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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 is a combinations problem (because the order doesn’t matter), and, specifically, a “Pairing” question.  We at Integrated Learning single them out because they require a specific understanding of combinations, and come up frequently on the exam.

In combinations, we lay out the number of spots, fill in the number of options for each spot, multiply, and then divide by the factorial of the number of spots.  There are oft-learned formulae for combinations, but we ignore them for the GMAT in favor of a more conceptual approach.

There are only two spots in a handshake: the first person shaking hands and the second.

There are 35 people who can be in the first spot.  That’s because there are 7 teams with 5 people each.  Every one of those people are possible for the first spot in the handshake.

The second spot gets more constricted.  The constraint is that no one can shake hands in their same team.  So once one person is chosen from the original 35, there are now only 30 people left to shake hands with (6 teams with 5 people each).

So we have 35 x 30.  Multiply and get 1050.

As a final step though, because it’s a combinations question, we must divide by the factorial of the number of spots.  In this case, there are two spots, so we divide by 2!, or, simply, 2.

1050/2 = 525.

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