95- x^2 + 2x + 1 or x^2

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sandy
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GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink] New post   Updated on: 20 Feb 2020, 00:35
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Quantity A
Quantity B
\(x^2 + 2x + 1\)
\(x^2\)



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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D

Originally posted by sandy on 09 May 2015, 11:12.
Last edited by Carcass on 20 Feb 2020, 00:35, edited 1 time in total.
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GreenlightTestPrep
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GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink] New post   07 Aug 2017, 08:14
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sandy wrote:
Quantity A: \(x^2 + 2x + 1\)

Quantity B: \(x^2\)

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined


Given:
Quantity A: x² + 2x + 1
Quantity B: x²

Subtract x² from both quantities to get:
Quantity A: 2x + 1
Quantity B: 0

Now let's test some values of x

Try x = 1
We get:
Quantity A: 2(1) + 1 = 3
Quantity B: 0
In this case, Quantity A is greater

Try x = -1
We get:
Quantity A: 2(-1) + 1 = -1
Quantity B: 0
In this case, Quantity B is greater

Answer: D

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sheila
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GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink] New post   12 Jul 2021, 07:21
Hello, I'm curious to know why you would not solve this by factoring (x-1)2 for A and x2 for B? Could you please explain how?
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Re: GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink] New post   04 Aug 2022, 04:08
1
Quantity A can be written as
\((x + 1)^2\)

Which is greater than \(x^2\) when x is positive, and smaller than \(x^2\) when x is negative.

Hence, the answer is D
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Re: GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink] New post   10 Aug 2024, 10:45
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: GRE Math Challenge #95- x^2 + 2x + 1 or x^2 [#permalink]
10 Aug 2024, 10:45
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