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# Compare for x > 0

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 106

Kudos [?]: 1820 [1] , given: 397

Compare for x > 0 [#permalink]  17 May 2016, 18:05
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Expert's post
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Question Stats:

80% (00:35) correct 19% (00:39) wrong based on 97 sessions
$$x > 0$$

 Quantity A Quantity B $$\frac{1}{x}$$ $$\frac{(1 + x)}{x^2}$$

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.

Practice Questions
Question: 2
Page: 81
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 106

Kudos [?]: 1820 [0], given: 397

Re: Compare for x > 0 [#permalink]  17 May 2016, 18:11
Expert's post
Explanation

Note that Quantity B, $$\frac{(1 + x)}{x^2}$$ can be expressed as $$\frac{1}{x^2}+\frac{x}{x^2}$$, which can be simplified to $$\frac{1}{x^2}+\frac{1}{x}$$.

Note that Quantity A is $$\frac{1}{x}$$, and for all nonzero values of $$x$$, $$\frac{1}{x^2} >0$$. It follows that $$\frac{1}{x^2}+\frac{1}{x} > \frac{1}{x}$$; that is, Quantity B is greater than Quantity A. Thus the correct answer is Choice B.
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Sandy
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Manager
Joined: 23 Jan 2016
Posts: 137
Followers: 3

Kudos [?]: 110 [0], given: 15

Re: Compare for x > 0 [#permalink]  18 May 2016, 00:14
As x > 0, no matter what 1/x^2 + 1/x will always be great than 1/x, Hence B
Intern
Joined: 26 Dec 2016
Posts: 4
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Kudos [?]: 7 [2] , given: 0

Re: Compare for x > 0 [#permalink]  20 Jan 2017, 15:38
2
KUDOS
Quantity A Quantity B
1/X (1+X)/X^2
Multiply both by X
1 (1+X)/X
1 1/X + X/X
1 1/X + 1
Since X Always >0 , Then Quantity B is always greater.
GRE Instructor
Joined: 10 Apr 2015
Posts: 1647
Followers: 57

Kudos [?]: 1572 [2] , given: 8

Re: Compare for x > 0 [#permalink]  25 Jan 2017, 11:10
2
KUDOS
Expert's post
sandy wrote:
$$x > 0$$

 Quantity A Quantity B $$\frac{1}{x}$$ $$\frac{(1 + x)}{x^2}$$

Another approach is to use Matching Operations

Given:
Quantity A: 1/x
Quantity B: (1 + x)

Since x ≠ 0, we can be certain that x² is POSITIVE
So, we can safely multiply both quantities by x² to get:
Quantity A: x²/x
Quantity B: (1 + x)

Simplify to get:
Quantity A: x
Quantity B: 1 + x

Subtract x from both sides to get:
Quantity A: 0
Quantity B: 1

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Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1647
Followers: 57

Kudos [?]: 1572 [0], given: 8

Re: Compare for x > 0 [#permalink]  29 Sep 2018, 07:53
Expert's post
sandy wrote:
$$x > 0$$

 Quantity A Quantity B $$\frac{1}{x}$$ $$\frac{(1 + x)}{x^2}$$

Given:
Quantity A: 1/x
Quantity B: (1 + x)/x²

USEFUL FRACTION PROPERTY: (a + b)/c = a/b + a/c

So, we can rewrite Quantity B as follows:
Quantity A: 1/x
Quantity B: 1/x² + x/x²

Simplify Quantity B:
Quantity A: 1/x
Quantity B: 1/x² + 1/x

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

Since x > 0, we know that x² > 0, which means 1/x² > 0

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_________________

Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 1647
Followers: 57

Kudos [?]: 1572 [0], given: 8

Re: Compare for x > 0 [#permalink]  14 Dec 2018, 06:48
Expert's post
sandy wrote:
$$x > 0$$

 Quantity A Quantity B $$\frac{1}{x}$$ $$\frac{(1 + x)}{x^2}$$

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.

If we're not sure how to proceed, we can always test some values to at least eliminate some answer choices.

We're told that x > 0

So, let's first test x = 1
We get:
QUANTITY A: 1/1 = 1
QUANTITY B: (1 + 1)/1² = 2/1 = B
In this case, Quantity B is greater
This means we can ELIMINATE A and C. So, if we must guess, we're down to a 50-50 proposition!

Let's test some more values.

Test x = 0.1
QUANTITY A: 1/0.1 = 10
QUANTITY B: (1 + 0.1)/0.1² = 1.1/0.01 = 110
In this case, Quantity B is greater

Test x = 3
QUANTITY A: 1/3 = 1/3
QUANTITY B: (1 + 3)/3² = 4/9
In this case, Quantity B is greater

Test x = 10
QUANTITY A: 1/3 = 1/10
QUANTITY B: (1 + 10)/10² = 11/100
In this case, Quantity B is greater

At this point, it SEEMS like Quantity B will always be greater?
Can we be 100% sure that the answer B?
No, but B would be a reasonable guess, and guess what? The correct answer IS B.

Cheers,
Brent

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Brent Hanneson – Creator of greenlighttestprep.com

Re: Compare for x > 0   [#permalink] 14 Dec 2018, 06:48
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