Good Question : Average Score of two classes.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Thu Jun 04, 2015 1:00 am

The students of two classes appeared for an exam. The average score for both classes combined was 70. The students of the first class registered an average score of 80. If the total number of students was 50 and the number of students in the first class was greater than the number of students in the second class, which of the following could be the average score for the second class?

1.30
2.60
3.75

A. I only

B. II only

C. III only

D. I, II and III

E. Neither I nor II and III

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Source: Beat The GMAT — Data Sufficiency | Thu Jun 04, 2015 1:00 am

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 » Thu Jun 04, 2015 3:02 am

nikhilgmat31 wrote:The students of two classes appeared for an exam. The average score for both classes combined was 70. The students of the first class registered an average score of 80. If the total number of students was 50 and the number of students in the first class was greater than the number of students in the second class, which of the following could be the average score for the second class?

1.30
2.60
3.75

A. I only

B. II only

C. III only

D. I, II and III

E. Neither I nor II and III

Use ALLIGATION to evaluate the three statements.
Let F = the number of students in the first class and S = the number of students in the second class.

Statement I: 30

Step 1: Plot the 3 averages on a number line, with the averages for F and S on the ends and the average for the mixture of classes in the middle.
F 80-----------------70----------------30 S

Step 2: Calculate the distances between the averages.
F 80--------10-------70--------40------30 S

Step 3: Determine the ratio in the mixture.
The ratio of F to S is equal to the RECIPROCAL of the distances in red.
F:S = 40:10.

Here, F=40 and S=10, for a total of 50 students.
Since Statement I is possible, eliminate B, C and E.

Statement II: 60

Step 1: Plot the 3 averages on a number line, with the averages for F and S on the ends and the average for the mixture of classes in the middle.
F 80-----------------70----------------60 S

Here, the average for the mixture (70) is HALFWAY between the averages for F and S, implying that the two classes have the SAME NUMBER OF STUDENTS.
Since the first class must have more students than the second, Statement II is not possible.
Eliminate D.

The correct answer is A.

For two similar problems, check here:

https://www.beatthegmat.com/ratios-fract ... 15365.html

Last edited by GMATGuruNY on Thu Jun 04, 2015 4:27 am, edited 1 time in total.

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Thu Jun 04, 2015 4:25 am

Thanks GMATGuruNY.

I solved it using linear equation

f*80 + (50-f)x = 70*50

where x is average of second class.

if x = 30 then
f*80 + (50-f)30 = 3500 leads f=40 so its possible as f=40 & s =10

if x = 60 then
f*80 + (50-f)60 = 3500 leads f=25 so its possible as f=25 & s =25 not possible

if x = 75 then
f*80 + (50-f)75 = 3500 leads f=comes -negative so its not possible.

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GMAT_AS: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Jun 04, 2015 7:19 am

by GMAT_AS » Thu Jun 04, 2015 7:22 am

nikhilgmat31 wrote:Thanks GMATGuruNY.

I solved it using linear equation

f*80 + (50-f)x = 70*50

where x is average of second class.

if x = 30 then
f*80 + (50-f)30 = 3500 leads f=40 so its possible as f=40 & s =10

if x = 60 then
f*80 + (50-f)60 = 3500 leads f=25 so its possible as f=25 & s =25 not possible

if x = 75 then
f*80 + (50-f)75 = 3500 leads f=comes -negative so its not possible.

Thanks Nikhil - simple & easy approach.

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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 » Thu Jun 04, 2015 7:51 am

nikhilgmat31 wrote:The students of two classes appeared for an exam. The average score for both classes combined was 70. The students of the first class registered an average score of 80. If the total number of students was 50 and the number of students in the first class was greater than the number of students in the second class, which of the following could be the average score for the second class?

I. 30
II. 60
III. 75

A. I only
B. II only
C. III only
D. I, II and III
E. Neither I nor II and III

There's a useful concept covered at 5:45 in the following free video on weighted averages: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here's what we know:
Group #1:
Average score = 80

Group #2:
Average score = x

COMBINED average score = 70

Key concept (covered in video): Since Group #1 has MORE PEOPLE than Group #2, the COMBINED average score (70) will be closer to 80 than it is to x

Check the 3 options.

I. 30
Can 30 be the average for Group #2?
Yes.
Since 70 is closer to 80 than it is to 30, it is POSSIBLE that the average could be 30

II. 60
Can 60 be the average for Group #2?
NO.
Since 70 is NOT closer to 80 than it is to 60, it is NOT possible for the average to be 60

NOTE: Since statement I is possible and statement II is not possible, we already know the correct answer is A (since no other answer choice allows for this). However, we can address statement III for "fun."

III. 75
Can 75 be the average for Group #2?
NO.
We cannot combine two groups with averages of 75 and 80 and get a COMBINED average of 70. The combined average must be BETWEEN 75 and 80

Answer: A

Cheers,
Brent

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

Brent Hanneson - Creator of GMATPrepNow.com

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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 » Thu Jun 04, 2015 8:38 am

I. 30
Can 30 be the average for Group #2?
Yes.
Since 70 is closer to 80 than it is to 30, it is POSSIBLE that the average could be 30

Careful.
Because this approach does not take into account that the total number of students = 50, it could lead to selecting an incorrect answer choice.
Let's stay that Statement I read as follows:
I: 50
The following alligation would be implied:
F 80--------10-------70--------20------50 S
Here, 70 is closer to 80 than to 50.
But the implied ratio for the two classes -- F:S = 20:10 = 2:1 -- is not possible for a total of 50 students.
Before deeming that a statement is possible, we must first confirm that it implies a valid ratio for 50 students.

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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 » Thu Jun 04, 2015 8:40 am

Good point, Mitch!

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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