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Compare for x > 0

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Retired Moderator
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Compare for x > 0 [#permalink] New post 17 May 2016, 18:05
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Question Stats:

73% (00:41) correct 26% (00:57) wrong based on 262 sessions
\(x > 0\)

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


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.




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

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Re: Compare for x > 0 [#permalink] New post 18 May 2016, 00:14
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As x > 0, no matter what 1/x^2 + 1/x will always be great than 1/x, Hence B
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Re: Compare for x > 0 [#permalink] New post 20 Jan 2017, 15:38
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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.
Answer is B.
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GRE Instructor
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Joined: 10 Apr 2015
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Re: Compare for x > 0 [#permalink] New post 25 Jan 2017, 11:10
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Expert's post
sandy wrote:
\(x > 0\)

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




Explanation

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

Answer: B

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1 KUDOS received
GRE Instructor
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Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4651 [1] , given: 70

Re: Compare for x > 0 [#permalink] New post 29 Sep 2018, 07:53
1
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Expert's post
sandy wrote:
\(x > 0\)

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



Another approach

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

Answer: B

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1 KUDOS received
GRE Instructor
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Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4651 [1] , given: 70

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