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Confusing Information-Each of the three charities

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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!!
The mind is everything. What you think you become. -Lord Buddha



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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?
The mind is everything. What you think you become. -Lord Buddha



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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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