Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 13 Feb 2012
Posts: 14
WE: Other (Transportation)

A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
Updated on: 17 Feb 2012, 05:19
Question Stats:
57% (01:59) correct 43% (02:00) wrong based on 514 sessions
HideShow timer Statistics
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probability that the number of women on the committee will increase? (1) n + k = 12 (2) k/n = 1/3
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by tom09b on 15 Feb 2012, 11:07.
Last edited by tom09b on 17 Feb 2012, 05:19, edited 2 times in total.




Math Expert
Joined: 02 Sep 2009
Posts: 58991

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
15 Feb 2012, 12:20
A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?Notice that the probability of selecting a woman from 4 alternates is 1/2. Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2. (1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient. Answer: B.
_________________




Current Student
Joined: 09 Apr 2013
Posts: 39
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GPA: 3.55
WE: General Management (NonProfit and Government)

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
07 Jun 2013, 09:17
tom09b wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
(1) n + k = 12 (2) k/n = 1/3 Rewording of the question: What is the probability that a man is chosen to be replaced and the alternate to replace him is a woman. What you need is (probability of man chosen) x (probability of woman alternate) \(\frac{k}{k+n} * \frac{2}{4} = \frac{k}{2(k+n)}\) (1) n+k = 12 if n=1 and k=11, \(\frac{11}{2(12)} = \frac{11}{24}\) if n=2 and k=10, \(\frac{10}{2(12)} = \frac{10}{24}\) insufficient(2) \(\frac{k}{n} = \frac{1}{3}\) if k=1 and n=3, \(\frac{1}{2(4)} = \frac{1}{8}\) if k=2 and n=6, \(\frac{2}{2(8)} = \frac{1}{8}\); etc... sufficientAnswer is B




Intern
Joined: 13 Feb 2012
Posts: 14
WE: Other (Transportation)

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
15 Feb 2012, 12:31
Bunuel wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
Notice that the probability of selecting a woman from 4 alternates is 1/2.
Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient.
Answer: B. My intuition drove me to B, as well but.. I couldn't find the way! Thank you!!



Manager
Joined: 19 Oct 2010
Posts: 155
Location: India
GPA: 3

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
03 Jul 2012, 09:40
Here is how I analyzed it if it helps: The probability of selecting a woman from the alternates as given is  (2/4) = (1/2) The probability of selecting a woman from the committee is  n/(n+k) Now, we need to figure out the probability of pick a woman from the committee AND from the alternates [P(W&W)]. Therefore this is an AND problem. 1. n/12 Insufficient 2. k/n=1/3. Therefore n/(n+k)=3/4 Sufficient because P(W&W)=(3/4)*(1/2)
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58991

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
07 Jun 2013, 06:12
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Intern
Joined: 24 Dec 2012
Posts: 19
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
20 Mar 2014, 05:34
Bunuel wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
Notice that the probability of selecting a woman from 4 alternates is 1/2.
Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient.
Answer: B. . Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.Please elaborate on this ..



Math Expert
Joined: 02 Sep 2009
Posts: 58991

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
20 Mar 2014, 05:57
tusharGupta1 wrote: Bunuel wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
Notice that the probability of selecting a woman from 4 alternates is 1/2.
Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient.
Answer: B. . Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.Please elaborate on this .. For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates. The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n); The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2. Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2. Hope it's clear.
_________________



Intern
Joined: 24 Dec 2012
Posts: 19
Concentration: Entrepreneurship, Social Entrepreneurship
WE: Design (Computer Software)

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
20 Mar 2014, 06:33
Bunuel wrote: tusharGupta1 wrote: Bunuel wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
Notice that the probability of selecting a woman from 4 alternates is 1/2.
Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient.
Answer: B. . Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.Please elaborate on this .. For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates. The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n); The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2. Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2. Hope it's clear. Thankx a ton ............................................................................................................................................................



