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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Permutations/Combinations
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vaibhav101
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arosman
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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
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
Adam Rosman, MD
University of Chicago Booth School of Business, Class of 2020
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University of Chicago Booth School of Business, Class of 2020
[email protected]
Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock.
https://www.alldaytestprep.com
