On the GMAT, you may see a 3 to 5 ratio expressed in a variety of ways:
3 to 5
x/y = 3/5
5x = 3y (Yes, that’s the same as the other 3. Think about it.)
In the real world, we encounter ratios in drink recipes more often than anywhere else (3 parts vodka, 5 parts cranberry), perhaps explaining why–after drinks that strong–we forget how to handle them.
Keep in mind: ratios express a “part to part” relationship, whereas fractions and percentages express a “part to whole” relationship. So the fraction of the above drink is 3/8 vodka (or 37.5% of the whole). Either way, hold off on mixing that drink until after this post.
I like to set up ratios using a “ratio box.” The box is a variant on the “Unknown Multiplier” technique from page 65 of our FDPs book, but it’s a nice way to visually manage ratios without resorting to algebra.
Let’s take the beginning of a typical ratio question:
“The ratio of men to women in a class is 3:2…”
Instead of doing anything fancy with variables, I just set up a tracking chart:
From this point alone, I have sufficient information to answer a bunch of questions.
-What fraction of the students are men? (3/5)
-What percent of the students are women? (40%)
-What is the probability of choosing a man? (3/5)
However, I have nowhere near enough information to answer anything about the REAL numbers of students in this class. Suppose the GMAT were to add a little more information:
“The ratio of men to women in a class is 3:2. If there are 35 students in the class…”
Now we can calculate almost everything about the real numbers of people. First, make a bigger box with 3 lines. The unfilled box looks like this: