Last visit was: 19 Jul 2025, 10:03 It is currently 19 Jul 2025, 10:03
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,620
Own Kudos:
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,620
Kudos: 742,732
 [101]
5
Kudos
Add Kudos
94
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,965
Own Kudos:
5,161
 [23]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,965
Kudos: 5,161
 [23]
16
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
User avatar
pushpitkc
Joined: 26 Feb 2016
Last visit: 19 Feb 2025
Posts: 2,819
Own Kudos:
5,874
 [16]
Given Kudos: 47
Location: India
GPA: 3.12
Posts: 2,819
Kudos: 5,874
 [16]
11
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,132
 [4]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,132
 [4]
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, 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

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
General Discussion
User avatar
Luckisnoexcuse
User avatar
Current Student
Joined: 18 Aug 2016
Last visit: 16 Apr 2022
Posts: 520
Own Kudos:
657
 [7]
Given Kudos: 198
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Products:
GMAT 2: 740 Q51 V38
Posts: 520
Kudos: 657
 [7]
3
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
Bunuel
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, 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

Male : Average : Female
96 : 92 : 84

92-84: 96-92
8:4
2:1
D
User avatar
danlew
Joined: 03 Feb 2017
Last visit: 21 Jan 2018
Posts: 66
Own Kudos:
115
 [3]
Given Kudos: 31
Location: Australia
GMAT 1: 720 Q48 V40
GMAT 1: 720 Q48 V40
Posts: 66
Kudos: 115
 [3]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Jul 2025
Posts: 21,145
Own Kudos:
26,204
 [4]
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,145
Kudos: 26,204
 [4]
3
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, 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

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
User avatar
Sharidaxamritas
Joined: 12 Oct 2023
Last visit: 05 May 2025
Posts: 2
Given Kudos: 8
Posts: 2
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why isn't this M:F 1:2? I understand the average of the men's sold are higher but they want to know M;F ratio right? What am I missing?

Bunuel
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, 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
avatar
ManifestDreamMBA
Joined: 17 Sep 2024
Last visit: 18 Jul 2025
Posts: 1,003
Own Kudos:
Given Kudos: 194
Products:
Posts: 1,003
Kudos: 652
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The weighted avg is closer to the heavily weighted side. Here, since 92(weighted avg) is closer to 96 than 84, the number of males must be greater than women. Hence
M/F = (92-84)/(96-92) = 2/1
Sharidaxamritas
Why isn't this M:F 1:2? I understand the average of the men's sold are higher but they want to know M;F ratio right? What am I missing?

Bunuel
A club sold an average (arithmetic mean) of 92 raffle tickets per member. Among the female members, 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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,620
Own Kudos:
742,732
 [1]
Given Kudos: 98,235
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,620
Kudos: 742,732
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sharidaxamritas
Why isn't this M:F 1:2? I understand the average of the men's sold are higher but they want to know M;F ratio right? What am I missing?

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

The average tickets sold per member (92) is closer to the average tickets sold to males (96) than it is to the average tickets sold to females (84). This means there must be more males than females to skew the overall average closer to the male average. The average tickets sold to males is 4 tickets more than the overall average, while the average tickets sold to females is 8 tickets less than the overall average. Therefore, there must be twice as many males as females.

Hope it's clear.
Moderators:
Math Expert
102620 posts
PS Forum Moderator
698 posts