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# Each of the three charities in X state has 8 persons serving

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Each of the three charities in X state has 8 persons serving [#permalink]  16 Feb 2004, 20:30
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Each of the three charities in X state has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?

a - 8

b - 16

c - 24

d - 13

e - 27
Manager
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I didnt understand the question at all.
Manager
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me too........its tooooooooooooo confusing man
Director
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As far as I understood the question , guess the answr is 8
GMAT Instructor
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Re: PS [#permalink]  17 Feb 2004, 06:05
moma wrote:
Each of the three charities in X state has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?

a - 8

b - 16

c - 24

d - 13

e - 27

this question is fine and unambiguous. don't be lazy and give up - and wait for the answer. That is one of the worse studying habits. YOU MUST ASSUME EVERY QUESTION IS FAIR (unless someone expert tells you it is not ) Draw a picture or diagram with 3 columns and read carefully again and MAKE AN EFFORT. Part of what you are tested on is your ability to understand a seemingly confusing question. In fact, this question is EXTREMELY EASY.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

GMAT Instructor
Joined: 07 Jul 2003
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Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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BG wrote:
As far as I understood the question , guess the answr is 8

could you explain the logic?

You asked me how to get faster at word problems. One short answer is you have to try -- not throw up hands and ask for the answer.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Last edited by AkamaiBrah on 23 Feb 2004, 06:53, edited 1 time in total.
Senior Manager
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I got 13.

Draw a Venn diagram. Place 4 in the intersection for all three circles to show members that belong to all three boards. Place 1 in the intersection of any 2 circles to show the extra member from each charity.

1 + 4 = 5 shared members

So, for each charity, we'll have 8-4-1-1=2 members that exclusively belong to that charity.

so, 2+2+2+1+1+1+4 = 13
Senior Manager
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Akamai, you are so right.. you inspired me to try this out.. and i did some of my own calculations.. and got 8
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shubhangi

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shubhangi wrote:
Akamai, you are so right.. you inspired me to try this out.. and i did some of my own calculations.. and got 8

EVen if you get it wrong, or if you do it wrong, the exercise of working it through will teach you not to make the same mistake again and is indeed quite valuable as long as you go back and understand THOROUGHLY the proper technique (or techniques).

Even if you get it right, ask yourself, "was there a better way that I could have done it" and think about it, noodle around. See what works, what doesn't, try to understand why it worked/didn't work.

THEN go to the next problem.

_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Senior Manager
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Yep the answer should be 13.

The key to solve this problem is to understand the meaning of the statement in the bold.

Each of the three charities in X state has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?
Senior Manager
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shubhangi wrote:
Akamai, you are so right.. you inspired me to try this out.. and i did some of my own calculations.. and got 8

In addition to what Akamai has said, my 2 cents. The answer could not have been 8. Because the very first statement in the problem states that "Each of the three charities in X state has 8 persons serving on its board of directors." Now we know that there is an overlap between the members to different charities. So the answer would be less than (8+8+8) = 24. But at the same time it would be more than just 8. This kind of checks could at least naroow down the choices.
Senior Manager
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Good question...even I was lost...followed the thread...bumped into Akamai's hard hitting suggestions...worked up a venn diagram...did not get the right answer...saw ndidi204's explantation...realised my folly...had not taken all the circles of the venn diagram into consideration...did it once again..voila...I got 13 too.

Thanks a bunch to all those who contributed to this thread...this thread personifies the very mission of this forum of growing and helping others grow too.

Vivek.
_________________

"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

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Re: PS [#permalink]  17 Feb 2004, 08:40
AkamaiBrah wrote:
moma wrote:
Each of the three charities in X state has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?

a - 8

b - 16

c - 24

d - 13

e - 27

this question is fine and unambiguous. don't be lazy and give up - and wait for the answer. That is one of the worse studying habits. YOU MUST ASSUME EVERY QUESTION IS FAIR (unless someone expert tells you it is not ) Draw a picture or diagram with 3 columns and read carefully again and MAKE AN EFFORT. Part of what you are tested on is your ability to understand a seemingly confusing question. In fact, this question is EXTREMELY EASY.

Akamai,

I do have one general question. Initially while solving this problem, I misinterpreted that bold, underlined statement in the problem and arrived at a different solution (16 or something). But in order to arrive at that solution, I did not use all the information given in the problem. To be more precise, I did not use the given fact that "each pair of the charities has 5 common directors". I realized this at the time of solving the problem and thought that since I am not using the given information, I must be doing something wrong. Then I looked at the problem again and then was able to arrive at the correct solution.

My question: For GMAT questions, is it safe to assume that all the given information will always have to be used in order to solve the question? Can there be a GMAT problem which can be solved without using all the information given in the problem? I know that kind of problems can exist in math courses and in material other than GMAT. But I need to know the nature of GMAT quesion. I need to understand this because for this problem that understnding allowed me to come up with the correct solution.
GMAT Instructor
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Re: PS [#permalink]  17 Feb 2004, 15:07
gmatblast wrote:
AkamaiBrah wrote:
moma wrote:
Each of the three charities in X state has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors ?

a - 8

b - 16

c - 24

d - 13

e - 27

this question is fine and unambiguous. don't be lazy and give up - and wait for the answer. That is one of the worse studying habits. YOU MUST ASSUME EVERY QUESTION IS FAIR (unless someone expert tells you it is not ) Draw a picture or diagram with 3 columns and read carefully again and MAKE AN EFFORT. Part of what you are tested on is your ability to understand a seemingly confusing question. In fact, this question is EXTREMELY EASY.

Akamai,

I do have one general question. Initially while solving this problem, I misinterpreted that bold, underlined statement in the problem and arrived at a different solution (16 or something). But in order to arrive at that solution, I did not use all the information given in the problem. To be more precise, I did not use the given fact that "each pair of the charities has 5 common directors". I realized this at the time of solving the problem and thought that since I am not using the given information, I must be doing something wrong. Then I looked at the problem again and then was able to arrive at the correct solution.

My question: For GMAT questions, is it safe to assume that all the given information will always have to be used in order to solve the question? Can there be a GMAT problem which can be solved without using all the information given in the problem? I know that kind of problems can exist in math courses and in material other than GMAT. But I need to know the nature of GMAT quesion. I need to understand this because for this problem that understnding allowed me to come up with the correct solution.

No. You cannot assume that all of the information given is essential. However, it usually is.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Actually, I didn't use Venn diagram for this one at all. Sometimes it is easier to understand for me if I can see it more intuitively.

So what I did is this:
For people served in all the three boards. Lets say they are ABCD.
Then each pair of boards have one more common person.
Code:
Board1 Board2 Board3
E         E
F       F
G                 G

The each board have two more distinct people to make it 8 people each board.

And then I counted them. ABCDEFG is seven, plus 3*2=6 is 13.
Senior Manager
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HERE IT IS:
Attachments

VENN.JPG [ 13.94 KiB | Viewed 603 times ]

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