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# All of the members of club Y are either Democrats or Republi

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Director
Joined: 20 Aug 2007
Posts: 849
Location: Chicago
Schools: Chicago Booth 2011
All of the members of club Y are either Democrats or Republi  [#permalink]

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Updated on: 14 Sep 2013, 06:08
1
10
00:00

Difficulty:

55% (hard)

Question Stats:

69% (02:22) correct 31% (02:25) wrong based on 252 sessions

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All of the members of club Y are either Democrats or Republicans. If 1/2 of the male members and 3/5 of the female members are Democrats, what is the ratio of the number of males to the number of females in the club?

(1) In club Y the number of female members is one less than the number of male members.
(2) In club Y the number of male Republican members is equal to the number of female Democratic members.

Originally posted by sonibubu on 28 Jan 2008, 12:41.
Last edited by Bunuel on 14 Sep 2013, 06:08, edited 1 time in total.
Edited the question and added the OA.
Director
Joined: 12 Jul 2007
Posts: 843
Re: DS - club members  [#permalink]

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28 Jan 2008, 12:58
Statement 1
6:5 works, but so does 30:29 and those are different ratios.
INSUFFICIENT

Statement 2
1/2(m) = 3/5(f)
5/10(m) = 6/10(f)
30/60(m) = 30/50(f)
Ratio of 6:5 males to female
SUFFICIENT

Intern
Joined: 08 Jan 2013
Posts: 33
Re: All of the members of club Y are either Democrats or  [#permalink]

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Updated on: 15 Sep 2013, 04:51
You have solved the ratio for M:F in Republicans. Where did you get 30:29 from?

The question asks for M:F in Club Y, which is Republicans + Democrats. The question provides 4 categories, which can be referred to as MD, MR, FD and FR. Each member is a whole number because you can't have half a member in any category, so FD + FR is a multiple of 5 and that MD + MR is a multiple of 2. The question also states that FD > FR, and that MD = MR.

Statement 1: M = F + 1, or MD + MR = FD + (FR + 1).

If FD + FR = 5, then MR + MD = 6. This satisfies the information given, where FR = 2 and MD = 3.
If FD + FR = 10, then MR + MD = 11. This breaks with the information that MR + MD is divisible by 2.
If FD + FR = 15, then MR + MD = 16. This satisfies the information given, where FR = 6 and MD = 8.

Insufficient, but there is more information. Rearranging statement 1 gives MD - FD = FR + 1 - MR, or D = R + 1. In other words the ratio of M:F is equal to the ratio of D:R.

If FD = 3, FR =2 then MD = 3, MR = 3. D = 5, R = 6. This satisfies the information given.
If FD + FR = 15, then FD = 9 and FR = 6 and MD = 8 and MR =8. This means D = 17, R = 14. This breaks with the information that D = R + 1.

Therefore Statement 1 is sufficient to deduce the ratio of M:F is 6:5, no?

Originally posted by stormbind on 14 Sep 2013, 06:04.
Last edited by stormbind on 15 Sep 2013, 04:51, edited 10 times in total.
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Re: All of the members of club Y are either Democrats or Republi  [#permalink]

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14 Sep 2013, 08:44
1
1
sonibubu wrote:
All of the members of club Y are either Democrats or Republicans. If 1/2 of the male members and 3/5 of the female members are Democrats, what is the ratio of the number of males to the number of females in the club?

(1) In club Y the number of female members is one less than the number of male members.
(2) In club Y the number of male Republican members is equal to the number of female Democratic members.

Let the total # of males be 2m and females be 5f.
Given that m males are democrats and m are republicans. Again, 2f are republicans and 3f are democrats.

F.S 1 states that 5f = 2m-1. Clearly Insufficient.

F.S 2 states that m=3f. Thus, the ratio of # of males to the # of females : $$\frac{2m}{5f} = \frac{6f}{5f} = \frac{6}{5}$$. Sufficient.
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Re: All of the members of club Y are either Democrats or Republi  [#permalink]

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15 Sep 2013, 04:18
* bump *

Why is my solution using only Statement 1, not equally valid?
Math Expert
Joined: 02 Sep 2009
Posts: 51263
Re: All of the members of club Y are either Democrats or Republi  [#permalink]

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15 Sep 2013, 08:20
stormbind wrote:
All of the members of club Y are either Democrats or Republicans. If 1/2 of the male members and 3/5 of the female members are Democrats, what is the ratio of the number of males to the number of females in the club?

(1) In club Y the number of female members is one less than the number of male members.
(2) In club Y the number of male Republican members is equal to the number of female Democratic members.

Why is my solution using only Statement 1, not equally valid?

Cannot fully understand your solution but consider the following examples:

If m=6 and f=5, then the ratio is 6/5.
If m=16 and f=15, then the ratio is 16/15.

Two different ratios. Hence insufficient.

Hope it helps.
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Re: All of the members of club Y are either Democrats or Republi  [#permalink]

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02 Jul 2018, 21:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: All of the members of club Y are either Democrats or Republi &nbs [#permalink] 02 Jul 2018, 21:17
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