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How many people are in room A ?

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How many people are in room A ?  [#permalink]

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New post Updated on: 13 Dec 2015, 22:09
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A
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Question Stats:

80% (00:50) correct 20% (00:52) wrong based on 264 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, 01:57.
Last edited by chetan2u on 13 Dec 2015, 22:09, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: How many people are in room A ?  [#permalink]

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New post 16 Oct 2008, 02:05
1
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.
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Re: How many people are in room A ?  [#permalink]

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New post 11 Apr 2014, 14:35
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)
D is the answer
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Re: How many people are in room A ?  [#permalink]

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New post 12 Apr 2014, 00:29
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
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Re: How many people are in room A ?  [#permalink]

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New post 12 Apr 2014, 02:23
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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Re: How many people are in room A ?  [#permalink]

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New post 08 May 2014, 01:58
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 ?
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Re: How many people are in room A ?  [#permalink]

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New post 08 May 2014, 02:10
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: How many people are in room A ?  [#permalink]

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New post 31 Oct 2018, 20:42
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Re: How many people are in room A ? &nbs [#permalink] 31 Oct 2018, 20:42
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