# Re-learning Ratios

- Aug 21, 04:00 AM Comments [0]

The key to ratio problems on the GMAT is to remember all of the different ways a ratio can be written. Most students are used to seeing ratios denoted by a colon; the ratio of 3 to 5 would be written as 3:5. However, ratios can also be written as fractions – $\frac{3}{5}$ – or decimals – .6 – as well. These last two are especially important because in many problems that ask for a ratio, you will be able to determine a fraction or decimal value without actually being able to solve for either component individually. So if a problem asks for the ratio of x to y and you determine that $\frac{x}{y} = .4$, you know the ratio.

Alongside the ability to recognize the different ways to write out a ratio, you must be able convert ratios quickly. The fastest way to do this is to pull out a trick you probably have not used since high school: cross multiplication.

Let’s say you are given the ratio of men to women at a party as 4:7, are told that there are 21 women at the party and asked for the total number of partygoers. To answer this question you must first see that the ratio of women to total partygoers is 7:11 – the eleven comes from adding four and seven together. Then you write your ratio as a fraction: $\frac{7}{11}$. Next, set this fraction equal to a new fraction that puts the actual number of women on the same side of the fraction bar as they were in the initial ratio. You will end up with $\frac{7}{11} = \frac{21}{P}$, where $P$ is the number of people at the party. Then multiply the numerator of each fraction with denominator of the other and set these equal to each other. This gives you 7(P) = 11(21). Once you are here, simply solve for $P$. Remember, you can start by dividing both sides by seven in this case, which gives you P = 11(3) = 33.

Bret Ruber
Kaplan GMAT