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M13-34

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:50
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Each of the $$N$$ members of a club agreed to contribute $$X$$ dollars to buy a new computer. If the club contained 2 more members, how much less would everyone have to contribute?

A. $$\frac{NX}{(N + 2)}$$
B. $$X(N + \frac{N}{(N + 2)})$$
C. $$\frac{N}{(XN + 2X)}$$
D. $$X(1 - \frac{N}{(N + 2)})$$
E. $$XN - \frac{N}{(N + 2)}$$

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16 Sep 2014, 00:50
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Official Solution:

Each of the $$N$$ members of a club agreed to contribute $$X$$ dollars to buy a new computer. If the club contained 2 more members, how much less would everyone have to contribute?

A. $$\frac{NX}{(N + 2)}$$
B. $$X(N + \frac{N}{(N + 2)})$$
C. $$\frac{N}{(XN + 2X)}$$
D. $$X(1 - \frac{N}{(N + 2)})$$
E. $$XN - \frac{N}{(N + 2)}$$

The computer costs $$NX$$ dollars. If the club contained 2 more members, everyone would have to contribute $$Y$$ dollars. Because $$(N + 2)Y = NX, Y = \frac{NX}{(N + 2)}$$. This is by $$X - \frac{NX}{(N + 2)}$$ less than the actual contribution of $$X$$.

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16 Aug 2016, 04:01
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(# of members) * (Contribution per member) = Total contribution ===> Let's N = 8 and X = $5 N * X XN 8 * 5 = 40 (Plus 2 members) * New Contr. per member = Total contribution (N + 2) * (XN/N+2) = XN 10 * 4 = 40 Now everybody pays$1 (i.e., 5 - 4) less after the addition of two more members.

Now backsolve using the answer choices:

Only D results in 1
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Intern
Joined: 10 Jul 2017
Posts: 6
Location: United States
Schools: Stanford MSx"19
GMAT 1: 720 Q47 V41
GPA: 3.56

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13 Aug 2017, 06:40
1
Wording on this one is tricky...

I read it as "Each of the N members agreed to (collectively) contribute X dollars" when it is actually asking "Each of the N members agreed to contribute X dollars (each)"
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Joined: 19 Nov 2012
Posts: 26

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21 Jun 2018, 05:18
Hi Bunuel

Doesn't the solution given ans the question " how much less would EACH ONE have to contribute? " rather than "how much less EVERYONE would have to contribute?"
For the latter, I guess we need to multiply the amount less for each one by the total number of people. So shouldn't the actual answer by the current ans X N ?

Though, it's a brilliant question. I struggled quite a bit and most things became clear only after seeing your solution.

Thanks.
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21 Jun 2018, 23:20
sanjay1810 wrote:
Hi Bunuel

Doesn't the solution given ans the question " how much less would EACH ONE have to contribute? " rather than "how much less EVERYONE would have to contribute?"
For the latter, I guess we need to multiply the amount less for each one by the total number of people. So shouldn't the actual answer by the current ans X N ?

Though, it's a brilliant question. I struggled quite a bit and most things became clear only after seeing your solution.

Thanks.

All, or everyone as you understood it, should still contribute the same NX, which is the price of the computer. So, if this were the intended meaning of the question the answer would have been 0.

Does this make sense?
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22 Jun 2018, 23:12
Bunuel: Thanks! Took me a while but yes now I understand. That's because ultimately the total sum is the same only.

Although it's not verbal, I guess "each" should be a more appropriate word choice instead of "everyone". I'm not sure how GMAT Q writers use terms. If test takers have to deal with such kind of stuff, then makes sense.

Cheers!
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09 Sep 2018, 07:30
Hi,

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Joined: 19 Nov 2012
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21 Sep 2018, 01:51
Megha1119 wrote:

Hi Megha1119:

8 people X $10 per head =$ 80 = 8 +2 people X \$ Y per head
80 = 10. Y so Y = 8
earlier per head share = 10, new per head share = 8
difference 2

option d> substitute x = 10, n = 8 and n + 2 = 10 we get 10 ( 1- 0.8) = 2= same as above.
Re: M13-34 &nbs [#permalink] 21 Sep 2018, 01:51
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