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Rabia must earn an average (arithmetic mean) score of S percent to pas
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16 Sep 2021, 09:40
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Question Stats:
60% (02:08) correct
40% (03:16) wrong based on 15 sessions
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Rabia must earn an average (arithmetic mean) score of S percent to pass her physics course. If her average score on the first 60 percent of her assignments was (S + 10) percent, and each of her assignments is weighted equally, then what is the maximum percentage below S that she can earn on her remaining assignments and still pass the course?
Re: Rabia must earn an average (arithmetic mean) score of S percent to pas
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16 Sep 2021, 10:05
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Carcass wrote:
Rabia must earn an average (arithmetic mean) score of S percent to pass her physics course. If her average score on the first 60 percent of her assignments was (S + 10) percent, and each of her assignments is weighted equally, then what is the maximum percentage below S that she can earn on her remaining assignments and still pass the course?
A) 10% B) 15% C) 20% D) 85% E) 90%
We can solve this question using weighted averages: Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
Let x = the average percent score of the remaining 40% of Rabia's assignments So, for this question, we can write: Average score = (60%)(S + 10) + (40%)(x) Since we want the total average to be at least S, we can write: S = (60%)(S + 10) + (40%)(x) Rewrite has: S = (0.6)(S + 10) + (0.4)(x) Expand to get: S = 0.6S + 6 + 0.4x Multiply both sides by 10 to get: 10S = 6S + 60 + 4x Subtract 6S from both sides by 10 to get: 4S = 60 + 4x Subtract 60 from both sides to get: 4S - 60 = 4x Divide both sides by 4 to get: S - 15 = x So, we need an average score of S - 15 on the remaining 40% of the assignments to ensure that Rabia gets a total score of S.
The question asks "What is the maximum percentage below S that she can earn on her remaining assignments and still pass the course?" Answer: 15 = B
Re: Rabia must earn an average (arithmetic mean) score of S percent to pas
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05 Feb 2025, 10:06
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Re: Rabia must earn an average (arithmetic mean) score of S percent to pas [#permalink]
16 Sep 2021, 09:40 
60% (02:08) correct
