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# The members of a company’s board of directors must select

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Director
Joined: 08 Jun 2013
Posts: 560
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
The members of a company’s board of directors must select  [#permalink]

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Updated on: 24 Sep 2018, 11:13
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Difficulty:

95% (hard)

Question Stats:

25% (02:07) correct 75% (01:56) wrong based on 211 sessions

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The members of a company’s board of directors must select a subcommittee to decide the compensation level for a new Chief Executive Officer. The by-laws of the board state that no more than half of the members of the board can serve on this subcommittee. Is the number of combinations of board members that can be selected to serve on the subcommittee greater than 900?

(1) The board decides to select 6 members for the subcommittee.

(2) There are 12 members of the board.

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Originally posted by Helium on 22 Sep 2018, 19:55.
Last edited by Helium on 24 Sep 2018, 11:13, edited 1 time in total.
Intern
Joined: 30 Jan 2018
Posts: 17
Re: The members of a company’s board of directors must select  [#permalink]

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22 Sep 2018, 22:39
Harshgmat wrote:
The members of a company’s board of directors must select a subcommittee to decide the compensation level for a new Chief Executive Officer. The by-laws of the board state that no more than half of the members of the board can serve on this subcommittee. Is the number of combinations of board members that can be selected to serve on the subcommittee greater than 900?

(1) The board decides to select 6 members for the subcommittee.

(2) There are 12 members of the board.

Hi,

I think the answer should be B.

Let's take each option and solve the question:
Given Info: no more than half of the members of the board can serve on this subcommittee.

So from option A, we don't know the total number of members in the original committee.
For eg: If the total number of members in the committee is 12 than the condition total number of combinations will be 12C6<900 but if total number of members in the committee is 15 than the total number of combinations will be 15C6>900(here 6 is < half of 15).
Hence option A does not give the answer.

Now, let's take option B,
we are given the initial total number of members in the board committee and we select the maximum number of members for subcommittee i.e. 12/2=6 then the total number of combinations will be 12C6<900. hence this option is sufficient to give the answer.

Hence answer should be option B.

Kindly let me know where I am going wrong.

Hit the kudos if I am right.
Intern
Joined: 22 Sep 2018
Posts: 11
Re: The members of a company’s board of directors must select  [#permalink]

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24 Sep 2018, 05:13
1
jainanurag470 wrote:
Harshgmat wrote:
The members of a company’s board of directors must select a subcommittee to decide the compensation level for a new Chief Executive Officer. The by-laws of the board state that no more than half of the members of the board can serve on this subcommittee. Is the number of combinations of board members that can be selected to serve on the subcommittee greater than 900?

(1) The board decides to select 6 members for the subcommittee.

(2) There are 12 members of the board.

Hi,

I think the answer should be B.

Let's take each option and solve the question:
Given Info: no more than half of the members of the board can serve on this subcommittee.

So from option A, we don't know the total number of members in the original committee.
For eg: If the total number of members in the committee is 12 than the condition total number of combinations will be 12C6<900 but if total number of members in the committee is 15 than the total number of combinations will be 15C6>900(here 6 is < half of 15).
Hence option A does not give the answer.

Now, let's take option B,
we are given the initial total number of members in the board committee and we select the maximum number of members for subcommittee i.e. 12/2=6 then the total number of combinations will be 12C6<900. hence this option is sufficient to give the answer.

Hence answer should be option B.

Kindly let me know where I am going wrong.

Hit the kudos if I am right.

12C6 is 924. So 12C6>900.
In this case the answer will always be yes.
So statement 1 is sufficient.
In statement 2:
You can select a maximum of 6 and even a minimum of 2.
Thus insufficient.
Director
Joined: 20 Feb 2015
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Concentration: Strategy, General Management
Re: The members of a company’s board of directors must select  [#permalink]

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24 Sep 2018, 05:27
Harshgmat wrote:
The members of a company’s board of directors must select a subcommittee to decide the compensation level for a new Chief Executive Officer. The by-laws of the board state that no more than half of the members of the board can serve on this subcommittee. Is the number of combinations of board members that can be selected to serve on the subcommittee greater than 900?

(1) The board decides to select 6 members for the subcommittee.

(2) There are 12 members of the board.

let the total number of board members be x
then according to bylaws
number of members for deciding the CEO $$<=$$ x/2 say n

(1) The board decides to select 6 members for the subcommittee.
x can be 12 or 100 or any other number > 12
not sufficient

(2) There are 12 members of the board.
The subcommittee can have 0<n<7 members
total number of combinations can be 6 members + 5 members + 4 members + 3 .....+1 member
If the subcommittee has 6 members = 12C6 = 924 > 900
therefore the number of such combinations will always be > 900

sufficient
B
Manager
Joined: 20 Jul 2018
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WE: Corporate Finance (Investment Banking)
Re: The members of a company’s board of directors must select  [#permalink]

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17 Nov 2018, 12:01
1
The members of a company’s board of directors must select a subcommittee to decide the compensation level for a new Chief Executive Officer. The by-laws of the board state that no more than half of the members of the board can serve on this subcommittee. Is the number of combinations of board members that can be selected to serve on the subcommittee greater than 900?

(1) The board decides to select 6 members for the subcommittee.

(2) There are 12 members of the board.

(1) SUFFICIENT

No more than half of the members of the board can serve on subcommittee. If the board decides to select 6 members, it means that there are at least 12 members of company's board of directors. It can be 13, 14, 15 (...). That means 924+ combinations.

(2) NOT SUFFICIENT

There are 12 members. If we were to choose 6 of them, there are 924 (12C6) combinations. If less, the number of combinations declines.
Intern
Joined: 12 Nov 2018
Posts: 3
Re: The members of a company’s board of directors must select  [#permalink]

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18 Nov 2018, 16:16
12C6 = 12!/(6!(12-6)!) = (12*11*10*9*8*7)/6!

Is there any quick way to multiply this last part out?
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Joined: 20 Jul 2018
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WE: Corporate Finance (Investment Banking)
Re: The members of a company’s board of directors must select  [#permalink]

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18 Nov 2018, 16:23
2
Iorek wrote:
12C6 = 12!/(6!(12-6)!) = (12*11*10*9*8*7)/6!

Is there any quick way to multiply this last part out?

$$\frac{(12*11*10*9*8*7)}{(1*2*3*4*5*6)}$$

10 = 2*5
12 = 3*4

you're now left with

$$\frac{(11*9*8*7)}{(1*6)}$$

div. 9 and 6 by 3; 8 with 2

$$\frac{(11*3*4*7)}{(1)}$$

11*7*3 = 77 * 3 = 70*3+7*3=210+21 = 231
231*4 = 200*4+31*4 = 800 + 124 = 924

I employ the above method myself. I am known for being extremely fast at arithmetic and, in my opinion, this is the best method one can use.
Cheers.
Re: The members of a company’s board of directors must select   [#permalink] 18 Nov 2018, 16:23
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