Remember these basic rules when dealing with proportional relationships.
We encounter proportions frequently in everyday life. When we cook, we add proportional measurements of ingredients. If you are arranging flowers in a vase, you might want to add 2 stems of one type of bloom for every 3 stems of another.
On the GMAT proportions appear in word problems involving mixtures and probability, but they are most frequently seen in ratios.
Understanding ratios on the GMAT
The ratios you encounter on Test Day may be part to part (boys to girls = 2:1), part to whole (boys to all children = 2:3), or even measure to measure (miles per hour, dollars per gallon). Here I will remind you of a few key tips to help you brush up on ratios for the Quantitative Reasoning section.
- Ratio values are reduced by common factors. If the quantities of items in a ratio have a common factor, reduce the values to get the ratio. For example, if a GMAT question involved a restaurant offering 6 types of sandwiches and 3 kinds of soup each day, the sandwich-to-soup ratio would not be 6:3, because that can be reduced; the ratio would be 2:1.
- If you solve a ratio problem and do not see your answer among the choices, be sure to reduce the values to their lowest form. The GMAT will not list 6:3 among answer choices; that ratio would be 2:1 instead.
- If you know a ratio between quantities, you only know their proportional relationship. You do not know actual values if you only know the ratio. Think of ratios as having an invisible x; we write 3:2 (or 3/2), but the actual value is really 3x:2x (or 3x/2x). If you know a fruit basket contains oranges and apples in a ratio of 3:2, you might have 3 oranges and 2 apples. But you also could have 300 oranges and 200 apples; either way, the ratio remains 3:2.
- If you know a ratio between quantities, you know the actual value of each quantity will be a multiple of the ratio value. For example, if the ratio of boys to girls in a certain classroom is 3:4, you know the number of boys is a multiple of 3 (because boys are represented by 3 in the ratio). The number of girls is a multiple of 4. And, because you can add the parts gives to determine the ratio component of the total, you know the number of children in the classroom is a multiple of 3+4, or 7.
- If you know a:b and b:c, you can find a:c. Imagine that the ratio of roses to carnations in a flower shop is 2:5, and the ratio of carnations to tulips is 7:3. You could write that as follows:
We can’t just “smush” these ratios together to say roses:tulips = 2:3; we need to make the shared quantity the same. Both ratios include a value for carnations, but they are different values. Find the least common multiple of the different values to make them the same. Multiply each ratio as needed to combine:
If we are asked to find the ratio of roses to tulips at this flower shop, we ignore the number of carnations and only look at roses and tulips; the ratio is 14:15.
Brushing up on ratios boosts your confidence as well as your score. Proportional relationships are constrained by a short list of tidy rules; spend some time learning them to land your best GMAT score on Test Day.
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