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

Question Stats: 32% (00:41) correct 67% (00:45) wrong based on 67 sessions

$$\frac{2}{d}= \frac{2-d}{d-2}$$

 Quantity A Quantity B d 0

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

_________________ GRE Instructor Joined: 10 Apr 2015
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Re: 2/d= 2-d/d-2 [#permalink]
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KUDOS
Expert's post
Carcass wrote:

$$\frac{2}{d}= \frac{2-d}{d-2}$$

 Quantity A Quantity B d 0

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.

Great question!!!!!

Given: $$\frac{2}{d}= \frac{2-d}{d-2}$$

Cross multiply to get: 2(d - 2) = d(2 - d)

Expand: 2d - 4 = 2d - d²
Subtract 2d from both sides to get: -4 = -d²
Multiply both sides by -1 to get: 4 = d²
So, either d = 2 or d = -2
It SEEMS that we have two solutions, but this is not the case

If we plug d = -2 into the given equation,$$\frac{2}{d}= \frac{2-d}{d-2}$$, we get: $$\frac{2}{-2} = \frac{4}{-4}$$
Since this equation checks out, we can conclude that d = -2 is a valid solution

HOWEVER, if we plug d = 2 into the given equation,$$\frac{2}{d}= \frac{2-d}{d-2}$$, we get: $$\frac{2}{2} = \frac{0}{0}$$
Since this equation does NOT check out, we can see that d = 2 is NOT a valid solution

Since there's only one possible value of d (d = -2)

So, we get:
Quantity A: -2
Quantity B: 0

[Reveal] Spoiler:
B

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Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Day emails Intern Joined: 17 Jul 2017
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Re: 2/d= 2-d/d-2 [#permalink]
1
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Great question. Please do post some more like this?
Moderator  Joined: 18 Apr 2015
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Re: 2/d= 2-d/d-2 [#permalink]
Expert's post Intern Joined: 23 Nov 2017
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Re: 2/d= 2-d/d-2 [#permalink]
1
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I am not sure mine was the best approach but it did work.

Just by looking at the denominators, we know d will not be equal 0 or 2 because if d = (0 or 2), the denominators would be 0 which is undefined.

What happens if d is a positive number?

if d = 1 then you end up with 2 = -1 which is false.
If d is greater than 2, then 2/d will ALWAYS be a positive number. The numerator (2-d) will ALWAYS be a negative number and the denominator (d-2) will ALWAYS be a positive number. Since a positive number divided by a negative number always equals a negative number, you know d cannot be a positive number since d/2 is positive and 2-d/d-2 is negative.

What if d is less than 0?

When d is a negative number, 2/d will ALWAYS be negative. The numerator (2 - d) will ALWAYS be a positive number. The denominator (d - 2) will ALWAYS be negative. A positive number divided by a negative number will always be negative.

We do not know what d will be, but at least we know it will be a negative number because that is the only way both sides of the equation will have the same sign. Since 0 is more than any negative number, we can conclude quantity b is bigger.

I hope i didn't make a mistake here. If I did, I apologize in advance. Intern Joined: 11 Jan 2018
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Re: 2/d= 2-d/d-2 [#permalink]
1
KUDOS
Great question.
It was tricky one.

After solving the equation, we'll get
either d = 2 or d = -2

But d cannot be equals to 2, because the equation will become undefined.

Thus d = -2

So, Quantity B is greater.
Choice B correct.
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Last edited by GREMasterBlaster on 04 Mar 2018, 01:42, edited 1 time in total.
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Re: 2/d= 2-d/d-2 [#permalink]
great question, thanks, I just unconscionably assumed that it's D, since the d yielded -+2.
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Re: 2/d= 2-d/d-2 [#permalink]
tricky question. I thought we could not do cross multiplication due to being unsure whether denominator was going to be 0 or not. It turns out we need to assume it's not going to be 0. Intern Joined: 09 Dec 2018
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Re: 2/d= 2-d/d-2 [#permalink]
1
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(a-b)/(b-a) is always equal to -1, so it simplifies to 2/d = -1, which means d is negative. Answer B.
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Re: 2/d= 2-d/d-2 [#permalink]
Expert's post
Carcass wrote:

$$\frac{2}{d}= \frac{2-d}{d-2}$$

 Quantity A Quantity B d 0

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.

You can cross multiply as shown above or range fractions to get the answer straight..
$$\frac{2}{d}= \frac{2-d}{d-2}$$..
$$\frac{2}{d}= \frac{-(d-2)}{(d-2)}$$=-1..
So $$\frac{2}{d}=-1$$..
Only possibility is d=-2

Hence B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: 2/d= 2-d/d-2   [#permalink] 13 Dec 2018, 00:49
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