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# How many people are in room A ?

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Manager
Joined: 14 Oct 2008
Posts: 118
How many people are in room A ?  [#permalink]

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Updated on: 13 Dec 2015, 23:09
1
1
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Difficulty:

5% (low)

Question Stats:

80% (01:04) correct 20% (01:10) wrong based on 287 sessions

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How many people are in room A ?

(1) A total of 15 different pairs of people can be selected from the people in room A .

(2) If there were one fewer person in room A , a total of 10 different pairs of people could be selected from room A .

Originally posted by gameCode on 16 Oct 2008, 02:57.
Last edited by chetan2u on 13 Dec 2015, 23:09, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 16 Oct 2008
Posts: 45
Re: How many people are in room A ?  [#permalink]

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16 Oct 2008, 03:05
2
I think the answer is D:

1) 6! which make 15 diff pairs
2) 5! makes 10 diff pairs

So there are 6 people in room.
Senior Manager
Joined: 21 Oct 2013
Posts: 411
Re: How many people are in room A ?  [#permalink]

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11 Apr 2014, 15:35
As for the combination formula in reverse, this simply means setting up a formula to solve for the value of n and k given the number of sets possible.
(Use "n" to present the actual number of people in the room. Combination of 2 people to make 15 groups)
(1) 15 = n!/2!(n-2)! = nC2 (i.e. Sufficient)
(2) 10 = (n-1)!/2!((n-1)-2)! = (n-1)C2 (i.e. Sufficient)
Intern
Joined: 10 Apr 2014
Posts: 29
Re: How many people are in room A ?  [#permalink]

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12 Apr 2014, 01:29
gameCode wrote:
How many people are in room A ?

(1) A total of 15 different pairs of people can be selected from the people in room A .

(2) If there were one fewer person in room A , a total of 10 different pairs of people could be selected from room A .

The answer can be D or E. Each statement is sufficient to answer the qs, but the answers are different for both of them , for the first its 30 and second its 21 , So shud it be D or E then ?

If both the statements are individually sufficient to answer the question, In any DS question the answer should be D.
It does not matter if the answers are same or different.

-----------------------------
Kudos, if the post helped
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: How many people are in room A ?  [#permalink]

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12 Apr 2014, 03:23
1
ind23 wrote:
gameCode wrote:
How many people are in room A ?

(1) A total of 15 different pairs of people can be selected from the people in room A .

(2) If there were one fewer person in room A , a total of 10 different pairs of people could be selected from room A .

The answer can be D or E. Each statement is sufficient to answer the qs, but the answers are different for both of them , for the first its 30 and second its 21 , So shud it be D or E then ?

If both the statements are individually sufficient to answer the question, In any DS question the answer should be D.
It does not matter if the answers are same or different.

-----------------------------
Kudos, if the post helped

That's not true: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Having said that the question at hand does not give different answers, from each statement we can get that the total number of people in the room is 6.

Hope it helps.
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Joined: 28 Apr 2014
Posts: 195
Re: How many people are in room A ?  [#permalink]

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08 May 2014, 02:58
Bunuel wrote:
ind23 wrote:
gameCode wrote:
How many people are in room A ?

(1) A total of 15 different pairs of people can be selected from the people in room A .

(2) If there were one fewer person in room A , a total of 10 different pairs of people could be selected from room A .

The answer can be D or E. Each statement is sufficient to answer the qs, but the answers are different for both of them , for the first its 30 and second its 21 , So shud it be D or E then ?

If both the statements are individually sufficient to answer the question, In any DS question the answer should be D.
It does not matter if the answers are same or different.

-----------------------------
Kudos, if the post helped

That's not true: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Having said that the question at hand does not give different answers, from each statement we can get that the total number of people in the room is 6.

Hope it helps.

Bunuel on your point the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

once we get the clarity that both are able to give the answer independently , are we expected to check as to whether these answers are same or not ?

For eg here I was able to get that A is nC2 and B is n-1C2. So now is one required to solve both and confirm is the answers are same ?
Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: How many people are in room A ?  [#permalink]

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08 May 2014, 03:10
himanshujovi wrote:
Bunuel wrote:
ind23 wrote:

If both the statements are individually sufficient to answer the question, In any DS question the answer should be D.
It does not matter if the answers are same or different.

-----------------------------
Kudos, if the post helped

That's not true: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

Having said that the question at hand does not give different answers, from each statement we can get that the total number of people in the room is 6.

Hope it helps.

Bunuel on your point the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other.

once we get the clarity that both are able to give the answer independently , are we expected to check as to whether these answers are same or not ?

For eg here I was able to get that A is nC2 and B is n-1C2. So now is one required to solve both and confirm is the answers are same ?

If you are sure that both formulas are correct, then they must give the same answers and you don't need not to solve. If you are not sure, then solving might be a good way to check whether your approach is correct.
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Re: How many people are in room A ?  [#permalink]

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31 Oct 2018, 21:42
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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).

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Re: How many people are in room A ?   [#permalink] 31 Oct 2018, 21:42
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