There are 5 chess amateurs playing in Villa's chess club...

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BTGmoderatorLU: Moderator; Posts: 2550; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Dec 15, 2017 1:41 pm

There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total numbers of chess games possible to be played in the tournament?

A) 10
B) 20
C) 40
D) 60
E) 120

The OA is A.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Fri Dec 15, 2017 1:41 pm

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by [email protected] » Fri Dec 15, 2017 3:37 pm

Hi LUANDATO,

We're told that there are 5 chess amateurs playing in a tournament and that each chess amateur plays with exactly 4 other amateurs (meaning that each amateur plays each of the other amateurs once). We're asked for the total numbers of chess games played in the tournament. This question can be solved in a couple of different ways. Since the number of chess players is so small, you might find it easiest to just list out the possible matches:

Let's call the chess players A, B, C, D and E

Since each amateur plays each other amateur just once, the matches would be...
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE
10 total matches

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMATWisdom: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Nov 29, 2017 4:38 pm; Thanked: 14 times

by GMATWisdom » Sat Dec 16, 2017 9:13 am

LUANDATO wrote:There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total numbers of chess games possible to be played in the tournament?

A) 10
B) 20
C) 40
D) 60
E) 120

The OA is A.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

since in every game are there two players hence number of games would be 5C2=5!/3!2!=10
hence option A

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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 » Sat Dec 16, 2017 9:28 am

LUANDATO wrote:There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total numbers of chess games possible to be played in the tournament?

A) 10
B) 20
C) 40
D) 60
E) 120

There are 5 players altogether.

If you ask any chess player, "How many people did you play chess against?", he/she will say 4.

So, the TOTAL number of games played = (5)(4) = 20

But wait, we have counted every game TWICE. For example, Player A counted his/her game with Player D, and Player D counted his/her game with Player A.

To account for this duplication, we must divide 20 by 2 to get 10.

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Sat Dec 16, 2017 11:26 am

Hi LUANDATO,

We're told that there are 5 chess amateurs playing in a chess club tournament and each chess amateur plays with EXACTLY 4 other amateurs (meaning that each player plays each other player once). We're asked for the total numbers of chess games played in the tournament. This question can be solved in a couple of different ways - and since the number of chess players is so SMALL, you can simply list out all of the possible games.

Let's call the chess players A, B, C, D and E.

The games played would be....
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE

Ten total games.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8147; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Sep 23, 2019 4:33 pm

BTGmoderatorLU wrote:There are 5 chess amateurs playing in Villa's chess club tournament. If each chess amateur plays with exactly 4 other amateurs, what is the total numbers of chess games possible to be played in the tournament?

A) 10
B) 20
C) 40
D) 60
E) 120

The OA is A.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

The total number of games is 5C2 =(5 x 4)/2! = 10 games.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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