GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jun 2018, 07:48

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A teacher gave the same test to three history classes: A, B,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager
Joined: 03 Oct 2008
Posts: 61
A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

Updated on: 21 Dec 2013, 05:28
3
15
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:50) correct 22% (02:04) wrong based on 667 sessions

### HideShow timer Statistics

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

Originally posted by albany09 on 07 Oct 2008, 10:16.
Last edited by Bunuel on 21 Dec 2013, 05:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1734
Re: math--teacher and students [#permalink]

### Show Tags

07 Oct 2008, 10:23
11
2
albany09 wrote:
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

ratio is 4:6:5 , numbers are 4x, 6x, 5x

total scores of each class is (65*4x + 6x * 80 + 77*5x) = 260x+480x+385x = 1125x

total number of students = 15x

average = 1125x/15x = 75

B is the answer
Director
Joined: 26 Aug 2014
Posts: 826
Concentration: Marketing
GPA: 3.4
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

28 Oct 2014, 18:28
1
is this the fastest way? I am def. error prone when I do these longer multiplications...so wondering if there is a better way to estimate it? I looked at the numbers and thought majority of students got 80 or 77 so the average of all would be skewed that way and just picked 78. is there a way i could have thought about that and got the right answer or just multiply everything?
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

29 Oct 2014, 01:54
8
1
angelfire213 wrote:
is this the fastest way? I am def. error prone when I do these longer multiplications...so wondering if there is a better way to estimate it? I looked at the numbers and thought majority of students got 80 or 77 so the average of all would be skewed that way and just picked 78. is there a way i could have thought about that and got the right answer or just multiply everything?

Combined Average $$= \frac{65 * 4 + 80 * 6 + 77 * 5}{4+6+5} = \frac{1125}{15} = 75$$

_________________

Kindly press "+1 Kudos" to appreciate

Director
Joined: 26 Aug 2014
Posts: 826
Concentration: Marketing
GPA: 3.4
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

29 Oct 2014, 03:12
1
so there isn't a way around multiplying the numbers out?
PareshGmat wrote:
angelfire213 wrote:
is this the fastest way? I am def. error prone when I do these longer multiplications...so wondering if there is a better way to estimate it? I looked at the numbers and thought majority of students got 80 or 77 so the average of all would be skewed that way and just picked 78. is there a way i could have thought about that and got the right answer or just multiply everything?

Combined Average $$= \frac{65 * 4 + 80 * 6 + 77 * 5}{4+6+5} = \frac{1125}{15} = 75$$

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

29 Oct 2014, 03:24
angelfire213 wrote:
so there isn't a way around multiplying the numbers out?
PareshGmat wrote:
angelfire213 wrote:
is this the fastest way? I am def. error prone when I do these longer multiplications...so wondering if there is a better way to estimate it? I looked at the numbers and thought majority of students got 80 or 77 so the average of all would be skewed that way and just picked 78. is there a way i could have thought about that and got the right answer or just multiply everything?

Combined Average $$= \frac{65 * 4 + 80 * 6 + 77 * 5}{4+6+5} = \frac{1125}{15} = 75$$

Not that I'm aware of.............

Usually I would have done in this way to avoid the multiplication

$$\frac{65*4}{15} + \frac{80*6}{15} + \frac{77*5}{15}$$

However, as you can see, the numbers are "tricked" such that it cannot be simplified at this point (Not divisible by 3); hence the calculation
_________________

Kindly press "+1 Kudos" to appreciate

Current Student
Joined: 21 Aug 2014
Posts: 156
Location: United States
Concentration: Other, Operations
GMAT 1: 700 Q47 V40
GMAT 2: 690 Q44 V40
WE: Science (Pharmaceuticals and Biotech)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

02 Nov 2014, 17:45
3
A good way to answer this question and have a good guess is realizing the fact that they are all almost in the same proportion. 4:6:5 is close to 5:5:5.

So you can calculate the average of all three direcly $$(65+80+77)/3=74$$

Since you can realize that there is slightly more weight to a higher average (80 and 77 are at slighlty higher proportion) you can guess that the answer will be 75.

This would be a good aproach if faced with a similar question when running out of time.

Hope it helps.
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 423
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

04 Jan 2015, 10:10
I used a longer way - for some reason the concept of weighted average manage to slip my mind even though I love it...

