BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Average/ Ratio Problem Exam Pack 1

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Jan 23, 2016 4:01 am
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Jan 23, 2016 10:12 am
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
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 23, 2016 10:41 am
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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 am
Location: New York, NY
Thanked: 39 times
Followed by:22 members

by Jeff@TargetTestPrep » Fri Jan 26, 2018 9:52 am
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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Post new topic Post Reply
• Page 1 of 1