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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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Post Sun Nov 29, 2015 6:48 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post Sun Nov 29, 2015 7:15 pm
    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
    Sum of all 5 scores = (number of scores)(average score) = 5*80 = 400.
    Sum of the first 4 scores = (number of scores)(average score) = 4*78 = 312.
    Score on the 5th test = (sum of all 5 scores) - (sum of the first 4 scores) = 400-312 = 88.

    The correct answer is E.

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    Post Sun Nov 29, 2015 10:41 pm
    Hi MalcolmW,

    The standard average formula 'approach' is likely the easiest for most Test Takers to use on these types of prompts. However, there is another way to think about this prompt - since the average of the first 4 tests is 78, we can think of those tests as four 78s. For a 5th exam to raise the overall average to 80, that exam has to score 80 points on its own AND raise each of the other 4 tests to 80. Those 4 tests would require an extra 2 points apiece...

    80 + 4(2) = 88 points

    Final Answer: E

    GMAT assassins aren't born, they're made,
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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

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    gary391 Junior | Next Rank: 30 Posts Default Avatar
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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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