At the beginning of a party, each person present shook hands with all

Question

At the beginning of a party, each person present shook hands with all other people present and there were in all 28 handshakes. In the midst of the party,2 persons left due to an emergency. Now, the number of males and females present in the party was equal. At the end, each female shook hands only with every female present and each male shook hands only with every male present. What is the total number of handshakes that took place at the party?

(A) 52
(B) 45
(C) 35
(D) 34
(E) 33

(A) 52
(B) 45
(C) 35
(D) 34
(E) 33

chetan2u · Accepted Answer

Number of handshakes is same as choosing two persons. 
So, if n persons were there, nC2=28
 \frac{n(n-1)}{2}=28........n(n-1)=56=8*7

That means there are 8 people at the beginning of the party. Two leave, so 6 remain. 
In these 6, we have equal numbers of men and women, so 3 each.

Handshakes within men=3C2=3.
Similarly within women, 3C2 or 3 handshakes.

Now, the number of handshakes are to be found for entire party. 
Total 28+3+3=34.

D

ScottTargetTestPrep · Answer

Solution:

Let n be the number of people originally at the party. Since there were 28 handshakes exchanged, we can create the equation:

nC2 = 28

n(n - 1) / 2 = 28

n(n - 1) = 56

Without solving the equation any further, we can see that n must be 8 since 8 x 7 = 56. Now, since 2 people have left and there are an equal number of men and women, there must be 3 men and 3 women. Since the men shake hands only with men, there are 3C2 = 3 handshakes between the men. Likewise, since the women shake hands only with women, there are also 3C2 = 3 handshakes between the women. Therefore, including the first 28 handshakes, there are a total of 28 + 3 + 3 = 34 handshakes.

Answer: D

aniruddhawarang29 · Answer

I agree to all the numerical values calc..
But in the end the task of Women shaking hands with women AND men shaking hand with men.

As per my learnings..

since the two tasks are necessary tasks and not optional tasks, then should we not use X (Multiplication sign) between 3 & 3 instead of + sign?
Or am I confusing my self with this task related concept?

bumpbot · Answer

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At the beginning of a party, each person present shook hands with all

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At the beginning of a party, each person present shook hands with all

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