Discussion
In a business meeting, each person shakes hands with each other person once. A person arrives after 5 people have left and he shakes hands only with those present. If the total number of handshakes is exactly 100, then the initial number of people in the party, is
Answer: C
There were 14 people initially.
With n people, everyone shakes hands with everyone once: \(\binom{n}{2}\) handshakes. After 5 leave, the newcomer shakes hands with the n − 5 still present.
\[ \begin{aligned} \frac{n(n - 1)}{2} + (n - 5) &= 100 \\ n = 14: \ 91 + 9 &= 100 \end{aligned} \]
Checking the neighbours shows 14 is the only fit: n = 13 gives 78 + 8 = 86 and n = 15 gives 105 + 10 = 115.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development