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OG The average score on a test taken by 10 students

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by AbeNeedsAnswers » Thu Jul 27, 2017 9:20 pm
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 - (2/x)

A
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by Jay@ManhattanReview » Thu Jul 27, 2017 9:25 pm
AbeNeedsAnswers 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 - (2/x)

A
Total score of all the 10 students = Total score of the first batch of 5 students + Total score of the second batch of 5 students

We have,

Total score of all the 10 students = 10*x = 10x;
Total score of the first batch of 5 students = 5*8 = 40;

Thus,
Total score of the second batch of 5 students = 10x - 40 = 10(x - 4);

Thus, the average score of the second batch of 5 students = 10(x - 4) / 5 = 2(x - 4) = [spoiler]2x - 8[/spoiler].

The correct answer: A

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by [email protected] » Fri Jul 28, 2017 10:56 am
Hi AbeNeedsAnswers,

This question can be solved by TESTing VALUES.

We're told that average score on a test taken by 10 students = X and that the average score for 5 of those students was 8. We're asked for the average score of the OTHER 5 students.

IF... X = 10, then the TOTAL points for ALL 10 students = (10)(10) = 100
Since 5 of those students averaged 8 points, that accounts for (5)(8) = 40 of those 100 points.
This leaves 100 - 40 = 60 points for the remaining 5 students, which is an average of 60/5 = 12.

So we're looking for an answer that equals 12 when X=10... There's only one answer that matches...

Final Answer: A

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by Ian Stewart » Fri Jul 28, 2017 11:54 am
The two groups are equal in size (5 students each), so the overall average score will just be the ordinary average of the scores of each group, because each group is equally important. If x is the average of two things, then 2x is the sum of those two things. So if y is the average we want to find,

y + 8 = 2x
y = 2x - 8
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by Matt@VeritasPrep » Sun Aug 06, 2017 11:22 pm
Sum = Average * # of Things in the Set

For the whole group, Sum = 10x. For five of the group, the sum = 5*8, so the sum for the other five = 10x - 40.

The average for those five is the sum divided by five, or (10x - 40)/5, or 2x - 8.
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by Jeff@TargetTestPrep » Wed Aug 09, 2017 12:39 pm
AbeNeedsAnswers 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 - (2/x)

A
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

Answer: A

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