500 ps test6 #20

Expert replies

dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Thu Apr 05, 2007 3:12 pm

Hi,

I though the answer is 10P9 C) but the correct answer is D).....

. If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

Like this post

Source: Beat The GMAT — Problem Solving | Thu Apr 05, 2007 3:12 pm

vk.neni: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Tue Mar 27, 2007 2:53 pm

by vk.neni » Thu Apr 05, 2007 7:47 pm

Hi, This is the sum of a progression kind of problem.

The 1st person would shake with 9 others, the 2nd would do with 8 others etc. So, the final answer would 9+8+...+1 = 9*(9+1)/2 = 45.
Answer D.

Like this post

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Thu Apr 05, 2007 8:56 pm

Simply put, we are asked to find the number of ways 10 people can
shake hands with each other.

10C2 is the answer

Like this post

dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Thu Apr 05, 2007 9:28 pm

Thank you.

I am always confursed using P and C... (if you could a bit explain, that would be soo great...)

In this case, 10C2, 10 is obviously 10 people, but where the number 2 come from? meaning avoiding duplication?

Thanks!

Like this post

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

by jayhawk2001 » Thu Apr 05, 2007 9:44 pm

dunkin77 wrote:Thank you.

I am always confursed using P and C... (if you could a bit explain, that would be soo great...)

In this case, 10C2, 10 is obviously 10 people, but where the number 2 come from? meaning avoiding duplication?

Thanks!

You might want to check out the GMAT resource wiki. It has a lot of
useful info in there that I have personally found helpful

https://www.beatthegmat.com/wiki/doku.ph ... _resources

Like this post

Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Sat Apr 07, 2007 12:21 am

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A) 10•9•8•7•6•5•4•3•2•1
(B) 10•10
(C) 10•9
(D) 45
(E) 36

For a handshake 2 people are required. Hence 2 people can be selected from a group of 10 in 10C2 ways

= 45

Hence Choice D

Like this post

BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Sun Oct 29, 2017 9:45 am

since each person shakes hands exactly once with each of the others, this is just the same as grouping two people together without considering the order.
e.g in {a,b,c,d}, the number of handshakes will be 6. i.e {a,b], {a,c}, {a,d}, {b,c}, {b,d} and {c,d}.
This is given by $$n_{Cr}$$ , where n is the total number of people and r is the number of people shaking hands once.
Total number of handshakes is thus given as
$$_{10_{C2}=\ \frac{10!}{\left(10-2\right)!2!}\ =\ \frac{\left(10\cdot9\cdot8!\right)}{8!\cdot2!}=\frac{\left(10\cdot9\right)}{2}=45}$$
$$Therefore,\ there\ will\ be\ 45\ handshakes\ if\ two\ people\ do\ not\ shake\ hands\ with\ each\ other\ more\ than\ one\ time$$

Like this post

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 30, 2017 8:47 am

If 10 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?

(A) 10!
(B) 10*10
(C) 10*9
(D) 45
(E) 36

Another approach:

Once everyone has shaken hands, ask each of the 10 people, "How many people did you shake hands with?"
We'll find that EACH PERSON shook hands with 9 people, which gives us a total of 90 handshakes (since 10 x 9 = 90).

From here we need to recognize that every handshake has been counted TWICE. For example, if Person A and Person B shake hands, then Person A counts it as a handshake, AND Person B also counts it as a handshake. Of course only one handshake occurred.

To account for the duplication, we'll divide 90 by 2 to get 45

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review