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Permutations and Combination

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by BTGmoderatorRO » Sun Dec 24, 2017 9:18 am
The 180 students in a group are to be seated in rows so that there is an equal number of students in each row. Each of the following could be the number of rows EXCEPT

(A) 4
(B) 20
(C) 30
(D) 40
(E) 90

OA is D
In how many ways can this be arranged? I need an Expert contribution.Thanks
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by elias.latour.apex » Sun Dec 24, 2017 11:21 am
This problem could easily be backsolved by just plugging in answer choices until we realize that 180 does not divide evenly by 40.

However, a more elegant solution would be to factor 180 into its prime factors. 180 = 18 * 10 , which breaks down into (2)(2)(3)(3)(5) as prime factors.

We can combine these prime factors to come up with all of the answer choices except (D).
(A) = 2*2
(B) = 2*2*5
(C) = 2*3*5
(D) cannot be constructed because we don't have enough 2s as prime factors.
(E) = 2*3*3*5
Elias Latour
Verbal Specialist @ ApexGMAT
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