## Rabia must earn an average (arithmetic mean) score of $$S$$ percent to pass her physics course. If her average score on

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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

by VJesus12 » Thu Sep 16, 2021 11:07 am

00:00

A

B

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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?

A) $$10\%$$
B) $$15\%$$
C) $$20\%$$
D) $$85\%$$
E) $$90\%$$

Answer: B

Source: Princeton Review

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### Re: Rabia must earn an average (arithmetic mean) score of $$S$$ percent to pass her physics course. If her average score

by [email protected] » Thu Sep 16, 2021 3:21 pm
VJesus12 wrote:
Thu Sep 16, 2021 11:07 am
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) $$90\%$$

Answer: B

Source: Princeton Review
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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