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M13-34

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M13-34  [#permalink]

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New post 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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Re M13-34  [#permalink]

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New post 16 Sep 2014, 00:50
1
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 \(X\).

Answer: D
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Re: M13-34  [#permalink]

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New post 16 Aug 2016, 04:01
1
(# 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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Re: M13-34  [#permalink]

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New post 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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M13-34  [#permalink]

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New post 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 ?

Please clarify.

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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Re: M13-34  [#permalink]

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New post 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 ?

Please clarify.

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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M13-34  [#permalink]

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New post 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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Re: M13-34  [#permalink]

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New post 09 Sep 2018, 07:30
Hi,

After substituting values, none of the answer choices seems right. Could anyone please help me as to where I'm going wrong?
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Re: M13-34  [#permalink]

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New post 21 Sep 2018, 01:51
Megha1119 wrote:
Hi, After substituting values, none of the answer choices seems right. Could anyone please help me as to where I'm going wrong?


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.
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Re: M13-34 &nbs [#permalink] 21 Sep 2018, 01:51
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