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

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

BrentGMATPrepNow sir

Can you please validate my approach?

Looks good to me!

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

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

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

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