In a room of 12 people, each person shook hands with exactly 3 other p

Question

In a room of 12 people, each person shook hands with exactly 3 other people. How many handshakes took place?

A) 18
B) 36
C) 55
D) 110
E) 220

100mitra · Answer

Correct Option A

12 * 3 = 36 (counted 2 times)
36/2 = 18 Nos (single time)

rocky620 · Answer

IMO Option A.

Since if every person shook hands with every other person total handshakes would be 66. But if every person shook hands with only 3 person. This number will be less.

In order to meet the above condition, lets divide people in groups of 4. There will be 3 such groups. Now we can satisfy the limitation of 3 handshakes.

Per group there will be 6 hand shakes. So, total handshakes will be 3*6 =  18

BrentGMATPrepNow · Answer

Let's say the 12 people are  A, B, C, D, ...., K and L

If each person shook hands with exactly  3  other people, then person A participated in 3 handshakes.
Similarly, person B participated in  3  handshakes. 
Person C participated in  3  handshakes. 
.
.
.
Person K participated in  3  handshakes. 
Person L participated in  3  handshakes.

So, the total number of handshakes = (12)( 3 ) =   36   (but the correct answer is not B)

Notice that every handshake has been counted TWICE. 
For example, if B and G shook hands, then person B counted the handshake, AND person G counted the same handshake.

To account for this duplication, we'll divide   36   by 2 to get  18

Answer: A

rocky620 · Answer

BrentGMATPrepNow  sir

Can you please validate my approach?

BrentGMATPrepNow · Answer

Looks good to me!

I might explain why each group of 4 will have a total of 6 handshakes (i.e., 4C2 = 6)

Abhishek009 · Answer

A shakes hand with  B , C  &  D  = 3
B shakes hand with  A , C  &  D  = 3
C shakes hand with  A , B  &  D  = 3

A shaking hand with B is the same as B shaking hand with A  and we have considered it twice, actual countable handshake is 1

Now,  12  people will make  12*3 = 36  Handshakes

Since Handshakes are counted twice, actual no of handshakes will be  \frac{36}{2} = 18 , Answer must be (A) 18

Aryaa03 · Answer

Sol:
 Option-A

Let's imagine two rows of 6 people standing opposite each other (Just like a sports team in front of award presenters).
For round 1: 
They shake hands with the person right in front. - Total handshakes per person - 1; Total Handshake = 6
For round 2: 
Keep presenters at the same spot, and move the other row by one place in any one direction - 1st person moves to the last, 2nd moves in the place of 1st and so on
Total handshakes per person - 1 + 1 = 2; Total Handshake = 6 + 6 = 12
For round 3: 
Move the team's row by one place again
Total handshakes per person - 1 + 1 + 1 = 3; Total Handshake = 6 + 6 + 6 =18

Condition for 3 handshake each met. Total no. of handshakes = 18

Kinshook · Answer

Given: In a room of 12 people, each person shook hands with exactly 3 other people. 
Asked: How many handshakes took place?

Total handshakes = 12*3 = 36
But the handshakes are counted twice, therefore, total handshakes without repetition = 36/2 = 18

IMO A

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In a room of 12 people, each person shook hands with exactly 3 other p

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