Question: There are 10 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?

1. 15
2. 30
3. 45
4. 60
5. 120

Correct Answer: A
Solution and Explanation:
Approach Solution 1:

Due to the "spread out" nature of the answer options, there is an intriguing method that uses "brute force" and comparison instead of intricate math to arrive at the right answer:
There are ten people in the room, and each one is instructed to shake hands with three other individuals.
Assume there were 4 individuals, whom we will refer to as A, B, C, and D.

These would be the handshakes:
AB
AC
AD
BC
BD
CD

There were a total of 6 handshakes in this instance, 3 handshakes per person.
Three times as many people would result in 12 people and three times as many handshakes (6 x 3 = 18).

A is the correct answer.

Approach Solution 2:

Everyone exchanges handshakes with exactly three other people.
As a result, there are a total of 30 handshakes between our 10 participants.

It's crucial to note that every handshake has now been counted twice at this stage. For instance, if two people, A, and B, shake hands, A counts it as a handshake, and B counts it as a handshake. Of course, there was only one handshake.

We'll split the duplicate by two to get 15 in order to account for it.
The correct answer is option A.

Approach Solution 3:

Every team competes against "all" other teams in the game (so each team plays with 7 other teams). There are always exactly two teams in each game.
Games = 8 * 7 2 = 28

Each participant in the handshake puzzle shakes hands with three additional individuals. There are exactly two people involved in each handshake.
Handshakes = 10 * 1/3 = 15

A is the correct choice.

“There are 10 people in a room. If each person shakes hands with exactly 3 other people" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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