In an earlier post, we tackled a medium-level GMATPrep weighted average question; click here to read that article before reading this one. This week, we’re trying a harder GMATPrep weighted average question in order to test whether you learned the concept as well as you thought you did. : )
As we discussed earlier, every weighted average problem I’ve seen (so far!) on GMATPrep is a Data Sufficiency question. This doesn’t mean that they’ll never give us a Problem Solving weighted average problem, but it does seem to be the case that the test-writers are more concerned with whether we understand how weighted averages work than with whether we can actually do the calculations. Last week, we focused on understanding how weighted averages work via writing some equations. We’ll try to apply that understanding to our harder problem this week, along with a more efficient solution method.
Let’s start with a sample problem. Set your timer for 2 minutes. and GO!
* A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?
(1) y = 10
(2) z = 16
There are two kinds of gravel: 10% gravel and 2% gravel. These are our two sub-groups. When the two are combined (in some unknown “ for now! “ amounts), we get a 3rd kind:5% gravel. The number of tons of 10% gravel (x) and the number of tons of 2% gravel (y) will add up to the number of tons of 5% gravel (z), or x + y = z. We need to find the number of tons of 10% gravel used in the mixture.
The problem this week throws in a new wrinkle: we’re not just trying to calculate a ratio this time. We have to have enough info to calculate the actual amount of 10% gravel used. Last week, we never had to worry about the actual number of employees. We’ll have to keep that in mind to see how things might change.