weighted averages

[b.shmorhun]

Can someone help me with this (altered) mgmat question?

A mixture of 20 grams of lean ground beef is mixed with 50 grams of fatty ground beef to create a ground beef mix with 8% fat. How many grams of fat does the lean ground beef have?

My method:

20 grams lean : 50 grams fatty : 70 grams total
x% fat : y% fat : 10% fat
(2 x (-diff) ) x (5 x (+diff) ) = 0
(10-5) = 5% (10+2)= 12%

20x.05 = 1 gram of fat.


Is there an easier way?? If we didn't know that one was fattier than the other -- would it be impossible to find the percentage?

[Twan N]

I looked at the original question and your altered question, I don't understand where you get 10% in your problem; no where in your problem does it state that.

Also, 20:50:70 ratio would result in an equation of:

20(x%) + 50(y%) = 70(8%)

Here the grams of each, lean beef and fatty beef, act as the weight. So basically the extended equation would look like this:

(20x% + 50y%)/(20 +50) = 8%, which if you cross multiply the denominator (20+50) to the right side, you would arrive at the first equation above.

With that said, your problem as it is set up, you have 1 equation with 2 unknowns (x% and y%). If this is a Problem Solving question, it is a badly written one as the GMAT would never have such a question. On the other hand, this question could be applied to Data Sufficiency, since you know there are more of the fatty beef than the lean beef as per the ratio 2 lean:5 fat; thus you know that y%>x%, any statement that states so would be sufficient; however I don't think the GMAT DS would give you all the info like this as that would be too easy; it's probably somewhere along the line of:

A mixture of 8% beef resulted from combining lean beef and fatty beef. Is there more lean beef than fatty beef in the mixture?

1. There are 20 grams of lean beef in the 70 grams mixture
2. There are 50 grams of fatty beef in the mixture

Sufficiency is achieved if you can get a yes or a no answer; a yes results in lean beef > fatty beef, and a no results in lean beef < fatty beef.

Statement 1 is sufficient because you know the ratio of the lean beef to the mixture which is 2:7 (part:whole) so you can get lean beef to fatty beef (part:part), which is 2:5.

Statement 2 is insufficient because you only know of the concrete value for fatty beef and nothing else.

Sorry for the long answer.

[RonPurewal]

Hi,
Don't "alter" MGMAT questions. Just post the original question in the appropriate folder (MGMAT CAT if it's from a practice test; MGMAT non-CAT if it's from anywhere else in our materials).

In this case, you've created a question that doesn't contain enough information to answer it.