Manager
Joined: 20 Oct 2013
Posts: 50

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
12 May 2014, 05:12
Bunuel wrote: tusharGupta1 wrote: Bunuel wrote: A committee consists of n women and k men. In addition there are 4 alternates, 2 of whom are women. If one of the committee members is selected at random to be replaced by one of the alternates, also selected at random, what is the probabilty that the number of women on the committee will increase?
Notice that the probability of selecting a woman from 4 alternates is 1/2.
Now, the number of women on the committee will increase if we replace a man from the committee with a woman from 4 alternates. Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.
(1) n + k = 12. Not sufficient as we can not get the probability of selecting a man from the committee. (2) k/n = 1/3 > k/(k+n)=1/4. Sufficient.
Answer: B. . Hence, the probabilty that the number of women on the committee will increase is k/(k+n)*1/2.Please elaborate on this .. For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates. The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n); The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2. Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2. Hope it's clear. Dear Bunnel Statement A: was clearly insufficient as we didnt know n & k individually. statement B: ratio of m:w = 1:3 so suppose, 1 m and 3 women r there in the committee and if we replace the man with women, then the no. of women will increase. now we have no man just 4 women.. probability of a new alternate as women in the committee: 3/4*1/2 = 3/8... lesser than 3/4 but if we replace the man with a man... there should be no change right as there will be 1 man and 3 women still ans is diff therefore insufficient.. Please explain.
_________________
Hope to clear it this time!! GMAT 1: 540 Preparing again



Math Expert
Joined: 02 Sep 2009
Posts: 58991

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
12 May 2014, 08:53
nandinigaur wrote: Dear Bunnel Statement A: was clearly insufficient as we didnt know n & k individually. statement B: ratio of m:w = 1:3 so suppose, 1 m and 3 women r there in the committee and if we replace the man with women, then the no. of women will increase. now we have no man just 4 women.. probability of a new alternate as women in the committee: 3/4*1/2 = 3/8... lesser than 3/4 but if we replace the man with a man... there should be no change right as there will be 1 man and 3 women still ans is diff therefore insufficient.. Please explain. Don't understand what is your question... The question asks what is the probability that the number of women on the committee will increase? The probability that the number of women on the committee will increase is k/(k+n)*1/2. From (2) we get that k/(k+n)*1/2 = 1/4*1/2 = 1/8.
_________________



Manager
Joined: 13 Sep 2015
Posts: 82
Location: United States
Concentration: Social Entrepreneurship, International Business
GPA: 3.84

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
01 Nov 2015, 13:56
unnecessary to get a number:
in order to increase the number of women, the only way is to replace a man with a woman
1. if a woman is replaced by a woman, the number will remain;
2. if a woman is replaced by a man, the number will decrease;
3. if a man is replaced by a man, the number will remain
so the possibility is:
(k/n+k)*(2/4), the key is the ratio of woman to man
(1) n+k=12, insufficient
(2)k/n=1/3, so k/n+k=1/4, sufficient
B



Manager
Joined: 06 Oct 2015
Posts: 86
Location: Bangladesh
Concentration: Accounting, Leadership

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
17 Oct 2016, 08:01
Hi Bunuel, Why does k/(k+n)*1/2 will represent the number of woman increase? How it relates to increment. Will you explain it?



Math Expert
Joined: 02 Sep 2009
Posts: 58991

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
17 Oct 2016, 08:05
NaeemHasan wrote: Hi Bunuel, Why does k/(k+n)*1/2 will represent the number of woman increase? How it relates to increment. Will you explain it? For the number of women on the committee to increase we must replace a man from the committee with a woman from 4 alternates. The probability of selecting a man from the committee is (# of men in the committee)/(total # of people in the committee) = k/(k+n); The probability of selecting a woman from 4 alternates is (# of women)/(total # of people) = 2/4 = 1/2. Therefore, the probability that we select a man from the committee AND a woman from 4 alternates is k/(k+n)*1/2. Hope it's clear.
_________________



Director
Joined: 14 Dec 2017
Posts: 510
Location: India

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
02 Jun 2018, 22:56
Given, A committee of n  women k  men Alternate choices, in case of replacement, available are 2 women & 2 men. The probability of increasing the # of women, is by replacement of 1 man in the committee with 1 woman from the alternates. Consider this as a selection of 2 people, one man from k men & one woman from the 2 alternates. #of ways selecting 1 man from k men = k #of way of selecting 1 woman from 2 women = 2 Required Probability = Probability of selecting 1 man from (n+k) members * Probability of selecting 1 woman from 4 alternates Therefore required Probability is \({k/(n+k)}*{2/4}\) Ok now lets check Statement 1 : \(n+k = 12\), clearly not sufficient, as n=10, k= 2 or n=7, k=5, or many other combinations. Statement 2: \(k/n =1/3\) which is \(n/k = 3/1\) By adding 1 to each side can be converted to \((n+k)/k = 4/1\) \(k/(n+k) = 1/4\) Hence statement 2 is sufficient to find the required probability.
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 13575

Re: A committee consists of n women and k men. In addition there
[#permalink]
Show Tags
11 Jun 2019, 19:31
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.
_________________




Re: A committee consists of n women and k men. In addition there
[#permalink]
11 Jun 2019, 19:31






