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Lee Colle insures its students for thefts up to $1000. The college mak

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Lee Colle insures its students for thefts up to $1000. The college mak  [#permalink]

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New post 04 Dec 2019, 00:52
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Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


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Lee Colle insures its students for thefts up to $1000. The college mak  [#permalink]

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New post 04 Dec 2019, 13:07
Bunuel wrote:
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


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I got the expected number of thefts is 200 and feel free to correct me if I'm not understanding properly.

The $1000 is merely a distractor. For every 100 people, the cost of the insurance is n * 120, where n is the number of claims expected from every 100 students. The revenue is 100 * 24 = 2400. So we should get 10% * Cost = Revenue according to the problem.

10% * n * 120 = 2400
12n = 2400
n = 200
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Re: Lee Colle insures its students for thefts up to $1000. The college mak  [#permalink]

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New post 08 Dec 2019, 12:48
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TestPrepUnlimited wrote:
Bunuel wrote:
Lee Colle insures its students for thefts up to $1000. The college makes no profit but sets the premium to cover administrative costs of 10% on average claim of $120. If the annual premium per students is 24$. What is the expected number of thefts per 100 students per year?

(A) 12
(B) 14
(C) 16
(D) 18
(E) 20


I got the expected number of thefts is 200 and feel free to correct me if I'm not understanding properly.

The $1000 is merely a distractor. For every 100 people, the cost of the insurance is n * 120, where n is the number of claims expected from every 100 students. The revenue is 100 * 24 = 2400. So we should get 10% * Cost = Revenue according to the problem.

10% * n * 120 = 2400
12n = 2400
n = 200


I had the same answer. Although I think the issue is that the administration is providing the entire insurance so they are paying out the claim in addition to the administration fee. If that is the case, it is fairly unclear and becomes more about understanding how insurance works.

1.10 * n * 120 = 2400
132 * n = 2400
n ~ 18
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Re: Lee Colle insures its students for thefts up to $1000. The college mak   [#permalink] 08 Dec 2019, 12:48
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