A committee consists of n women and k men. In addition there

My intuition drove me to B, as well but.. I couldn't find the way! Thank you!!

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)

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

. 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 ............................................................................................................................................................

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.

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

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.

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.