M01, Q24 : GMAT Club Tests

M01, Q24

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Joined: 28 Dec 2011

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Location: United States (IL)

Concentration: International Business, Nonprofit

Schools: HBS '15 (D), Kellogg '15 (WL), Booth '15 (M), Ross '15 (A), Duke '15 (A), Darden '15 (A)

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M01, Q24 [#permalink]

29 Dec 2011, 15:55

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If 5 noble knights are to be seated at a round table, then how many different ways can they be seated?

120
96
60
35
24

Fix a knight in a spot to arrange the rest. The formula is (5-1)!, or 4!

The correct answer is E.

Why is the answer 4! and not (5!)?

I can't wrap my head around that.

When I see 5 people, 5 empty spots, I automatically think - ok

5x4x3x2x1 = 5!

1st seat can have any of the 5
2nd seat will have one of the remaining 4...etc etc etc.
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Joined: 28 Dec 2011

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Re: M01, Q24 [#permalink]

29 Dec 2011, 16:56

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Great question! I'm happy to help!

You are SO close --- in fact, if we were seating these five knights in a straight line (for example, on a long bench), then the number of arrangements would be 5! = 120

Here's what's diabolically tricky about this question: they're at a ROUND table.

Suppose the 5 knights are A, B, C, D, and E.

If they sit as ABCDE vs.CDEAB on a bench, those are two very different arrangements. At a round table though (assuming there are five seats equally spaced around the table), those two are identical arrangements: each knight has the same two neighbors on his same respective sides. These two seating plans are shown in the diagram below.

So, really the question is: let's say A sits in a seat --- that could be any seat, since they are all symmetrical. Once A has sat, there are 4! ways for the other four knights to fill those other four spaces. Thus, only 4! possibilities.

I hope that was clear and helpful. Please let me know if you have any questions.

Mike

Attachments

knights' seating plans.PNG [ 25.5 KiB | Viewed 291 times ]

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Mike McGarry
Magoosh Test Prep

Intern

Joined: 28 Dec 2011

Posts: 9

Location: United States (IL)

Concentration: International Business, Nonprofit

Schools: HBS '15 (D), Kellogg '15 (WL), Booth '15 (M), Ross '15 (A), Duke '15 (A), Darden '15 (A)

GMAT 1: 750 Q48 V44

GPA: 2.84

WE: Military Officer (Military & Defense)

Followers: 0

Kudos [?]: 6 [0], given: 1

Re: M01, Q24 [#permalink]

29 Dec 2011, 20:19

Once I posted, the similar threads thing on the bottom popped up and I found the answer. But your explanation was very clear and concise. Thank you.
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"Never doubt that a small group of thoughtful, committed citizens can change the world. Indeed, it's the only thing that ever has" - Margaret Mead

Re: M01, Q24 [#permalink] 29 Dec 2011, 20:19

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M01, Q24

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