The average number of students per class

[danielle.wipperfurth]

5th Edition, Word Problems, p. 108

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

The book explains that the thing that really matters is which school has more classes. I understand the general principles of weighted averages but am having a hard time applying that knowledge here. Can you help me make the mental leap? Thanks!

Danielle

[tim]

okay try figuring out what would happen if one or the other of the two schools had no classes, or if the two schools had an equal number of classes. note that 29 is halfway between the two other values, so that's where the average would be if we had the same number of classes in each school. the average would become higher or lower than 29 if one school had more than the other..

[aparna.k.aditya]

what is the answer..Is it right that the answer is B.

[jnelson0612]

what is the answer..Is it right that the answer is B.

Yes. :-)

[danielle.wipperfurth]

Thanks I understand now

[jnelson0612]

Thanks I understand now

Great! :-)

[ScottS374]

Can someone explain to me, using algebra, how statement 1 is insufficient?

If you were to convert the question stem into algebra, it would be [(25x + 33y)/(x+y)] < 29, where x is the number of classes in School X and y is the number of class in School Y, correct? If you simplify that, you find that you're trying to see if x>y, which is confirmed in the strategy guide.

With statement 1 telling you that there are 12 classes in School X (x=12 from statement), you can plug the given x value into the question stem expression and determine a value that y has to be greater than or less than. This is how my math went:

[(25(12) + 33y)/(12+y)] < 29
300+33y < 29(12+y)
300 + 33y < 348 +29y
4y < 48
y < 12

Since we know that x is 12 and y has to be less than 12, and since we're determining if x is greater than y (as found in the question stem), how is this statement not sufficient? I can't seem to figure out where I'm going wrong with the algebra/logic in statement 1.

Thanks!

[RonPurewal]

the problem here is pretty simple: you're forgetting that the question is... well... the question.

if you plug a value into a question... it's still a question.

With statement 1 telling you that there are 12 classes in School X (x=12 from statement), you can plug the given x value into the question stem expression and determine a value that y has to be greater than or less than. This is how my math went:

Is [(25(12) + 33y)/(12+y)] < 29?
Is 300+33y < 29(12+y)?
Is 300 + 33y < 348 +29y?
Is 4y < 48?
Is y < 12?

...and, of course, with only statement 1 we have no idea whether y is actually less than 12.

[RonPurewal]

the take-home point is that, if you're working with the question in some way, you should ALWAYS write the "is" and the "?", in EVERY SINGLE STEP that you write down.