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This topic has 3 expert replies and 1 member reply
MalcolmW Junior | Next Rank: 30 Posts Default Avatar
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01 Nov 2015
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avg

Post Sun Nov 29, 2015 6:48 pm
A student’s average (arithmetic mean) test score on 4 tests is 78. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80 ?
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

I have an explanation for the answer to this question but the breakdown does not make sense to me.

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gary391 Junior | Next Rank: 30 Posts Default Avatar
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09 Nov 2010
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11 messages
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Post Fri Aug 19, 2016 9:35 pm
In order for 4 numbers to have an average of 78, each number should be at least 78. Using same logic for 5 number to have an average of 80, each number should be at least 80. Thus, for both the averages to be equal, the student should score 88 in the 5th test.

----------------
|78|78|78|78| ?|=> Average = 78
----------------
|80|80|80|80|80| => Average = 80
----------------
| 2| 2| 2| 2|80| => Difference = 88

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Post Mon Nov 30, 2015 10:26 am
MalcolmW wrote:
A student’s average (arithmetic mean) test score on 4 tests is 78. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80 ?
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

My first approach would be identical to Mitch's. However, we can also solve the question using the weighted averages formula:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

We want the TOTAL average to equal 80
4/5 of the 5 scores have an average of 78
Let x = average of the 1 remaining test, which is worth 1/5 of the total average.

We get: 80 = (4/5)(78) + (1/5)(x)
Multiply both sides by 5 to get: 400 = 312 + x
Solve: x = 88

Answer: E

For more information on weighted averages, you can watch this free GMAT Prep Now video: http://www.gmatprepnow.com/module/gmat-statistics?id=805

Here are some additional practice questions related to weighted averages:
- http://www.beatthegmat.com/weighted-averages-t117237.html
- http://www.beatthegmat.com/weighted-average-t114506.html
- http://www.beatthegmat.com/average-weight-of-men-and-women-t57853.html
- http://www.beatthegmat.com/averages-question-t87118.html

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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gary391 Junior | Next Rank: 30 Posts Default Avatar
Joined
09 Nov 2010
Posted:
11 messages
Upvotes:
1
Post Fri Aug 19, 2016 9:35 pm
In order for 4 numbers to have an average of 78, each number should be at least 78. Using same logic for 5 number to have an average of 80, each number should be at least 80. Thus, for both the averages to be equal, the student should score 88 in the 5th test.

----------------
|78|78|78|78| ?|=> Average = 78
----------------
|80|80|80|80|80| => Average = 80
----------------
| 2| 2| 2| 2|80| => Difference = 88

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Post Mon Nov 30, 2015 10:26 am
MalcolmW wrote:
A student’s average (arithmetic mean) test score on 4 tests is 78. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80 ?
(A) 80
(B) 82
(C) 84
(D) 86
(E) 88

My first approach would be identical to Mitch's. However, we can also solve the question using the weighted averages formula:

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

We want the TOTAL average to equal 80
4/5 of the 5 scores have an average of 78
Let x = average of the 1 remaining test, which is worth 1/5 of the total average.

We get: 80 = (4/5)(78) + (1/5)(x)
Multiply both sides by 5 to get: 400 = 312 + x
Solve: x = 88

Answer: E

For more information on weighted averages, you can watch this free GMAT Prep Now video: http://www.gmatprepnow.com/module/gmat-statistics?id=805

Here are some additional practice questions related to weighted averages:
- http://www.beatthegmat.com/weighted-averages-t117237.html
- http://www.beatthegmat.com/weighted-average-t114506.html
- http://www.beatthegmat.com/average-weight-of-men-and-women-t57853.html
- http://www.beatthegmat.com/averages-question-t87118.html

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

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