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

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A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post Updated on: 01 Oct 2019, 20:56
1
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EMPOWERgmat PS Series:
Block 1, Question 4

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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Originally posted by EMPOWERgmatRichC on 28 Sep 2019, 15:50.
Last edited by EMPOWERgmatRichC on 01 Oct 2019, 20:56, edited 1 time in total.
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Re: A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post 28 Sep 2019, 17:17
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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= \(\frac{Sum of weighted terms}{Total number of terms}\)
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Re: A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post 29 Sep 2019, 01:36
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EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Block 1, Question 4

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



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
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Re: A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post 29 Sep 2019, 03:24
1
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Block 1, Question 4

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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To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.


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.
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Re: A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post 30 Sep 2019, 20:13
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)(14.2) + (3)(12.2)] / (2 + 3) = [28.4 + 36.6] / 5 = 65/5 = 13

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Re: A College runs 25 classes on Monday. Ten of the classes  [#permalink]

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New post 10 Oct 2019, 22:43
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
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Re: A College runs 25 classes on Monday. Ten of the classes   [#permalink] 10 Oct 2019, 22:43
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