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TAGS: Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2973  , given: 394

Compare for x > 0 [#permalink]
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Expert's post 00:00

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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Sandy
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Re: Compare for x > 0 [#permalink]
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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
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Re: Compare for x > 0 [#permalink]
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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. GRE Instructor Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4651  , given: 70

Re: Compare for x > 0 [#permalink]
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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

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_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  GRE Instructor Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4651  , given: 70

Re: Compare for x > 0 [#permalink]
1
KUDOS
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

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_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  GRE Instructor Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4651  , given: 70

Re: Compare for x > 0 [#permalink]
1
KUDOS
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
If you enjoy my solutions, you'll like my GRE prep course.  Re: Compare for x > 0   [#permalink] 14 Dec 2018, 06:48
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