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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A committee of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

22 Jan 2011, 03:06

7

This post received KUDOS

21

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

37% (02:05) correct
63% (02:42) wrong based on 753 sessions

HideShow timer Statistics

A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?

(1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25? (1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

Given: \(m+w=8\). Question: is \(\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}\)? --> is \(m(m-1)>14\) --> is \(m\geq{5}\)? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> \(m>0.4*8\) --> \(m>3.2\): there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> \(\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}\) --> \(w(w-1)>11.2\) --> is \(w\geq{4}\): there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Re: A committee of 2 people is to be formed [#permalink]

Show Tags

19 May 2012, 09:39

gmihir wrote:

A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men.If P is the probability that both the selected people are men, is P > 0.25? (1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

This is my first answer here... so I dont know how to use maths symbols here...

Probability that both men are selected is MC2/8C2. We have to find whether this is greater than 1/4. If you solve : MC2/8C2 > 1/4, it gives you M^2 - M - 14 >0 which is true for M > 4.

So the first option is ruled out because 40% of 8 is 3.2, which means M can either 4 or greater than 4.

2. If you solve the second option, WC2/8C2 > 1/2, it gives W^2 - W- 11 > 0, which is true for W >= 4. Since total people are 8, M <= 4.

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

20 May 2012, 10:48

(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

can you explain what this equaiton means? W(W-1) >11.2 How do we know its SUFF by this equation?

A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25?

(1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

Merging similar topics. Please refer to the solution above.

dchow23 wrote:

(2) The probability that both the selected people will be women is more than 20% -> \frac{w}{8}*\frac{w-1}{7}>\frac{1}{5} --> w(w-1)>11.2 --> is w\geq{4}: there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

can you explain what this equaiton means? W(W-1) >11.2 How do we know its SUFF by this equation?

The question asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7). From (2) we have that \(w(w-1)>11.2\). Now, if the # of women is 3 then 3(3-1)=6<11.2, so w>3, which means that there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 8-4=4, 8-5=3, ... So, the answer to the question whether there are more than or equal to 5 men is NO.

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

17 Feb 2014, 05:40

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 of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

01 Apr 2015, 07:29

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.
_________________

There are a couple of ways to approach this question, depending on how comfortable you are with the math concepts involved. There's a great 'brute force' element to the question that you can take advantage of (as long as you write everything down and label your work).

We're told that we have a group of 8 people (some men and some women). We're told to randomly select 2 of the 8 people and we're asked if the probability that they're BOTH men is greater than .25 This is a YES/NO question.

Since there are only 8 people, we can have from 0 - 8 men in the group. We can do a bit of work up-front so that we can move faster through the two Facts later. We want to figure out the point at which the probability will be > .25

IF.... There are 4 men and 4 women Probability of selecting 2 men is (4/8)(3/7) = 3/14 Since 3/12 = .25, 3/14 must be LESS than .25 (since the denominator of that fraction is bigger than 12)

IF..... There are 5 men and 3 women Probability of selecting 2 men is (5/8)(4/7) = 5/14 Since 5/15 = .333333, 5/14 must be BIGGER than .3333 (since the denominator of that fraction is smaller than 15)

So, with 4 OR FEWER men, the answer to the question is NO With 5 OR MORE men, the answer to the question is YES

We now know that the question is really asking if the number of men is 5 OR GREATER. Again, this is a YES/NO question.

Fact 1: MORE than 40% of the employees are men.

(.4)(8) = 3.2, BUT since we CANNOT have a "fraction" of a man, we must have 4 OR MORE men....

IF...we have 4 men, then the answer to the question is NO IF...we have 5 men, then the answer to the question is YES Fact 1 is INSUFFICIENT

(2) The probability that both the selected people will be women is more than 20%.

For this Fact, we can use the calculations that we did at the beginning (with a little extra work).

IF.... There are 4 women and 4 men Probability of selecting 2 women is (4/8)(3/7) = 3/14 Since 3/15 = .2, 3/14 must be GREATER than .2 (since the denominator of that fraction is less than 15)

This tells us that we have 4 OR MORE women.

IF... we have 4 women, then the answer to the question is NO IF... we have MORE women, we have even FEWER men and the answer to the question is still NO. Fact 2 is SUFFICIENT

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

18 May 2015, 04:10

1

This post received KUDOS

Bunuel wrote:

MichelleSavina wrote:

Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25? (1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

Given: \(m+w=8\). Question: is \(\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}\)? --> is \(m(m-1)>14\) --> is \(m\geq{5}\)? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> \(m>0.4*8\) --> \(m>3.2\): there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> \(\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}\) --> \(w(w-1)>11.2\) --> is \(w\geq{4}\): there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Why is ,the total number of ways in which 2 people can be selected , 8*7 and not 8C2? that would mean we are taking order into consideration! For ex : out of 4 people A B C D

ways of choosing 2 people - to form a committee - is 4C2 = 6 AB AC AD BC BD CD

and not 4*3 => which is 12 and will include the reverse as well since there isn't any position or order mentioned here while forming the committee.

Q) A committee of 2 people is to be formed from a group of 8 people which includes some women and rest are men. If P is the probability that both the selected people are men, is P > 0.25? (1) More than 40% of the employees are men. (2) The probability that both the selected people will be women is more than 20%.

Given: \(m+w=8\). Question: is \(\frac{m}{8}*\frac{m-1}{7}>\frac{1}{4}\)? --> is \(m(m-1)>14\) --> is \(m\geq{5}\)? So the question basically asks whether the # of men in 8 people is more than or equal to 5 (5, 6, or 7).

(1) More than 40% of the employees are men --> \(m>0.4*8\) --> \(m>3.2\): there may be 4 men and in this case the answer to the question will be NO or there may be more than 4 men (5, 6, ...) and in this case the answer to the question will be YES. Not sufficient.

(2) The probability that both the selected people will be women is more than 20% -> \(\frac{w}{8}*\frac{w-1}{7}>\frac{1}{5}\) --> \(w(w-1)>11.2\) --> is \(w\geq{4}\): there are more than or equal to 4 women in 8 people: 4, 5, 6, ... hence there are less than or equal to 4 men: 4, 3, ... So answer to the question whether there are more than or equal to 5 men is NO. Sufficient.

Why is ,the total number of ways in which 2 people can be selected , 8*7 and not 8C2? that would mean we are taking order into consideration! For ex : out of 4 people A B C D

ways of choosing 2 people - to form a committee - is 4C2 = 6 AB AC AD BC BD CD

and not 4*3 => which is 12 and will include the reverse as well since there isn't any position or order mentioned here while forming the committee.

Re: A committee of 2 people is to be formed from a group of 8 [#permalink]

Show Tags

16 Nov 2016, 10:25

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.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...