Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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.

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.
_________________

Sandy If you found this post useful, please let me know by pressing the Kudos Button

Re: Compare for x > 0 [#permalink]
20 Jan 2017, 15:38

2

This post received 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. Answer is B.

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

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Dayemails

greprepclubot

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