GMAT Question of the Day - Problem Solving - Word Problem/Ratio/Algebra
Alice and Carl each completed a portion of a certain job. Alice completed 20% of the job while Carl completed the rest. If they were each paid the same amount, what proportion of her payment must Alice give to Carl so that they each are paid the amount of the total that is proportionate with the amount of work that they each performed?
GMAT Question of the Day Solution
The GMAT Quant section has a whole bunch of word problems so it's important to feel comfortable with them. These questions tend to have a tough image but are often simple in concept (this question of the day has this feel). One thing that seems to help GMAT tutoring students: Taking time to carefully read the question. You do not need to solve the question as you read. You don't even have to take notes. The important thing is to process the information. To understand what the question is asking you to do. This is the time to make a broad plan for solving the question.
In this case Alice will need to give Carl part of her payment so that the pay per work is equal. Sounds like we can set up an equation with Carl on one side and Alice on the other. Pick a variable for the original payment (let's call it x) and pick a variable for the amount that Alice needs to lose from her side and that Carl will gain (let's call this y). Solve for y in terms of x and that will tell you the proportion of her payment that Alice needed to give to Carl.
You might be thinking: how do I deal with the different proportions of the job done by Alice and Carl? Well - look at it this way. We're dealing with 20% and 80% (.2 and .8). So the ratio is 1:4. Carl did 4 units of work to Alice's 1 unit of work. So Carl's money divided by his effort of 4 units must be equal to Alice's money divided by her effort of one unit.