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:

40% (01:05) correct
60% (01:13) wrong based on 550 sessions

HideShow timer Statistics

From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

07 Aug 2014, 20:36

3

This post received KUDOS

2

This post was BOOKMARKED

mikemcgarry wrote:

From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

Statement 1: insufficient since we need to know M to solve for the probability Statement 2: N= M This turns to sit N people into N chairs For A is seated somewhere to the right of employee Georgia, we have (1+ 2+ 3+....+ (n-1)) possibilities To illustrate this, lets say 4 people sit in 4 chairs G in seat 1, A can be seated in 2,3, and 4 ( 3 possibilities) G in seat 2, A can be seated in 3,4 ( 2 possibilities) G in seat 3, A can be seated in 4 only (1 possibility) Sum = 1+ 2+ 3 After G and A are seated, there are (n-2)! possible combination ( for example, in this case, after G and A are seated, there are two seats left, we have 2! possible combination) The total possible combinations for N people in N chairs is N! The possible combinations that meet the requirement is (1+2+3+...(N-1))* (N-2)! = [(N-1)*N/2] * (N-2)! The probability = [(N-1)*N/2] * (N-2)!/N! = [(N-1)*N/2]/ [(N-1)*N] = 1/2 B is the answer.
_________________

......................................................................... +1 Kudos please, if you like my post

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

08 Aug 2014, 01:01

6

This post received KUDOS

4

This post was BOOKMARKED

Mmm:) That's easy.

(1) Not sufficient because we don't know M. (2) Sufficient. You need to arrange N people on N seats in such way that the employee Andrew is seated somewhere to the right of employee Georgia. The main idea that you have the same number of possibilities to put Andrew to the right of Georgia and to put him on the left. Just think that in each case when Andrew to the right of Georgia, you can switch their places. That's why, the probability is 1/2.

The correct answer is B.
_________________

I'm happy, if I make math for you slightly clearer And yes, I like kudos:)

Dear smyarga, Good job! You took the very elegant solution to this.

Dear vad3tha, You found the answer via brute force calculations, but recognize that this approach can be costly, in terms of time & energy, on the real GMAT. If you want to achieve a truly elite GMAT score, part of what that requires is the ability to see the elegant solutions that involve few or no calculations. See: http://magoosh.com/gmat/2013/how-to-do- ... th-faster/

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

10 Aug 2014, 19:39

mikemcgarry wrote:

Dear smyarga, Good job! You took the very elegant solution to this.

Dear vad3tha, You found the answer via brute force calculations, but recognize that this approach can be costly, in terms of time & energy, on the real GMAT. If you want to achieve a truly elite GMAT score, part of what that requires is the ability to see the elegant solutions that involve few or no calculations. See: http://magoosh.com/gmat/2013/how-to-do- ... th-faster/

Does all this make sense? Mike

I agree with you, also. This is not what I did when I first saw the problem. I answered by trying out: 4 people in 4 chairs and 5 people in 5 chairs. I came up with 1/2. I posted this solution afterward in case if ppl want to see the conceptual part the problem. Thanks for reminding me that.
_________________

......................................................................... +1 Kudos please, if you like my post

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

29 Oct 2014, 10:52

mikemcgarry wrote:

From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

If the value of M is known for first option ( just for example...M=20) then how to calculate probability for first statement? Can you please help?
_________________

- Sachin

-If you like my explanation then please click "Kudos"

If the value of M is known for first option ( just for example...M=20) then how to calculate probability for first statement? Can you please help?

Dear sach24x7 I'm happy to respond.

My friend, that change would introduce an ambiguity into the question that doesn't exist in the original. If M = 20, and we are picking N = 15, do we mean a)what is the probability that Andrew & Georgia are both among the 15, and that Andrew is to the right of Georgia? or b)given that Andrea & Georgia definitely are among the 15 selected, what is the probability that Andrew is to the right of Georgia? The answer to (b) is simply 1/2, because of symmetry. That's an easy question. For the first question, question (a), we would need to use the techniques discussed here: https://magoosh.com/gmat/2013/gmat-prob ... echniques/

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

29 Oct 2014, 22:14

mikemcgarry wrote:

sach24x7 wrote:

Dear Mike,

If the value of M is known for first option ( just for example...M=20) then how to calculate probability for first statement? Can you please help?

