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

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Intern
Joined: 10 Jun 2016
Posts: 3
Location: India
How many 4 member committee can be formed from a group  [#permalink]

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30 Aug 2017, 21:57
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Difficulty:

85% (hard)

Question Stats:

42% (01:58) correct 58% (01:39) wrong based on 137 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
Senior Manager
Joined: 02 Mar 2017
Posts: 252
Location: India
Concentration: Finance, Marketing
Re: How many 4 member committee can be formed from a group  [#permalink]

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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
Intern
Joined: 23 Aug 2017
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Re: How many 4 member committee can be formed from a group  [#permalink]

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31 Aug 2017, 00:39
1
(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.

Intern
Joined: 15 Aug 2017
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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.

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?

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

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07 Apr 2019, 10:29
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Re: How many 4 member committee can be formed from a group   [#permalink] 07 Apr 2019, 10:29
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