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MalcolmW: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sun Nov 01, 2015 8:58 pm

by MalcolmW » 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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Source: Beat The GMAT — Problem Solving | Sun Nov 29, 2015 6:48 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » 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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by [email protected] » 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

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » 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: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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gary391: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Tue Nov 09, 2010 7:23 pm; Thanked: 1 times

by gary391 » 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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by Scott@TargetTestPrep » Wed Apr 04, 2018 4:55 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

We use the formula: average = sum/quantity, or, equivalently, average x quantity = sum.

Even though we don't know the individual scores for each of the first 4 tests, we know the sum of the 4 scores must be 78 x 4 = 312.

Let's let n = the score on the 5th test. Thus, the sum of the 5 tests is 312 + 5th test score, or 312 + n. Also, because the new average will be 80, we substitute 80 for the new average. We can now solve for n.

Average = sum/quantity

80 = (312 + n)/5

400 = 312 + n

88 = n

Answer: E

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