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The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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Question Stats: 86% (01:31) correct 14% (02:08) wrong based on 549 sessions

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The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A) 2x – 8
B) x – 4
C) 8 – 2x
D) 16 – x
E) 8 – ($$\frac{2}{x}$$)

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AbdurRakib wrote:
The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A) 2x – 8
B) x – 4
C) 8 – 2x
D) 16 – x
E) 8 – ($$\frac{2}{x}$$)

We are given that the average score on a test taken by 10 students was x and need to find the average score in terms of x if the average score for 5 of those students was 8.

Thus, the overall sum was 10x and the sum for the 5 students was (5)(8)= 40.

We need to determine the average of the 5 remaining students.

The sum for the 5 remaining students was 10x - 40, and thus the average is:

(10x - 40)/5 = 10x/5 - 40/5 = 2x - 8

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Re: The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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Given : The average (arithmetic mean) score on a test taken by 10 students was x. Therefore, sum of all scores = 10*x = 10x.
the average score for 5 of the students was 8. Thus, the total score contribution for these 5 students = 8*5 = 40.
Contribution of other 5 students = 10x - 40.
The average score, in terms of x, for the remaining 5 students = (10x - 40)/5 = 2x - 8. Hence A.
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Re: The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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AbdurRakib wrote:
The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A) 2x – 8
B) x – 4
C) 8 – 2x
D) 16 – x
E) 8 – ($$\frac{2}{x}$$)

Total = 10x

Total of first 5 = 40

So, Average of remaining 5 students is $$\frac{10x - 40}{5}$$ = $$2x – 8$$

Hence, answer will be (A) $$2x – 8$$

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Say B is the average grade for the 5 students:

$$\cfrac { w1 }{ w2 } =\cfrac { A2-Aavg }{ Aavg-A1 } \\ \cfrac { 5 }{ 5 } =\cfrac { 8-x }{ x-B } \\ \cfrac { 1 }{ 1 } =\cfrac { 8-x }{ x-B } \\ x-A=8-x\\ 2x-8=B$$
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The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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Think of this as a weighted average problem.

If first 5 students make the average 8 we are told to find out the average of the last 5.

Since the weights are 5 each lets assume that midpoint (Given as average of all = x) for all the students is 10
i.e x = 10

Creating a weighted average:

8(given).......................................................12 (assumed)
|_________________10(x assumed)_________________|

Substituting x = 10 should give us the value of 12

Only A gives us this answer.
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Re: The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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Given:
Sum of 10 students' marks= 10x
Average of 5 of the students = 8 --> sum of 5 students' marks= 8*5= 40

Let S be the sum of remaining students' marks.
40+S = 10x --> S= 10x-40
Thus, average of remaining 5 student's marks= (10x-40)/5 ==> 2x-8
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Re: The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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Although the equations make sense now, I couldn't think of how to set up the problem under the time restriction I set for myself

I let the average of the other 5 students be 10 and x = 9

so 10x = 90
5*10 = 50

40 (given) + 50 has to equal 90
plug in x = 9 to see which results in 10

A

AbdurRakib wrote:
The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A) 2x – 8
B) x – 4
C) 8 – 2x
D) 16 – x
E) 8 – ($$\frac{2}{x}$$)
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Re: The average (arithmetic mean) score on a test taken by 10 students was  [#permalink]

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AbdurRakib wrote:
The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

A) 2x – 8
B) x – 4
C) 8 – 2x
D) 16 – x
E) 8 – ($$\frac{2}{x}$$)

The average (arithmetic mean) score on a test taken by 10 students was x. If the average score for 5 of the students was 8, what was the average score, in terms of x, for the remaining 5 students who took the test?

Total score for 10 students = 10x
Total score for 5 students = 40
Total score for remaining 5 students = 10x-40
Average score for remaining 5 students = (10x-40)/5 = 2x -8

IMO A
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