Average/ Ratio Problem Exam Pack 1

[sukhman]

Please see Image attached [size=x-small]small text[/size]

[GMATGuruNY]

A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?

A. 74
B. 75
C. 76
D. 77
E. 78

Let:
Class A have 4 students, each scoring 65 points, for a total of 260 points.
Class B have 6 students, each scoring 80 points, for a total of 480 points.
Class C have 5 students, each scoring 77 points, for a total of 385 points.
Average score for all 15 students = (260+480+385)/15 = 75.

The correct answer is B.

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Hi sukhman,

This prompt is essentially a Weighted Average question, so it can be solved in a couple of different ways. TESTing VALUES will help in this situation (as Mitch showed in his solution). Here's another way to get to the correct answer:

IF.... we TEST....
4 students @ 65 each
5 students @ 77 each
6 students @ 80 each

We can calculate the 'effect' that each group has on the average.

To start, let's 'lock in' the 5 students @ 77. If it was JUST those 5 students, then the average would be 77. The ones who scored 80 bring the average "up", but the ones who score 65 bring the average "down." The issue is HOW MUCH those numbers would impact an average of 77?

Since 80 is "3 more" than 77, those 6 students "add (6)(3) = 18 points" to the total of all scores.
Since 65 is "12 less" than 77, those 4 students "subtract (4)(12) = 48 points" to the total of all scores.

18-48 = -30

So the sum of ALL 15 scores is (15)(77) - 30. We can rewrite this as....

(15)(77) - 30 =
(15)(77) - (15)(2) =
(15)(77 - 2) =
(15)(75)

So the average is 75

Final Answer: B

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

[Brent@GMATPrepNow]

A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?

A. 74
B. 75
C. 76
D. 77
E. 78

A slightly different approach:

This is a weighted averages question, so we can use the following formula:

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

Ratio of classes A, B, C = 4 : 6 : 5, respectively
4 + 6 + 5 = 15
So, class A represents 4/15 of the TOTAL population
Class B represents 6/15 of the TOTAL population
Class C represents 5/15 of the TOTAL population

So, weighted average of 3 groups combined = (4/15)(65) + (6/15)(80) + (5/15)(77)
= 260/15 + 480/15 + 385/15
= 1125/15
= 75
= B

-----------------------------
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

[Jeff@TargetTestPrep]

A teacher gave the same test to three history classes: A, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?

A. 74
B. 75
C. 76
D. 77
E. 78

The ratio of A : B : C = 4x : 6x : 5x, so the total is 15x. We can create a weighted average equation:

[65(4x) + 80(6x) + 77(5x)]/15x

5[13(4x) + 16(6x) + 77x]/15x

[13(4x) + 16(6x) + 77x]/3x

(52x + 96x + 77x)/3x

225x/3x = 75

Answer: B