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A student's score on the final test in a certain course was

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A student's score on the final test in a certain course was  [#permalink]

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New post Updated on: 02 Apr 2014, 05:33
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A student's score on the final test in a certain course was 60% greater than the average (arithmetic mean) score of the 2 other tests the student took in the course. The student's score on the final test was what percent of the student's average test score for the entire course?

A. \(33\frac{1}{3}%\)

B. 40%

C. 75%

D. \(133\frac{1}{3}%\)

E. 160%

Originally posted by goodyear2013 on 05 Feb 2014, 11:58.
Last edited by Bunuel on 02 Apr 2014, 05:33, edited 2 times in total.
Edited the question.
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Re: A student's score on the final test in a certain course was  [#permalink]

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New post 05 Feb 2014, 16:55
2
Given :
Let scores be s1,s2,s3
\(s3 = 1,6 (\frac{s1}{2}+ \frac{s2}{2})\)

(1) rearranging this :
\(s1+s2 = \frac{5}{4}*s3\)


(2) Average of 3 score is =
\(\frac{1}{3}*(s1+s2+s3)\)

We can use the information at (1) to replace \(s1+s2\) into equation (2)

\(Average =\frac{1}{3} * ( \frac{5}{4}*s3 +s3)\)

\(Average = \frac{1}{3} * ( \frac{9}{4}*s3)\)


\(Average = \frac{3}{4}*s3\)

\(s3 = \frac{4}{3}*Average\)


\(s3 = 1.33333 * Average\)

making s3 133% of the Average

Answer D
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Re: A student's score on the final test in a certain course was  [#permalink]

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New post 06 Mar 2014, 00:07
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Say Test1 = 100

Test2 = 100

Avg of Test1 & Test2 = 100

Final test is 60% more than above average = 160

Avg of all 3 tests combined \(= \frac{360}{2} = 120\)

% increase = \(\frac{160}{120}* 100 = 133 \frac{1}{3}\)

Answer = D
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Re: A student's score on the final test in a certain course was  [#permalink]

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New post 06 Mar 2014, 00:51
1
goodyear2013 wrote:
A student's score on the final test in a certain course was 60% greater than the average (arithmetic mean) score of the 2 other tests the student took in the course. The student's score on the final test was what percent of the student's average test score for the entire course?

A. 33(1/3)%
B. 40%
C. 75%
D. 133(1/3)%
E. 160%


Hi, I want to request the solution for this question, please.


You can use the concept of averages here: The score in the third test was 60% higher (say, it was 160) which means you have 60% extra which you should give equally to each of the three tests to get the average up to 120.
We need Final test score as a % of updated average score = (160/120)*100 = 133.33%

Answer (D)

To read up on the concept of averages, check: http://www.veritasprep.com/blog/2012/04 ... etic-mean/
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Re: A student's score on the final test in a certain course was  [#permalink]

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New post 24 Oct 2017, 05:12
goodyear2013 wrote:
A student's score on the final test in a certain course was 60% greater than the average (arithmetic mean) score of the 2 other tests the student took in the course. The student's score on the final test was what percent of the student's average test score for the entire course?

A. \(33\frac{1}{3}%\)

B. 40%

C. 75%

D. \(133\frac{1}{3}%\)

E. 160%


We can let a be the score on the final test and b and c be the scores on the other two tests. Thus, a = 1.6(b + c)/2 = 0.8(b + c), and the average score of all three tests is:

(a + b + c)/3 = (0.8(b + c) + b + c)/3 = 1.8(b + c)/3 = 0.6(b + c)

Thus, the final test score is 0.8(b + c)/[0.6(b + c)] x 100 = 0.8/0.6 x 100 = 8/6 x 100 = 133 ⅓ percent of the average score.

Answer: D
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Re: A student's score on the final test in a certain course was  [#permalink]

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