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# x > 1

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x > 1 [#permalink]  26 Nov 2017, 10:32
Expert's post
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Question Stats:

66% (00:38) correct 33% (00:46) wrong based on 18 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

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Re: x > 1 [#permalink]  26 Nov 2017, 10:36
Expert's post
Explanation

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

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Re: x > 1 [#permalink]  29 Nov 2017, 09:50
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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

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Re: x > 1 [#permalink]  01 Mar 2018, 04:59
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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.
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Re: x > 1   [#permalink] 01 Mar 2018, 04:59
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