Dear sach24x7 I'm happy to respond.

My friend, that change would introduce an ambiguity into the question that doesn't exist in the original. If M = 20, and we are picking N = 15, do we mean a)what is the probability that Andrew & Georgia are both among the 15, and that Andrew is to the right of Georgia? or b)given that Andrea & Georgia definitely are among the 15 selected, what is the probability that Andrew is to the right of Georgia? The answer to (b) is simply 1/2, because of symmetry. That's an easy question. For the first question, question (a), we would need to use the techniques discussed here: https://magoosh.com/gmat/2013/gmat-prob ... echniques/

Does all this make sense? Mike

Thanks Mike!..

For option a) Will it be (20C2 / 20C15) * (1/2)

Please correct me if i;m wrong....
_________________

- Sachin

-If you like my explanation then please click "Kudos"

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

29 Oct 2014, 23:17

mikemcgarry wrote:

From a group of M employees, N will be selected, at random, to sit in a line of N chairs. There are absolutely no restrictions, either in the selection process nor in the order of seating — both are entirely random. What is the probability that the employee Andrew is seated somewhere to the right of employee Georgia? Statement #1: N = 15 Statement #2: N = M

If the value of M is known for first option ( just for example...M=20) then how to calculate probability for first statement? Can you please help?

Dear sach24x7 I'm happy to respond.

My friend, that change would introduce an ambiguity into the question that doesn't exist in the original. If M = 20, and we are picking N = 15, do we mean a)what is the probability that Andrew & Georgia are both among the 15, and that Andrew is to the right of Georgia? or b)given that Andrew & Georgia definitely are among the 15 selected, what is the probability that Andrew is to the right of Georgia? The answer to (b) is simply 1/2, because of symmetry. That's an easy question. For the first question, question (a), we would need to use the techniques discussed here: https://magoosh.com/gmat/2013/gmat-prob ... echniques/

Does all this make sense? Mike

Thanks Mike!..

For option a) Will it be (20C2 / 20C15) * (1/2)

Please correct me if i;m wrong....

Dear sach24x7, I'm happy to respond.

Your denominator is right, but not your numerator.

Denominator = all possible group of 15 to be chosen from the 20 = 20C15

Numerator = all possible groups of 15 that include both Andrew & Georgia ---- well it's those two, and 13 others from the remaining 18, so that's 18C13.

P = [(18C13)/(20C15)]*0.5

You have to compare like to like. You can't compare all possible groups of 15 to all possible pairs, which is essentially what you did: that compares apples to oranges.

Please help me clarify a doubt - what if A seat on 2nd last seat towards right of George n George seat in middle wont probability would be different in that scenario. In Ds question if we have different ans - the ans will be not sufficient.

Please help me clarify a doubt - what if A seat on 2nd last seat towards right of George n George seat in middle wont probability would be different in that scenario. In Ds question if we have different ans - the ans will be not sufficient.

Dear Taleesh, I'm happy to respond. Believe it or not, where the two people sit doesn't matter. If there are N employees, and all N are selected to sit in some order in a row of N seats, then all permutations will be possible. For any scenario in which Georgia is to the right of Andrew, there's a matching scenario in which Georgia is to the left of Andrew.

Let's say N = 6, and the six employees are Andrew = A, Georgia = G, and four others {J, K, L, M}. We can create any scenario with A to the right, such as you describe: M, K, G, J, A, L and this is matched to a unique configuration with A to the left --- we simply switch the places of G & A M, K, A, J, G, L For each and every configuration with A to the right, we can find exactly one matching scenario with A to the left. That means, exactly half of the total scenarios have A to the right of G, and the other half, A to the left of G.

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

14 Nov 2015, 16:02

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: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

03 May 2016, 21:50

calculating the probability for this question is not at all necessary here, which is the great part about DS problems. The question we need to ask ourselves is not whether 'how to find the probability?' but 'Do i have enough data to find the probability eventually?'. Evaluating both the conditions will tell us that only second condition gives us the tools required to find the probability. No calculations required, just pure reasoning.
_________________

Re: From a group of M employees, N will be selected, at random, [#permalink]

Show Tags

17 Jun 2017, 06:38

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...