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

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28 Jan 2008, 13:41

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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.

Re: All of the members of club Y are either Democrats or [#permalink]

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14 Sep 2013, 07:04

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?

Last edited by stormbind on 15 Sep 2013, 05:51, edited 10 times in total.

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

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14 Sep 2013, 09:44

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Expert's post

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. _________________

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

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15 Sep 2013, 09:20

Expert's post

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.

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

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09 Sep 2015, 06:59

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