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# The Quest for 700: Weekly GMAT Challenge (Answer)

Yesterday, Integrated Learning posted a 700 level GMAT question on our blog. Today, they have followed up with the answer:

This problem is VERY tricky, but the logic is actually fairly straightforward.  This must be a combinations question because we know that each player shakes hands once.  In a combinations question, do the problem as if it were a permutations problem, and then just divide by the factorial of the number of spaces (there is a proper formula for this, but it’s completely unnecessary to learn it).

How many people take part in a handshake?  Two.  So there must be two spaces.  But in this case we have to use the logic of the problem to answer it correctly.  There are 35 people who can be in the first spot, but that person cannot shake hands with anyone on his own team.  So that person has only 30 people who’s hands he can shake!  That will be reflected in the combination.  So let’s approach it using the method and this logic:

Do the problem as if it was a permutations problem.
_35_ x _30_
Divide the answer by (the number of spaces)!
There are two spaces, so divide by 2!  And don’t forget to cancel!

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