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Weighted Average

by AndreiGMAT » Mon Apr 11, 2016 3:08 pm
I am practicing Weighted Average questions.

The average number of students per class at School X is 25 and the average number of students per class at School Y is 33. Is the average number of students per
class for both schools combined less than 29 ?

(1) There are 12 classes in School X.
(2)There are more classes in School X than in School Y.
My answer is: E (both not sufficient, because no data about student number).

What if the question would ask: Is the average number of students per
class for both schools combined less than 31?
My answer is: E

What will be the answer in both cases?
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Source: — Data Sufficiency |

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by [email protected] » Tue Apr 12, 2016 10:11 am
Hi AndreiGMAT,

What is the source of these questions? I ask because since you didn't provide the correct answers to these prompts, I'm curious whether the source provided the correct answer or not.

We're told that:
1) The average number of students per class at School X is 25
2) The average number of students per class at School Y is 33

We're asked if the average for ALL classes at both Schools is LESS than 29. This is a YES/NO question. Before we deal with the two Facts, we can 'rewrite' this prompt...

IF there were equal numbers of classes at each School, then the average number of students per class for BOTH Schools would be (25+33)/2 = 29. If there are MORE classes at School X than at School Y, then the average DECREASES; if there are MORE classes at School Y than at School X, then the average INCREASES. So when the question asks if the average for both Schools is LESS than 29, it's really asking if there are MORE classes at School X than at School Y...

1) There are 12 classes in School X.

This Fact tells us NOTHING about the number of classes at School Y.
Fact 1 is INSUFFICIENT.

2) There are more classes in School X than in School Y.

This Fact provides information that PROVES that the average MUST be less than 29. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: B

In your second example, if we're dealing with the same two Facts that we had in the first example, then the answer will be the same (for the same reasons).

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by Matt@VeritasPrep » Tue Apr 12, 2016 6:47 pm
One way of thinking about this: if x and y are weighted equally, then the average of x and y will be (x + y)/2.

So we can say that:

If x and y have the same number of classes, the average student per class would be (33 + 25)/2 = 29.

If x has more classes, then the average will be closer to x than y, something > 29.

If y has more classes, then the average will be closer to y than x, something < 29.

The crucial takeaway here is that (Average) * (# of Classes) = (# of Students), which does give us the student number in a sense.

For instance, suppose that X has k classes and that Y has (k + m) classes, where m > 0.

We know that X has 25k students and Y has 33*(k + m) => 33k + 33m students.

The average is thus (25k + 33k + 33m) / (2k + m) => (58k + 33m) / (2k + m).

We want to see if this is greater than 29, so we can set

(58k + 33m) / (2k + m) > 29

(58k + 33m) > 29*(2k + m)

58k + 33m > 58k + 29m

4m > 0

So this is true for any m greater than 0. We know m > 0, so the average must be greater than 29.
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by OptimusPrep » Thu Apr 14, 2016 7:24 pm
AndreiGMAT wrote:I am practicing Weighted Average questions.

The average number of students per class at School X is 25 and the average number of students per class at School Y is 33. Is the average number of students per
class for both schools combined less than 29 ?

(1) There are 12 classes in School X.
(2)There are more classes in School X than in School Y.
My answer is: E (both not sufficient, because no data about student number).

What if the question would ask: Is the average number of students per
class for both schools combined less than 31?
My answer is: E

What will be the answer in both cases?
Given: Average at school = 25, Average at school Y = 33
Required: Is the average at both schools < 29

Average at both schools = Total students at both schools / Total classes at both schools

Statement 1: There are 12 classes in School X
This means there are 25*12 = 300 students at school X
But we do not know anything about school Y.
Insufficient

Statement 2: There are more classes in School X than in School Y
If the number of classes were equal at both the schools, then the average would have been = (25 + 33)/2 = 29
Since, the number of classes at X are more (where the average is less)
Hence the average will also shift towards 25.
Therefore the total average < 29
Sufficient

Correct Option: B

For your other question too, the situation remains the same and the answer would be B
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