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Generalized Equation

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Intern
Joined: 27 Nov 2017
Posts: 2

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27 Nov 2017, 18:57
Suppose there are 4 schools participating in a state tennis tournament. Each school has 3 tennis players. Each tennis player must play a match with every tennis player except the ones from his or her own school. How many matches will there be?

With drawing this out I came up with 54.

The issue I'm having is that I can't come up with a generalized equation that would work for this problem. As well as if I wanted to add more schools or players.

Can anyone help me?
Intern
Joined: 27 Nov 2017
Posts: 2

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27 Nov 2017, 19:26
or is it just 108 and i'm overthinking the problem
SVP
Joined: 15 Jul 2015
Posts: 2011
Location: India
GMAT 1: 780 Q50 V51
GRE 1: Q170 V169

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27 Nov 2017, 22:17
Icejet wrote:
Suppose there are 4 schools participating in a state tennis tournament. Each school has 3 tennis players. Each tennis player must play a match with every tennis player except the ones from his or her own school. How many matches will there be?

With drawing this out I came up with 54.

The issue I'm having is that I can't come up with a generalized equation that would work for this problem. As well as if I wanted to add more schools or players.

Can anyone help me?
Did you get to 54 with 27+18+9?

Perhaps you could also go with the total number of matches LESS the number of intraschool matches:

[C(Total number of players, 2)] − [(Number of schools) × C(Number of players per school, 2)]

This is when the number of players per school is the same (and only 2 player matches).

In this case, we'll get C(12, 2) − [4 × C(3,2)] = 66 − 12 = 54
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28 Nov 2017, 12:22
Hi Icejet,

Your question presupposes that you're supposed to come up with a 'math equation' to answer the given question. However, most GMAT questions are designed so that they can be approached in more than one way - and in many cases the "math approach" takes more time than an alternative, more-strategic approach. For example, in this question, a bit of basic multiplication and some light note-taking is all that's needed to answer the question.

The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that requires lots of little calculations as you work through it. Beyond having the necessary Quant knowledge and abilities, to score at a higher level in this section, you will likely need to become more of a 'strategist' and less of a 'mathematician.'

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Re: Generalized Equation &nbs [#permalink] 28 Nov 2017, 12:22
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Generalized Equation

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