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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Rabia must earn an average (arithmetic mean) score of S percent to

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Intern  B
Joined: 22 Feb 2016
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Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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10 00:00

Difficulty:   35% (medium)

Question Stats: 72% (02:21) correct 28% (02:21) wrong based on 112 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?

A) 10%
B) 15%
C) 20%
D) 85%
E) 90%
Senior Manager  D
Joined: 05 Jul 2018
Posts: 459
Location: India
Concentration: General Management, Technology
GMAT 1: 600 Q47 V26 GRE 1: Q162 V149 GPA: 3.6
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Re: Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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Let there be 10 exams in all.

She got S+10 average on 6 of them (60%)

$$\frac{(6*(S+10) + (Score-in-4-other-exams) )}{10}$$ = S or higher to pass

$$(Score-in-4-other-exams) =4S-60$$...Remember that this is all percentage we are dealing in

Minimum score on each of the 4 exams = $$\frac{(4S-60)}{4}$$ = S-15

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Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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My Approach:

Assume:
- Total exams = 10,
- S= 50%,
- Max Marks Per exam = 100
- X = maximum percentage below S to pass.

- Now, equation is: 6 * 60 + 4 * (S-X) = 10 * 50 (as she need S% to pass the exam)
=> 360 +4(S-X) = 500 => S-X = 140/4 = 35
50 - X = 35 => X = 15.

Option B
Please correct if my approach is wrong!
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Originally posted by fauji on 03 Nov 2019, 11:59.
Last edited by fauji on 03 Nov 2019, 22:29, edited 1 time in total.
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Re: Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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anmolmakkarz17 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%

Let the total assignments = n
—> Her total score in 60% of tests = 0.6n*(S + 10)
Let her average score in remaining 40% tests = x
—> Total score = 0.4n*x

To just pass, average score = S
—> [0.6n(S + 10) + 0.4nx]/n = S
—> 0.6S + 6 + 0.4x = S
—> 0.4x = 0.4S - 6
—> x = (0.4S - 6)/0.4 = S - 60/4
—> x = S - 15

So, she can score a 15% less than her average to still pass the test

IMO Option B

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4226
Re: Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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Top Contributor
anmolmakkarz17 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?"

Cheers,
Brent
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Re: Rabia must earn an average (arithmetic mean) score of S percent to  [#permalink]

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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.

GMAT assassins aren't born, they're made,
Rich
_________________ Re: Rabia must earn an average (arithmetic mean) score of S percent to   [#permalink] 06 Dec 2019, 15:46
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