It is currently 13 Dec 2018, 22:28

### 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

# 2/d= 2-d/d-2

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5166
Followers: 77

Kudos [?]: 1033 [0], given: 4655

2/d= 2-d/d-2 [#permalink]  21 Jun 2017, 13:43
Expert's post
00:00

Question Stats:

33% (00:39) correct 66% (00:46) wrong based on 53 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
Posts: 1238
Followers: 46

Kudos [?]: 1126 [2] , given: 7

Re: 2/d= 2-d/d-2 [#permalink]  27 Jun 2017, 11:13
2
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

RELATED VIDEO

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Intern
Joined: 17 Jul 2017
Posts: 15
Followers: 0

Kudos [?]: 7 [1] , given: 13

Re: 2/d= 2-d/d-2 [#permalink]  26 Jul 2017, 01:20
1
KUDOS
Great question. Please do post some more like this?
Moderator
Joined: 18 Apr 2015
Posts: 5166
Followers: 77

Kudos [?]: 1033 [0], given: 4655

Re: 2/d= 2-d/d-2 [#permalink]  26 Jul 2017, 04:27
Expert's post
Intern
Joined: 23 Nov 2017
Posts: 45
Followers: 0

Kudos [?]: 44 [1] , given: 0

Re: 2/d= 2-d/d-2 [#permalink]  24 Nov 2017, 02:59
1
KUDOS
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
Posts: 44
Followers: 0

Kudos [?]: 26 [1] , given: 7

Re: 2/d= 2-d/d-2 [#permalink]  01 Mar 2018, 04:48
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.
_________________

Persistence >>>>>>> Success

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

Last edited by GREMasterBlaster on 04 Mar 2018, 01:42, edited 1 time in total.
Manager
Joined: 26 Jun 2017
Posts: 104
Followers: 0

Kudos [?]: 38 [0], given: 38

Re: 2/d= 2-d/d-2 [#permalink]  04 Mar 2018, 01:35
great question, thanks, I just unconscionably assumed that it's D, since the d yielded -+2.
_________________

What you think, you become.

Intern
Joined: 04 Dec 2018
Posts: 9
Followers: 0

Kudos [?]: 4 [0], given: 1

Re: 2/d= 2-d/d-2 [#permalink]  11 Dec 2018, 17:16
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
Posts: 1
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: 2/d= 2-d/d-2 [#permalink]  12 Dec 2018, 09:26
1
KUDOS
(a-b)/(b-a) is always equal to -1, so it simplifies to 2/d = -1, which means d is negative. Answer B.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 203
Followers: 3

Kudos [?]: 65 [0], given: 1

Re: 2/d= 2-d/d-2 [#permalink]  13 Dec 2018, 00:49
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
_________________

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
Display posts from previous: Sort by