A College runs 25 classes on Monday. Ten of the classes

Question

A College runs 25 classes on Monday. Ten of the classes have an average size of 14.2 students while the other fifteen classes have an average size of 12.2 students. What is the average class size, in students, of all 25 classes run on Monday?

A. 12.5
B. 13
C. 13.2
D. 13.5
E. 14

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DisciplinedPrep · Answer

Given information  
Total number of classes on Monday = 25
The average size of 10 classes = 14.2 students 
The average size of the other 15 classes = 12.2 students

Therefore, the average class size, in students, of all 25 classes run on Monday =  \frac{10x14.2 + 15x12.2}{25}  =  \frac{142 + 183}{25}  = 13

Hence, the correct answer is option B. 13

Note: 
The weighted average is an average in which each quantity to be averaged is assigned a weight. These weightings determine the relative importance of each quantity on average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Formula 
Weighted Average=  \frac{Sum of weighted terms}{Total number of terms}

Mo2men · Answer

We can use alligation method

Let the ten students in group A and other 15 in group B. The mix of 25 students is M

B..................................A 
12.2...........M..............14.2

B/A= 15/10 =3/2

B..................................A
12.2.... 2x .....M..... 3x ......14.2

5x = 14.2 -12.2 =2

x=2/5 =0.4
M= 12.2+0.8 =13

Answer: B

QuantMadeEasy · Answer

Total difference above the average = total difference below the average.

Lets say average is A
Total Difference above the average = (14.2-A) x 10
Total difference below the average = (A-12.2) x 15

(14.2-A) x 10 = (A-12.2) x 15
28.4 - 2A = 3A - 36.6
5A = 65
A = 13

B is correct.

EMPOWERgmatRichC · Answer

OFFICIAL EXPLANATION

Hi All,

We're told that a College runs 25 classes on Monday; 10 of the classes have an average size of 14.2 students while the other 15 classes have an average size of 12.2 students. We're asked for the AVERAGE class size, in students, of all 25 classes run on Monday. This prompt gives us all of the numbers that we need to perform a calculation, so that calculation is essentially all that's required to answer this question. That having been said, there is a 'ratio shortcut' that we can use to make the overall math a bit simpler.

Since we're calculating an AVERAGE, and we have a ratio of classes, we can reduce the ratio to simplify the calculation. The given ratio of classes is 10:15; we can reduce this to 2:3 (and the overall result of that calculation will be exactly the same as if we had used 10 and 15).

Average =   / (2 + 3) =   / 5 = 65/5 = 13

Final Answer:  B

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

saukrit · Answer

First 10 classes have a total of 142 students (14.2*10)
Next 15 classes have a total of 183 students (12.2*15)

Total students=325
Total classes =25

Average student per class= 325/25 = 13
 Hence B is the answer

mm229966 · Answer

(10*14.2 + 15*12.2)/25 = 13

hope its clear

A College runs 25 classes on Monday. Ten of the classes

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