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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Rockying** » Sun Sep 04, 2011 5:33 am
In a party, there one man dances exactly with 3 ladies & 1 woman dances exactly with 3 men . there are exactly two pairs are common with every men. how many people are there in party?
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by saketk » Tue Sep 06, 2011 11:49 pm
Rockying** wrote:In a party, there one man dances exactly with 3 ladies & 1 woman dances exactly with 3 men . there are exactly two pairs are common with every men. how many people are there in party?
Hi -- The language used in the question is not as per the GMAT standards, I'll rephrase the question for better understanding...

In a Party, each man dances with exactly 3 women, each women dances with exactly 3 men. Among each pair of men they have exactly two women in common. Find the no. of men and women

Then answer is 8
Solution:

Men -- M1, M2... etc
Women -- W1, W2.. etc

the pair can we arranged this way --

M1-W1; M1-W2; M1W3 -- FIRST PAIR

Now, we have a condition -- each men has exactly 2 women in common.
so, we need 1 extra woman for next pair

M2-W1; M2-W2; M2W4
LIKEWISE, WE CAN ARRANGE MEN FOR W4 AS WELL.

M3-W1; M3-W3; M3W4
Last Pair; -- M4-W2; M4-W3; M4-W4
TOTAL --

4 Men -- M1 M2 M3 M4
4 Women -- W1 W2 W3 W4 = 8 :)
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