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# x > 1

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x > 1 [#permalink]  17 Oct 2017, 14:51
Expert's post
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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
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Re: x > 1 [#permalink]  18 Oct 2017, 04:41
1
KUDOS
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
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Re: x > 1 [#permalink]  20 May 2018, 04:38
3
KUDOS
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
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Re: x > 1 [#permalink]  20 May 2018, 09:25
1
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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
_________________
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Re: x > 1 [#permalink]  20 May 2018, 19:14
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
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Re: x > 1 [#permalink]  21 May 2018, 04:27
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
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Re: x > 1 [#permalink]  21 May 2018, 06:09
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
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Re: x > 1 [#permalink]  30 Aug 2018, 07:33
1
KUDOS
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
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Re: x > 1 [#permalink]  02 Sep 2018, 02:40
1
KUDOS
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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