Last visit was: 19 Jul 2025, 10:23 It is currently 19 Jul 2025, 10:23
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:
742,735
 [4]
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: 742,735
 [4]
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
1,703
 [1]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,703
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
avatar
MWithrock
Joined: 13 Nov 2018
Last visit: 27 Apr 2019
Posts: 58
Own Kudos:
Given Kudos: 19
Location: United States (PA)
GMAT 1: 650 Q39 V40
GMAT 2: 660 Q44 V37
GPA: 2.91
GMAT 2: 660 Q44 V37
Posts: 58
Kudos: 24
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
1,703
 [1]
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,703
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MWithrock
Just to make sure I'm thinking about this conceptually, This question doesn't even really need math Right?

With W+3 = 1/2M ; M & W can equal anything giving us any ratio.

With W2/5 = M ; This specifically gives us a relationship that is a ratio.

Someone please tell me if I'm off.

Hi MWithrock ,

M and W must be positive integers therefore you don´t have "all freedom" in statement (1).

On the other hand, you are right in statement (2), although W*(5/2)=M, of course. I explain:
Once M/W is unique, the fact that it must be possible to be written as a ratio of positive integers is the examiner´s burden (not yours).

Regards,
Fabio.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Jul 2025
Posts: 102,620
Own Kudos:
742,735
 [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: 742,735
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fskilnik
Bunuel
What is the ratio of men to women enrolled in a certain class?


(1) The number of women enrolled in the class is 3 less than half the number of men enrolled.

(2) The number of women enrolled in the class is 2/5 of the number of men enrolled.
[Hi, Bunuel! Let me contribute to this simple but important problem.]

\(? = {m \over w}\,\,\,\,\,\,\,\left( {m,w\,\, \ge 1\,\,{\rm{ints}}} \right)\)

\(\left( 1 \right)\,\,w = {m \over 2} - 3\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {8,1} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{8}}\,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {10,2} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{? }}\,{\rm{ = }}\,\,{\rm{5}}\,\, \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\)

\(\left( 2 \right)\,\,w = {2 \over 5}m\,\,\,\,\,\mathop \Rightarrow \limits^{w\,\, \ne \,\,0} \,\,\,\,\,{5 \over 2} = {m \over w} = ?\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}\)

The correct answer is therefore (B).

Regards,
Fabio.

P.S.: Bunuel : please take out the typo (extra "2") in the statement (2).
________________________
Typo edited. Than you Fabio.
User avatar
eswarchethu135
Joined: 13 Jan 2018
Last visit: 19 Jun 2025
Posts: 277
Own Kudos:
Given Kudos: 20
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23
GMAT 2: 640 Q49 V27
GPA: 4
WE:Consulting (Consulting)
Products:
GMAT 2: 640 Q49 V27
Posts: 277
Kudos: 446
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Statement 1) The number of women enrolled in the class is 3 less than half the number of men enrolled.

w = \(\frac{m}{2} - 3\)

\(\frac{m}{w} = \frac{m}{\frac{m}{2}-3}\)

Clearly INSUFFICIENT.

Statement 2) The number of women enrolled in the class is 2/5 of the number of men enrolled.

w = \(\frac{2}{5}m\)

\(\frac{m}{w} = \frac{m}{\frac{2}{5}m}\)

\(\frac{m}{w} = \frac{5}{2}\)

SUFFICIENT.

OPTION: B
User avatar
ayakik
Joined: 15 Sep 2022
Last visit: 31 Jan 2023
Posts: 9
Given Kudos: 9
GMAT 1: 610 Q36 V37
GMAT 2: 650 Q39 V41
GMAT 2: 650 Q39 V41
Posts: 9
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi, I know this is a relatively simple question, but I got this wrong because I defaulted to thinking "there is a clear relationship between men and women presented here, therefore statement 1 must be sufficient." Does it not work because the "-3" means that it is not a directly proportional relationship but rather one that is slightly skewed? Would the best approach be to test out different numbers for Statement 1 to see if it still holds the same relationship, or would any ratio with such addition/subtraction provide different values?

fskilnik Bunuel
User avatar
gmatprepper94111
Joined: 17 Jul 2022
Last visit: 23 Nov 2022
Posts: 24
Own Kudos:
23
 [1]
Location: United States (CA)
Concentration: Finance, Strategy
Schools: Stanford '25
GPA: 3.9
WE:Corporate Finance (Finance: Venture Capital)
Schools: Stanford '25
Posts: 24
Kudos: 23
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ayakik
Hi, I know this is a relatively simple question, but I got this wrong because I defaulted to thinking "there is a clear relationship between men and women presented here, therefore statement 1 must be sufficient." Does it not work because the "-3" means that it is not a directly proportional relationship but rather one that is slightly skewed? Would the best approach be to test out different numbers for Statement 1 to see if it still holds the same relationship, or would any ratio with such addition/subtraction provide different values?

fskilnik Bunuel

Yeah I guess there's two ways to think about this. The first is to look for the intuitive / general idea. The second is to prove it's insufficient by counterexample.

Your intuition outlined here is right. It's the "3 less" thing that makes it insufficient. As m and n get large, the significance of that "3 less" shrinks, eventually approaching zero asymptotically.

-------------------------
Starting with the general idea
-------------------------

Let m be the count of men enrolled; let w be the count of women enrolled.

We want to know the ratio of men to women enrolled, i.e. we want a unique solution for m / w

(1) Tells us w = 0.5m - 3.

We can rearrange this a little bit:
---> w = 0.5m - 3
---> 0.5m = w + 3
---> 0.5m/w = 1 + 3 / w
---> m/w = 2 + 6 / w

We're forced to notice that the ratio of men to women depends on how many women there are (we could do it the same way to show that the ratio of men to women depends on how many men there are; it's the same thing).

It's not sufficient because we could create many different ratios.

(Actually, I'm reasonably sure we could identify a countably infinite number of pairings here. Note that w = 0.5m -3 resembles a y = mx + b equation (although well defined in this context only on a subset of integers),

----------------------
Just doing it by counterexample
----------------------

Again let m be the count of men enrolled; let w be the count of women enrolled.

If we can show two different ratios for two viable combinations of m and w, then we prove the statement is insufficient.

Let's start with m = 10, which means w = 2. Then the ratio of men to women is 5:1.

But we could also have m = 12, in which case w = 3. Then the ratio of men to women is 4:1.

Because we can show two distinct ratios, the information provided is insufficient to identify a unique ratio.
User avatar
ayakik
Joined: 15 Sep 2022
Last visit: 31 Jan 2023
Posts: 9
Given Kudos: 9
GMAT 1: 610 Q36 V37
GMAT 2: 650 Q39 V41
GMAT 2: 650 Q39 V41
Posts: 9
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Beautiful explanation, thank you!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,447
Own Kudos:
Posts: 37,447
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102620 posts
455 posts