Chess

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Mon Dec 20, 2010 7:51 am

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with
every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The
number of games in which one player was a boy and the other was a girl is

I. 200
2. 216
3. 235
4. 256
5. 171

According to me Answer is 171, What do you think Guys.

Saurabh Goyal
[email protected]
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EveryBody Wants to Win But Nobody wants to prepare for Win.

Source: Beat The GMAT — Problem Solving | Mon Dec 20, 2010 7:51 am

4GMAT_Mumbai: Master | Next Rank: 500 Posts; Posts: 161; Joined: Mon Apr 05, 2010 9:06 am; Location: Mumbai; Thanked: 37 times

by 4GMAT_Mumbai » Mon Dec 20, 2010 7:59 am

Hi,

If both players were girls in 45 games; then there are 10 girls

If both players were boys in 190 games; then there are 20 boys.

Hence, there are 200 games involving a boy and a girl.

PS ... Perhaps, 171 is the result if somebody goes with the construct that there are 9 girls and 19 boys ...

Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Mon Dec 20, 2010 8:05 am

goyalsau wrote:In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

1. 200
2. 216
3. 235
4. 256
5. 171

Let number of girls = g and number of boys = b
Then gC2 = 45 => g(g - 1) = 90 => g = 10
and bC2 = 190 => b(b - 1) = 380 => b = 20

Number of games in which one player was a boy and the other was a girl = (Number of ways to select a girl out of 10)*(Number of ways to select a boy out of 20) = 10*20 = 200

The correct answer is A.

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Mon Dec 20, 2010 8:15 am

4GMAT_Mumbai wrote:Hi,

If both players were girls in 45 games; then there are 10 girls

If both players were boys in 190 games; then there are 20 boys.

Hence, there are 200 games involving a boy and a girl.

PS ... Perhaps, 171 is the result if somebody goes with the construct that there are 9 girls and 19 boys ...

Thanks Buddy, I forgot to add 1

Thanks...

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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