3 grades of milk are 1%, 2%, and 3% fat by volume. If X

[mjtian]

Please enlighten me :shock:

3 grades of milk are 1%, 2%, and 3% fat by volume. If X gallons of 1% grade, Y gallons of the 2% grade and Z gallons of the 3% grade are mixed to give X+Y+Z gallons of a 1.5% grade, what is X in terms of Y and Z?

a) Y+3Z
b) Y+Z
------
4

3) 2Y+3Z
4) 3Y+Z
5) 3Y+4.5Z


I blitzed through this question and got it wrong. I figured since the mixture is only 1.5% there has to be more X than Y and Z. So based on that I picked B as my answer. However, the answer is A, and I have no idea why. Can someone please explain. Thanks a million.

[ekattur]

Think of grades in terms of % of something. In this case:
1%of x + 1%of y+1%of z = 1.5% (x + y + z )

Please enlighten me :shock:

3 grades of milk are 1%, 2%, and 3% fat by volume. If X gallons of 1% grade, Y gallons of the 2% grade and Z gallons of the 3% grade are mixed to give X+Y+Z gallons of a 1.5% grade, what is X in terms of Y and Z?

a) Y+3Z
b) Y+Z
------
4

3) 2Y+3Z
4) 3Y+Z
5) 3Y+4.5Z




I blitzed through this question and got it wrong. I figured since the mixture is only 1.5% there has to be more X than Y and Z. So based on that I picked B as my answer. However, the answer is A, and I have no idea why. Can someone please explain. Thanks a million.

[Guest]

[quote="ekattur"]Think of grades in terms of % of something. In this case:
1%of x + 1%of y+1%of z = 1.5% (x + y + z )


I am not sure if I follow? The overall mixture contains 1.5% grade milk shouldn't there be more of the 1% versus the 2% and the 3% grades? How then can "A" be the answer when it states for every 1% grade there are 1 (2%) and 3 (3%) grade milk? Shouldn't that be: [(1*1%) + 2(2%) + 3(3%)]/3 = (14%)/3 = 4.67%?

Granted, when I use that same formula for my answer, it still doesn't work: [1(1%) + (2%+3%)/2]/3 = 1.167%


Yikes!!!!! I am so lost

[StaceyKoprince]

Your logic is right - that you need more of the 1% grade than the other two. And answer A fits that logic (as do others, though - so this isn't a good method to do the problem).

A basically says X = Y + 3Z. In other words, to get the same number of gallons that I have of X, I have to use Y gallons PLUS three times Z gallons. That indicates that there's more X than either Y or Z.

Answer B, X = (Y+Z)/4 can be rearranged to 4X = Y+Z. That says I need to take X and multiply it by 4 in order to add up to Y+Z. That's not a lot of X.

Take a look at this thread for a great discussion of this problem and how to approach weighted average problems:
http://www.manhattangmat.com/forums/gmatprep-averages-t281.html