We can solve this question using weighted averages

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let F = the number of female members
Let M = the number of male members
This means F + M = the TOTAL number of members.
Also, F/(F + M) = the proportion of female numbers, and M/(F + M) = the proportion of male numbers.

When we substitute the given values into the weighted averages formula, we get: 92 = F/(F + M)(84) + M/(F + M)(96)
To eliminate the fractions, we'll multiply both sides of the equation by (F+M) to get: 92(F+M) = 84F + 96M
Expand the left side of the equation: 92F + 92M = 84F + 96M
Subtract 92M from both sides of the equation: 92F = 84F + 4M
Subtract 84F from both sides of the equation: 8F = 4M

We want to determine the ratio of the number of male members to the number of female members in the club.
In other words, we want to find the value of M/F

So we'll take: 8F = 4M
Divide both sides by F to get: 8 = 4M/F
Divide both sides by 4 to get: 8/4 = M/F
Simplify: 2/1 = M/F

So, the ratio of the number of male members to the number of female members = 2 : 1

Answer: D
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Thus, the ratio will be 8 : 4 = 2 : 1

Answer will be (D)
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Male : Average : Female
96 : 92 : 84

92-84: 96-92
8:4
2:1
D
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Let x be the female members and y the male members.

Since we are given that
-> the average number of raffle tickets sold among female members was 84
-> the average number of raffle tickets sold among female members was 96

From the question stem we can deduce the following :
\(\frac{(84x + 96y)}{(x+y)} = 92\)
\(84x + 96y = 92x + 92y\)
\(4y = 8x\)
\(\frac{y}{x} = \frac{2}{1}\)

Female members : Male members are in ratio 2:1(Option D)
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The average of 92 is closer to 96 (male) than 84 (female)
So there is more weightage on male number than female number which pulls the total average more towards Male average, so answer has to be D or E

using alligation: M:F = \(\frac{(Total average - Female average)}{(Male average - Total Average)}\) = \(\frac{(92-84)}{(96-92)}\)
=\(\frac{8}{4}\) = \(\frac{2}{1}\)

Answer D

awesome bro. need to develop this kind of thinking to attack problems.
although I know the concept, I almost fail in application when required.

Simple put nos In given option and you will be able to eliminate wrong ones and get the correct one as D


Sent from my iPhone using GMAT Club Forum

\(M:F = (92-84) : (96-92) = 8:4 = 2:1\). Ans - D.
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D.
84f + 96m =92(f+m)
Divide the eqn on both sides by f
Let (m/f) be x
84 + 96x = 92 + 92x
X = 2:1
(D)
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shouldn't the answer be 1:2, as it has asked about ratio of males to females?

pushpitkc if question is to find the ratio of the number of male members to the number of female members in the club?


And if \(x\) the number the female members and \(y\) is the# of male members.

how is it possible that answer is D ?

it should be vice versa 1 : 2 based on this \(4y = 8x\) ad not 2:1

can you explain

dave13,

Female is X and male is Y in his solution... So male to female will be y:x which is what is used. 2:1

I think you're mixing the variables up. Try solving again from scratch with m & f

Best
G
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Hi dave13

This can be solved in a way similar to mixture questions using allegation method

male = x
Female = y

Using allegation method, here the desired is the average

Desired - y/x - desired

So 92 - 84 = 8

96 - 92 = 4

x/y = 8/4 = 2/1

Refer to the link below

https://gmatclub.com/forum/tips-and-tri ... 51906.html

Posted from my mobile device

priyamba , I got it thanks to great people on GC

Female is X and male is Y in his solution... So male to female will be y:x which is what is used. 2:1

So when we get 4Y=8X to find ratio of male to female solve for Y ---> i.e. Y = \(\frac{8x}{4}\) ----> y = 2x

hence ratio of males to females is 2x to X i.e. 2:1



thanks guys Salsanousi Gladiator59

We are given that a club sold an average (arithmetic mean) of 92 raffle tickets per member, that among the female members, the average number sold was 84, and that among the male members, the average number sold was 96. We can let f = the number of females and m = the number of males, and we can create the following weighted average equation:

92 = (84f + 96m)/(m + f)

92m + 92f = 84f + 96m

8f = 4m

2f = m

2 = m/f

Answer: D
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Men = m
Women = n
Average = 92
=> 92 = (96m + 84n)/(m+n)
=> 92m + 92n = 96m + 84n
=> 4m = 8n
=> m:n :: 2:1

Answer: D
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