Last visit was: 19 Jul 2024, 05:02 It is currently 19 Jul 2024, 05:02
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28854 [81]
Given Kudos: 130
Most Helpful Reply
Tutor
Joined: 20 Apr 2012
Posts: 82
Own Kudos [?]: 763 [23]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Send PM
User avatar
Manager
Manager
Joined: 22 Feb 2009
Posts: 109
Own Kudos [?]: 540 [11]
Given Kudos: 148
Send PM
General Discussion
Tutor
Joined: 20 Apr 2012
Posts: 82
Own Kudos [?]: 763 [4]
Given Kudos: 39
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE:Education (Education)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
3
Kudos
1
Bookmarks
Expert Reply
You can apply the same idea in this problem if-bob-and-jen-are-two-of-5-participants-in-a-race-how-many-37225.html

Race can finish in 6!=120 ways, and exactly half of them Jen always finishes in front of Bob. The correct answer is 60.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28854 [1]
Given Kudos: 130
Re: From a group of M employees, N will be selected, at random, [#permalink]
1
Kudos
Expert Reply
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:
https://magoosh.com/gmat/2013/how-to-do- ... th-faster/

Does all this make sense?
Mike :-)
User avatar
Manager
Manager
Joined: 22 Feb 2009
Posts: 109
Own Kudos [?]: 540 [0]
Given Kudos: 148
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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:
https://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.
Manager
Manager
Joined: 15 Aug 2014
Status:Don't Give Up!
Posts: 77
Own Kudos [?]: 69 [0]
Given Kudos: 124
Location: India
Concentration: Operations, General Management
GMAT Date: 04-25-2015
WE:Engineering (Manufacturing)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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



For a set of DS questions on Probability, as well as the OE of this particular question, see:
https://magoosh.com/gmat/2013/gmat-data- ... obability/

Mike :-)


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?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28854 [1]
Given Kudos: 130
Re: From a group of M employees, N will be selected, at random, [#permalink]
1
Kudos
Expert Reply
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 :-)
Manager
Manager
Joined: 15 Aug 2014
Status:Don't Give Up!
Posts: 77
Own Kudos [?]: 69 [0]
Given Kudos: 124
Location: India
Concentration: Operations, General Management
GMAT Date: 04-25-2015
WE:Engineering (Manufacturing)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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....
Manager
Manager
Joined: 22 Jan 2014
Posts: 130
Own Kudos [?]: 246 [0]
Given Kudos: 212
WE:Project Management (Computer Hardware)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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



For a set of DS questions on Probability, as well as the OE of this particular question, see:
https://magoosh.com/gmat/2013/gmat-data- ... obability/

Mike :-)


Since we have the constraint of Andrew being to the right of Georgia so it is clear that this means the answer divided by 2!

1) N = 15
ways of selection = C(M,N) = C(M,15)
M is unknown so insufficient.

2) N=M
ways of selection = C(M,N) = C(M,M) = 1
so, answer = 1/2! = 1/2
sufficient.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28854 [1]
Given Kudos: 130
Re: From a group of M employees, N will be selected, at random, [#permalink]
1
Kudos
Expert Reply
sach24x7 wrote:
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 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.

Does this make sense?

Mike :-)
avatar
Intern
Intern
Joined: 18 Jul 2013
Posts: 26
Own Kudos [?]: 9 [0]
Given Kudos: 151
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
Hello Sir,(Magoosh)

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.
Manager
Manager
Joined: 15 Aug 2014
Status:Don't Give Up!
Posts: 77
Own Kudos [?]: 69 [0]
Given Kudos: 124
Location: India
Concentration: Operations, General Management
GMAT Date: 04-25-2015
WE:Engineering (Manufacturing)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
Dear Mike,

Clear!!.....Thanks ! :-D
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4490
Own Kudos [?]: 28854 [1]
Given Kudos: 130
Re: From a group of M employees, N will be selected, at random, [#permalink]
1
Kudos
Expert Reply
taleesh wrote:
Hello Sir,(Magoosh)

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.

Does this make sense?
Mike :-)
avatar
Intern
Intern
Joined: 18 Jul 2013
Posts: 26
Own Kudos [?]: 9 [0]
Given Kudos: 151
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
Thanks alot (Magoosh). Got it well.
Intern
Intern
Joined: 21 Jan 2016
Posts: 35
Own Kudos [?]: 106 [0]
Given Kudos: 31
Location: India
GMAT 1: 640 Q44 V34
WE:Manufacturing and Production (Manufacturing)
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34018
Own Kudos [?]: 852 [0]
Given Kudos: 0
Send PM
Re: From a group of M employees, N will be selected, at random, [#permalink]
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.
GMAT Club Bot
Re: From a group of M employees, N will be selected, at random, [#permalink]
Moderator:
Math Expert
94411 posts