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Confusing Information-Each of the three charities

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Confusing Information-Each of the three charities

by alivapriyada » Mon Sep 13, 2010 4:09 am
Each of the three charities in Novel Grove Estates has got 8 persons serving on its board of directors .If exactly 4 persons serve on three boards each and each pair of the 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. 13
C. 16
D. 24
E. 27
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by kmittal82 » Mon Sep 13, 2010 4:30 am
Let's break the 3 charities down

>If exactly 4 persons serve on three boards each

1: A B C D _ _ _ _
2: A B C D _ _ _ _
3: A B C D _ _ _ _

>each pair of the charities has 5 persons in common on their boards of directors

1: A B C D E F _ _
2: A B C D F G _ _
3: A B C D E G _ _

The remaining blanks could be distinct people, lets call them: H I J K L M

Thus total number of distinct people = A B C D E F G H I J K L M = 13

Should be (B), whats the OA?
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by alivapriyada » Mon Sep 13, 2010 4:37 am
Let's break the 3 charities down

>If exactly 4 persons serve on three boards each

1: A B C D _ _ _ _
2: A B C D _ _ _ _
3: A B C D _ _ _ _

>each pair of the charities has 5 persons in common on their boards of directors

1: A B C D E F _ _
2: A B C D F G _ _
3: A B C D E G _ _

The remaining blanks could be distinct people, lets call them: H I J K L M

Thus total number of distinct people = A B C D E F G H I J K L M = 13

Should be (B), whats the OA?
Hey M really sorry ,I didn't understand your approach.Could you please explain it further
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by sanju09 » Mon Sep 13, 2010 4:38 am
alivapriyada wrote:Each of the three charities in Novel Grove Estates has got 8 persons serving on its board of directors .If exactly 4 persons serve on three boards each and each pair of the 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. 13
C. 16
D. 24
E. 27
I am going to give it the closest ever look now, just make sure if it's properly copied, just once please!!
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by alivapriyada » Mon Sep 13, 2010 4:46 am
@Sanju09
yes it is properly copied
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by sanju09 » Mon Sep 13, 2010 4:52 am
alivapriyada wrote:@Sanju09
yes it is properly copied
then (B) and kmittal82 are right, what didn't you get in his approach, by the way?
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by kmittal82 » Mon Sep 13, 2010 5:01 am
Let the charities be 1,2 and 3.
I'm using alphabets to represent the people on each board.

Let A B C and D be the 4 people common to each charity.

1: A B C D _ _ _ _
2: A B C D _ _ _ _
3: A B C D _ _ _ _

_ represents an empty slot

Hope it makes deciphering my answer a bit easier.
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by alivapriyada » Mon Sep 13, 2010 5:19 am
got my doubt cleared!!!
Many thanx to you guys!!
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