 It is currently 14 Dec 2019, 15:10 ### GMAT Club Daily Prep

#### 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

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. # x > 1  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Founder  Joined: 18 Apr 2015
Posts: 9036
Followers: 180

Kudos [?]: 2143 , given: 8371

Expert's post 00:00

Question Stats: 65% (00:47) correct 34% (00:44) wrong based on 49 sessions

$$x > 1$$

 Quantity A Quantity B $$\frac{x}{x+1}$$ $$\frac{-x}{1-x}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Retired Moderator Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 146

Kudos [?]: 2346  , given: 393

5
KUDOS
Expert's post
Explanation

Here we have $$x > 1$$.

Now we can say that $$x < x+1$$. So rewriting $$\frac{x}{x+1} < 1$$ . Hence Quantity A is always less than 1.

Now we can say that $$x > x-1$$. So rewriting $$\frac{x}{x-1} > 1$$ . Multiplying -1 to the numerator or denominator $$\frac{-x}{1-x} > 1$$. Hence Quantity B is always greater than 1.

So combining these two Quantity A < 1 < Quantity B. Hence option B is correct.
_________________

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

Try our free Online GRE Test GRE Instructor Joined: 10 Apr 2015
Posts: 2632
Followers: 96

Kudos [?]: 2850  , given: 45

4
KUDOS
Expert's post
Carcass wrote:

$$X > 1$$

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

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

First recognize that we can rewrite quantity B by factoring out a -1 from the numerator and denominator.
That is: -x = (-1)(x) and 1-x = -1(-1 + x) = -1(x - 1)
So, -x/(1-x) = (-1)(x)/(-1)(x - 1) = x/(x - 1)

So we get:
Quantity A: x/(x + 1)
Quantity B: x/(x - 1)

Now let's find a common denominator.
To do so, we'll take Quantity A and multiply numerator and denominator by (x - 1)
And we'll take Quantity B and multiply numerator and denominator by (x + 1)

When we do this, we get:
Quantity A: (x² - x)/(x² - 1)
Quantity B: (x² + x)/(x² - 1)

Next, since x > 1, we know that x² > 1, which means x² - 1 is POSITIVE
As such, we can multiply both quantities by x² - 1 to get:
Quantity A: x² - x
Quantity B: x² + x

Now it's pretty easy from here. Subtract x² from both quantities to get:
Quantity A: -x
Quantity B: x

Add x to both quantities to get:
Quantity A: 0
Quantity B: 2x

Since x is POSITIVE, 2x must be POSITIVE, which means the correct answer is B

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Founder  Joined: 18 Apr 2015
Posts: 9036
Followers: 180

Kudos [?]: 2143  , given: 8371

2
KUDOS
Expert's post
Explanation

Plugin numbers > 1, for instance 3 or $$\frac{5}{2}$$. B will be always greater.

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. GRE Instructor Joined: 10 Apr 2015
Posts: 2632
Followers: 96

Kudos [?]: 2850  , given: 45

2
KUDOS
Expert's post
Carcass wrote:
$$x > 1$$

 Quantity A Quantity B $$\frac{x}{x+1}$$ $$\frac{-x}{1-x}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

We can rewrite (-x)/(1-x) in a "nicer" way.
Given: (-x)/(1-x)
Factor -1 from top and bottom to get: (-1)(x)/(-1)(-1 + x)
Rewrite part in red as follows: (-1)(x)/(-1)(x - 1)
The -1's cancel out to get: x/(x - 1)
In other words, (-x)/(1-x) = x/(x - 1)

We have:
Quantity A: x/ x + 1)
Quantity B: x/(x - 1)

Since x > 1, we know that x is POSITIVE
So, we can safely divide both quantities by x to get:
Quantity A: 1/(x + 1)
Quantity B: 1/(x - 1)

Also, since x > 1, we know that (x - 1) is POSITIVE
So, we can safely multiply both quantities by (x - 1) to get:
Quantity A: (x - 1)/(x + 1)
Quantity B: 1

At this point, we might already see that 1 must be greater than (x - 1)/(x + 1)
However, let's keep going with our strategy....

Since x > 1, we know that (x + 1) is POSITIVE
So, we can safely multiply both quantities by (x + 1) to get:
Quantity A: (x - 1)
Quantity B: (x + 1)

Subtract x from both quantities to get:
Quantity A: -1
Quantity B: 1

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com Intern Joined: 11 Jan 2018
Posts: 44
Followers: 0

Kudos [?]: 40  , given: 7

1
KUDOS
In such questions, plugin is not a good strategy.
Always simplify it first as much as you can, then go to see which Quantity is greater. Here's how you should do:

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

We can write Quantity B as: x/(x-1)

As we know x is positive and greater than 1, so we can cancel out x on both sides of the Quantity.
(Remember that Quantitative comparison has rule similar to inequality, so if we divide both sides by any positive number, inequality will not change;.

Thus, we'll get

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

Now, multiplying both sides by (x+1)(x-1), we'll get

Quantity A: (x-1)
Quantity B: (x+1)

Thus,
Quantity B > Quantity A

So, Choice B is Correct.
_________________

Persistence >>>>>>> Success

Don't say thanks, just give KUDOS.
1 kudos = 1000 Thanks

Manager Joined: 22 Feb 2018
Posts: 162
Followers: 2

Kudos [?]: 125 , given: 22

correct: B
x is a positive integer, so x+1 is more than x, and x divided by x+1 is something less than 1
we can write -x/ 1-x as x / x-1 by multiplying both the numerator and the denominator by -1. As x is a positive integer, x-1 is less than x and x divided by a thing less than x is something more than 1. So B is bigger than A.

_________________ Intern Joined: 05 Jun 2017
Posts: 8
Followers: 0

Kudos [?]: 8  , given: 0

1
KUDOS
X/X+1 ? -X/1-X
As we know x>1
So, B both A nd B will always be +ve
Re write B as X/X-1
now both the numerators are equal. W just have to compare denominator now
As X-1< X+1(We know that X>1, so X can not be negative or 1)
Hence B > A Re: x > 1   [#permalink] 24 Apr 2018, 18:52
Display posts from previous: Sort by

# x > 1  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.