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

Question

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.

mau5 · Accepted Answer

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.

eschn3am · Answer

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

Answer B

stormbind · Answer

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?

stormbind · Answer

* bump *

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

Bunuel · Answer

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.

bumpbot · Answer

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

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