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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Work/Rate

by BTGmoderatorRO » Sun Jan 07, 2018 7:44 am

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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

OA is d
Please I need an Expert to give me the mathematical approach to solve this question.

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Source: Beat The GMAT — Problem Solving | Sun Jan 07, 2018 7:44 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Work/Rate

by Scott@TargetTestPrep » Sat May 30, 2020 1:36 pm

BTGmoderatorRO wrote: ↑
Sun Jan 07, 2018 7:44 am
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

OA is d

Solution:

We can let 100 be the number of students in this college and n be the number of thefts. Furthermore, we can see that the administrative costs are $12 per theft; therefore, we have:

Total payout + Total admin. costs = Total revenue

120n + 12n = 24 x 100

132n = 2400

n = 2400/132 ≈ 18

Answer: D

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