BTGmoderatorDC 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

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

Hi All,

We're told that Rabia must earn an AVERAGE (arithmetic mean) score of S percent to pass her physics course, the average score on the first 60 percent of her assignments was (S + 10) percent, and each of her assignments is weighted equally. We're asked for the MAXIMUM percentage BELOW S that she can earn on her remaining assignments and still pass the course. Since this is a 'ratio' question, it can be approached in a number of different ways, including by TESTing VALUES.

Since 60% is 3/5, we can start by saying that there are 5 total assignments.
Let's also TEST S = 70, meaning that Rabia needs an average of 70% over the 5 assignments to pass.

On the first 3 of those assignments, she averaged (70+10) = 80 percent.... In simple terms, she needs 5(70) = 350 points and she already has 3(80) = 240 points. To put it another way, she is 3(10) = 30 points AHEAD of what she needs to pass the course. She would need another 350 - 240 = 110 points to pass.

With 2 assignments remaining, she would need to average 110/2 = 55 points to pass. That is 70 - 55 = 15 points BELOW S.

Final Answer: [spoiler=]B[/spoiler]

GMAT assassins aren't born, they're made,
Rich