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Average age of the whole class

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Average age of the whole class

by gmattesttaker2 » Sat Feb 08, 2014 5:59 pm
Hello,

Can you please assist with this:

In a certain MBA class the average male student is 26.8 years old and the average female student is 25.4 years old. What is the average age of the whole class?

1) The ratio of male to female students is 3 to 2
2) There are 180 male students in the class


OA: Is given as A but the solution is not there. Thanks a lot - Sri


My approach:

Statement 1:


26.8---------?--------25.4
M 2 3 F


m/f = 3/2

=> m/f = (average - 25.4)/(26.8 - average) = 3/2

=> 2 (average - 25.4) = 3 (26.8 - average)

=> average = 26. 24

Hence, suff.


Statement2 : In-suff.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Feb 08, 2014 6:21 pm
gmattesttaker2 wrote: In a certain MBA class the average male student is 26.8 years old and the average female student is 25.4 years old. What is the average age of the whole class?

1) The ratio of male to female students is 3 to 2
2) There are 180 male students in the class
Target question: What is the average age of the whole class?

Given: The average male student is 26.8 years old, and the average female student is 25.4 years old.

Statement 1: The ratio of male to female students is 3 to 2
In other words, 3/5 of the students are male, and 2/5 are female.
This information allows us to apply the following rule regarding weighted averages: Weighted average of combined groups = (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: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

So, Average age of whole class = (3/5)(26.8) + (2/5)(25.4)

Of course, we don't need to actually evaluate this. We need only recognize that we COULD do so, which means we could find the average age of the whole class.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: There are 180 male students in the class
There are several scenarios that satisfy this condition. Here are two:
Case a: there is 1 male and 179 females, in which case the average age of the whole class is very close to 25.4
Case b: there are 179 males and 1 female, in which case the average age of the whole class is very close to 26.8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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by GMATGuruNY » Mon Feb 10, 2014 3:53 am
To make the math easier, we can replace the values in the question stem with easier numbers.
gmattesttaker2 wrote: In a certain MBA class the average male student is 20 years old and the average female student is 10 years old. What is the average age of the whole class?

1) The ratio of male to female students is 3 to 2
2) There are 180 male students in the class
Statement 1: The ratio of male to female students is 3 to 2
Of every 5 students, 3 are male (with an average age of 20), while 2 are female (with an average age of 10).
Average age of every 5 students = (3*20 + 2*10)/5 = 16.
SUFFICIENT.

Statement 2: There are 180 male students in the class
No information about the number of female students.
Thus, the average age of the whole class cannot be determined.
INSUFFICIENT.

The correct answer is A.
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by ceilidh.erickson » Tue Feb 11, 2014 1:31 pm
To add to what Mitch and Brent have said, here's a general rule that will work for the vast majority of weighted average problems: usually, if you simply establish which group you have more of, you'll be able to solve. If you have the exact ratio of one group to another, you will always be able to solve.

For more, see:
https://www.manhattangmat.com/blog/index ... -problems/
https://www.manhattangmat.com/blog/index ... roblems-2/
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