Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
GMAT ratios are no different than other ratios. A ratio is simply a relationship between two numbers. You may see ratios of more than two numbers, and we will look at that soon; however, even that is just a series of relationships. Most often you will see a ratio represented with a colon (:). Yet, a ratio can be set up as a fraction or potentially even a decimal or percent. Shortly we will discuss how being able to move between formats can help cut down on time spent on individual problems.
One type of ratio is a “part to part” ratio. In part to part ratios you are looking at two independent items. For example, a ratio of 9 students to every 2 teaches would be represented as 9:2.
Another type of ratio is a “part to whole” ratio. In this type, a relationship is established between a part of the whole and the whole itself. An example of this would be when 3 of every 5 students in a class are wearing a red shirt - the students wearing red to total students would be 3:5.
It will be critical for you to distinguish between the difference between part to part and part to whole ratios. For example, if you have 4 boys and 3 girls in a group the part to part for boys to girls would be 4:3. Meanwhile, the boys to students ratio would be 4:7. The GMAT will try and trick you by moving between part to part and part to whole ratios in the same question. Make sure that you are using the right one.
As we said, a ratio is a relationship between two numbers. This relationship is displayed in its simplest form. If a school had 300 students and 30 teachers, the ratio of students to teacher would be 10:1. Here are some of the ways a ratio like this might be represented:
Fraction: 10/11. This means that 10 out of every 11 people are students. Notice that 11 is the sum of the two numbers compared in the ratio. This is a part to whole relationship.
Percent: 90.9%. This is just a conversion of the fraction to a percent. You will need a part to whole relationship.
Notice that the reduced ratio can be used to calculate the total number of people in the group.
Note that there is a multiplier to the 10:1 and 10:11 ratio of 30. Using these ratios with the multiplier and comfortably being able to move between them will help tremendously on the GMAT.
Thus, you can use ratios to calculate the counts for different items represented in the ratio. For example:
If you are given a ratio of boys to girls in a class is 3:4 and there are 15 boys in the class there are many things you can figure out.
Through cross multiplication, you can solve for x:
3x = 60
x = 20
Or, you can use a quicker method, by using what I call the ratio multiplier.
Ratio Multiplier: The number multiplied by the reduced ratio to get the actual numbers in the group.
In this case, ask yourself, “what number is multiplied by 3 to get 15?” Since, the answer is 5, multiply that by 4 and you get the same answer of x = 20.
Simply add the two components of the 15:20 boy to girl ratio you just calculated.
15 + 20 = 35 total students.
From there you can calculate any other ratio you need.
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