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Permutations/Combinations

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Permutations/Combinations

by vaibhav101 » Sat Jun 16, 2018 12:30 am

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B

C

D

E

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there are x people and y chairs in a room where x and y are positive prime numbers. How many ways can the x people be seated in y chairs (assuming that each chair can seat exactly one person)?

1) x+y=12
2) there are more chairs than people
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Source: — Data Sufficiency |
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by arosman » Wed Jun 20, 2018 2:39 pm

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B

C

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1) The only combinations of positive prime numbers that add to 12 are 7 & 5. This gives us two scenarios

Scenario 1:
- x = 7 people
- y = 5 chairs

Total combos = 7 * 6 * 5 * 4 * 3 = 2520

Scenario 2:
- x = 5 people
- y = 7 chairs

Even though there are only 5 people there are actually 7 options for what can fill each chair - one of the five people or one of the two empty spots=
Therefore answer is 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5040

-----> INSUFFICIENT


2) Doesn't help if we don't know the total
---> INSUFFICIENT

1 & 2) Scenario 2 from statement 1 is only possibility. Total combos = 5040.
-----> SUFFICIENT

Answer: C
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