More GMAT Preparation: Permutations with Restrictions

January 28, 2013

General

We’ve been talking a lot about GMAT preparation lately and today we’re taking a look at permutations with restrictions.

Beat the GMAT has come up with a great approach in your GMAT preparation to this type of Quant question. You have one of two ways to approach the permutation with restrictions: you can think like a rebellious teenager and violate the restrictions or you can embrace them.

What does this mean? Well, take a look at this sample question offered by Beat the GMAT:

“Donald is going to the Opera. He is going with six friends. Donald is a little claustrophobic and cannot have more than one person between him and the aisle. If the row is exactly six seats wide, how many different ways can Donald and his friends be seated if they are all seated in the same row?”

The standard way to approach this question is to embrace the restrictions and “only calculate those arrangements that are consistent with the restriction”–calculating only for those seats that Donald would find acceptable.

But real GMAT preparation means trying out many approaches, not just the standard way. Try out the rebellious teenager, who will ignore the restriction and “find the number of possibilities without the restriction and then subtract the number of arrangements that are prohibited by the restriction.”

“In other words, quickly solve for 6!…the number of possible ways for 6 people to sit in a row of 6 chairs. That equals 720. Now as for that restriction on Donald’s choice of seat – act like a teenager and violate it! If you are told that he cannot sit in the middle then put him there and see what happens!”

So which will you do: embrace or rebel? Of course, you should prepare for both during your GMAT preparation because, like the old saying goes, there will be a time and a place for everything. As you research and apply to Virginia business schools, keep all this in mind and don’t be afraid to rebel against the rules once in a while.


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