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Founder  Joined: 18 Apr 2015
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Expert's post 00:00

Question Stats: 47% (00:57) correct 52% (00:57) wrong based on 44 sessions

$$x > 1$$

 Quantity A Quantity B $$\frac{x+5}{x}$$ $$\frac{(x-1) +5}{x-1}$$

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

Last edited by amorphous on 20 Sep 2018, 01:58, edited 2 times in total.
Edit the OA Director Joined: 03 Sep 2017
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Here we are asked to compare $$\frac{x+5}{x}$$ and $$\frac{x+4}{x-1}$$. Given that x > 1, we just have to try and substitute integers from 2 on. This leads to the result that quantity B is greater. Answer B Manager Joined: 29 Nov 2017
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GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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I took X>1 as 3/2 = 1.5

and it turns out that option A is greater than B at this scenario.

However when I took 2 and 3 ..option B indeed truned out to be greater than A. Founder  Joined: 18 Apr 2015
Posts: 6885
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Kudos [?]: 1338  , given: 6306

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Expert's post
Think theoretically, it is much better than plug-in number this time. It is cumbersome.

QA $$\frac{x}{x} + \frac{5}{x}$$

QB $$\frac{(x-1)}{(x-1)} + \frac{5}{(x-1)}$$

$$\frac{x}{x}$$ and $$\frac{(x-1)}{(x-1)}$$ are both equal to one

so we will end up with $$\frac{5}{x}$$ and $$\frac{5}{x-1}$$

Now, if you plug an integer B > A but if you plug a fraction A > B. So the answer is D but the OE in the book is B.

Clearly a mistake. Hope this helps.

Regards
_________________
Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 79 , given: 99

Carcass wrote:
Think theoretically, it is much better than plug-in number this time. It is cumbersome.

QA $$\frac{x}{x} + \frac{5}{x}$$

QB $$\frac{(x-1)}{(x-1)} + \frac{5}{(x-1)}$$

$$\frac{x}{x}$$ and $$\frac{(x-1)}{(x-1)}$$ are both equal to one

so we will end up with $$\frac{5}{x}$$ and $$\frac{5}{x-1}$$

Now, if you plug an integer B > A but if you plug a fraction A > B. So the answer is D but the OE in the book is B.

Clearly a mistake. Hope this helps.

Regards

Great-- looks like I am learning now ..Thanks to this forum .what is OE book?
Founder  Joined: 18 Apr 2015
Posts: 6885
Followers: 114

Kudos [?]: 1338 , given: 6306

Expert's post
Actually the explanation I gave you. It takes into account only integers greater than one, which is impossible because you must take in account even fractions.

Hope this helps.
Regards
_________________
Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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Kudos [?]: 79 , given: 99

Carcass wrote:
Actually the explanation I gave you. It takes into account only integers greater than one, which is impossible because you must take in account even fractions.

Hope this helps.
Regards

Thanks GRE Forum Moderator
Joined: 17 May 2018
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I can't seem to make a clear decision. Everytime I am trying out any value I am getting B>A. Now, let's say after simplification we are dealing with

Quantity A Quantity B

1/X on side 1/ (X-1)

But if I take let's say X to be a fraction i.e. 8/3 (X has to be greater than 1)
then on side A we get 3/8= 0.375
and on side B we get 3/5= 0.6. in this case B>A

Again, when I try out an integer, say, 5,
I get 1/5 on side A
and 1/4 on side B.

In fact, when I apply the theory I get, that quantity B should be greater. Since X>1 that means X is a positive number. So, when X is in the denominator the result should be less than when a value less than X is in the denominator the result should be greater, provided that the numerator remains the same.

Could please explain at length. Cause I can't figure out a case where A>B.

Sincerely,
Scrat Intern Joined: 02 Jul 2018
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IshanGre wrote:
Carcass wrote:
Think theoretically, it is much better than plug-in number this time. It is cumbersome.

QA $$\frac{x}{x} + \frac{5}{x}$$

QB $$\frac{(x-1)}{(x-1)} + \frac{5}{(x-1)}$$

$$\frac{x}{x}$$ and $$\frac{(x-1)}{(x-1)}$$ are both equal to one

so we will end up with $$\frac{5}{x}$$ and $$\frac{5}{x-1}$$

Now, if you plug an integer B > A but if you plug a fraction A > B. So the answer is D but the OE in the book is B.

Clearly a mistake. Hope this helps.

Regards

Great-- looks like I am learning now ..Thanks to this forum .what is OE book?

This explanation is not right. Clearly, with x > 1, B is always greater, regardless of what you take for x, an integer or fraction>1

even after reducing it to

\frac{5}{x} and \frac{5}{(x-1)}, given that x>1 it can be clearly observed that \frac{5}{(x-1)} has a smaller denominator than \frac{5}{x} while the numerator in both cases is same. Hence \frac{5}{(x-1)} has to be greater. Correct answer is B. Re: x > 1   [#permalink] 02 Sep 2018, 02:40
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