Anyway, I still did it in about 90 seconds. So, it is not that bad I guess:
4x+6x+5x=15x The number of students. I picked 60 as 15x, because it is the LCM of 4,6,5. So, x=4

Then it goes like this:
65=s/4x | 65=s/16 | s= 1040
80=s/6x | s= 1920
77= s/20 | s= 1540

Total:
M=S/N
M= 4500/60
M=450/6
M=75 ANS B
Senior Manager
Joined: 02 Dec 2014
Posts: 353
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

06 Jan 2015, 11:12
7
Hi angelfire123
Yes there is faster way. 4+6+5=15 so look for a number that is multiple of 15. Only B looks good. Hope it is clear
_________________

"Are you gangsters?" - "No we are Russians!"

Current Student
Joined: 09 Aug 2015
Posts: 91
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

09 Sep 2015, 16:29
Konstantin1983 wrote:
Hi angelfire123
Yes there is faster way. 4+6+5=15 so look for a number that is multiple of 15. Only B looks good. Hope it is clear

This does not work. Consider the case where the ratios are 3:7:5.

65*3 + 80*7 + 77*5 = 1140

1140 / 15 = 76
Intern
Joined: 24 Jun 2013
Posts: 10
Location: India
Concentration: General Management, Economics
Schools: Tuck '19
GPA: 3.2
WE: Information Technology (Consulting)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

25 Jul 2016, 20:44
2
1
A slightly simpler way to calculate the average would be to choose a number between 65 and 80, say 65, and subtract it from all the numbers, ie $$(65-65, 77-65, 80-65)$$ -> $$(0, 12, 15)$$.

calculate the average of the new set of numbers: $$(0*4+12*5+15*6)/15=150/15=10$$

Now add this value with the number we chose, $$65+10=75$$.
Manager
Joined: 05 Apr 2014
Posts: 145
Location: India
Concentration: Economics, International Business
Schools: ISB '19, Fox"19
GMAT 1: 660 Q48 V33
GPA: 3
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

10 Aug 2016, 08:18
since we do not know the mean you can meanwhile assume the mean to be 70

So,

65 80 77
-5 +10 +7
ratio 4 6 5
-20 +60 +35

So, mean = 70 + (-20 +60 +35)/(4+6+5)= 75

this is deviation method,we calculate the total deviation from the assumed mean and then find the actual mean.
Manager
Joined: 09 Aug 2016
Posts: 68
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

25 Sep 2016, 04:55
Can this question worked in a opposite way? I mean

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. If the average score for the three classes combined is 75 what is the ratio of the numbers of students in each class who took the test?
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

25 Sep 2016, 07:04
albany09 wrote:
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

Score ( A : B : C ) = 65 : 80 : 77
Number ( A : B : C ) = 4 : 6 : 5

So, Weighted average score is = $$\frac{(65*4)+( 80*6)+(77*5)}{( 4 + 6 + 5 )}$$

Or, Weighted average score is = $$\frac{(260)+(480)+(385)}{(15)}$$

Or, Weighted average score is = $$\frac{(1125)}{(15)}$$

Or, Weighted average score is = $$75$$

So, Answer will be (B) 75

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

25 Sep 2016, 09:34
Ndkms wrote:
Can this question worked in a opposite way? I mean

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. If the average score for the three classes combined is 75 what is the ratio of the numbers of students in each class who took the test?

Let the ratio of students in 3 classes be a : b : c

So, $$75$$ = $$\frac{(65*a) + (80*b) + (77*c)}{(a + b + c)}$$

Or, 75a + 75b + 75c = 65a + 80b + 77c

Or, 10a = ( 5b + 2c )

Hope you understand now, that what we need...

We need the total number of students and relationship between the number of students in 2 classes....

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

VP
Joined: 07 Dec 2014
Posts: 1020
A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

25 Sep 2016, 12:33
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

4*65+6*80+5*77=1125
4+6+5=15
1125/15=75=average score for three classes
B.
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

26 Jan 2018, 10:46
albany09 wrote:
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

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
Joined: 12 Sep 2015
Posts: 2585
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

30 Jan 2018, 10:08
Top Contributor
albany09 wrote:
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

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) + ...

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

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

RELATED VIDEO

_________________

Brent Hanneson – Founder of gmatprepnow.com

Manager
Joined: 16 Jan 2018
Posts: 51
GMAT 1: 600 Q40 V33
Re: A teacher gave the same test to three history classes: A, B, [#permalink]

### Show Tags

03 Feb 2018, 20:33
Huh ! so basically no one managed to suggested a easier way to solve it in like 30 or so secs.. took me 90 sec using weighted avg.
Re: A teacher gave the same test to three history classes: A, B,   [#permalink] 03 Feb 2018, 20:33
Display posts from previous: Sort by

# A teacher gave the same test to three history classes: A, B,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.