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How many 4 member committee can be formed from a group

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Concentration: Operations, International Business
How many 4 member committee can be formed from a group [#permalink]

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New post 30 Aug 2017, 21:57
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Question Stats:

30% (01:46) correct 70% (01:53) wrong based on 61 sessions

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How many 4 member committee can be formed from a group of x men and y women such that 3 members are of one sex and 1 member of opposite sex
1. There are a total of 12 men and women together in the group
2. If the number of men was y and the number of women was x then the number of committees formed would not change
[Reveal] Spoiler: OA

Kudos [?]: 3 [0], given: 9

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Re: How many 4 member committee can be formed from a group [#permalink]

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New post 30 Aug 2017, 22:54
With Total number of women and men,Different groups cannot be found.
Same with statement 2,more than one possibilities exist.
Combining them will not give us the Ans
Hence E
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New post 31 Aug 2017, 00:39
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(1) definitely not sufficient alone, cause we need to know how many men and women (not how many total of men and women).
(2) is also not sufficient. Let's assume that x and y both larger than or equal to 3, so the number of committees that can be formed is (3Cx * 1Cy) + (1Cx * 3Cy)
Clearly if we swap x and y this sum is not changed, so (2) is always right for x, y >= 3
Combine (1) and (2) we see that (x, y) can be (3, 9), (4, 8), (5, 7) or (6, 6), hence we still can't calculate the result.

=> The answer is E

Kudos [?]: 6 [1], given: 4

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How many 4 member committee can be formed from a group [#permalink]

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New post 25 Sep 2017, 12:03
thanhtam269 wrote:
(1) definitely not sufficient alone, cause we need to know how many men and women (not how many total of men and women).
(2) is also not sufficient. Let's assume that x and y both larger than or equal to 3, so the number of committees that can be formed is (3Cx * 1Cy) + (1Cx * 3Cy)
Clearly if we swap x and y this sum is not changed, so (2) is always right for x, y >= 3
Combine (1) and (2) we see that (x, y) can be (3, 9), (4, 8), (5, 7) or (6, 6), hence we still can't calculate the result.

=> The answer is E


Hi Thanhtam, thanks for the explanation. I would like to ensure I am thinking about this correct
Case 1:
(3, 9), will result in one committee and will give the same exact value when reversed as modeled by your equation.

Case 2:
(6,6) will result in two committees and will give the exact same value when reversed as modeled.

My confusion comes in the equation you've written. I wanted to do this

W=3 M =9

3W:1M Only one group can be formed

3M:1W Three groups can be formed.

Total groups for case 1(Men =x and women =y) \(3+1=4\)
M=9 W=3


3W:1M Only one group can be formed


3M:1W Three groups can be formed

Total groups for case 2(Men = y and women = x ) \(3+1=4\)
Thus overall total groups = 8
In the case of 1W & 11M

3W:1M 0 group can be formed
1W:3m 1 group can be formed

Total groups from case 1: = 1

Case 2: 11W 1M
3W:1M = 1 group can be formed
3M: 1W = 0 groups can be formed

Total groups for this case = 2.
Therefore there are 2 different cases, one in which total groups = 8, and one in which total groups = 2

I know my method will take too long for the Gmat time constraint, can you explain to me how exactly you came to derive your equation?

Thanks in advance

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How many 4 member committee can be formed from a group   [#permalink] 25 Sep 2017, 12:03
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