A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number

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A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members in the club?

(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 2 : 1
(E) 3 : 1

Answer: D

Source: Official Guide

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Gmat_mission wrote:
Fri Jan 28, 2022 8:47 am
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, the average number sold was 84, and among the male members, the average number sold was 96. What was the ratio of the number of male members to the number of female members in the club?

(A) 1 : 1
(B) 1 : 2
(C) 1 : 3
(D) 2 : 1
(E) 3 : 1

Answer: D

Source: Official Guide
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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