Rabia must earn an average (arithmetic mean) score of S percent to pass her physics

BTGModeratorVI wrote: ↑

Sun Mar 15, 2020 12:43 pm

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

Say Rabia did 100 assignments.

So, she scored 60*(S + 10) in her first 60 assignments.

She has to score 100*S in her 100 assignments.

Say she earned (S – x) per assignment in her last 40 assignments to pass. So, she scored 40*(S – x) in the last 40 assignments.

Thus, 100S = 60*(S + 10) + 40*(S – x)

x = 15%

The correct answer: B

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Sun Mar 15, 2020 12:43 pm

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

BTGModeratorVI wrote: ↑

Sun Mar 15, 2020 12:43 pm

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 let her total number of assignments be 10 and x be the maximum percentage below S that she can earn on her remaining assignments and still pass the course. We can create the equation:

[6(S + 10) + 4(S - x)]/10 = S

6S + 60 + 4S - 4x = 10S

60 - 4x = 0

60 = 4x

15 = x

Answer: B