Time management is crucial for great scores on the GRE Test, and one way to improve your pacing is to become faster at some of the more accessible skill tags. Ratios and proportions are the basics of algebra, and better scores with this concept will help you get harder GRE Quantitative questions correct! Let’s review the fundamentals!
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A ratio is a comparison between two quantities. It is usually expression as a fraction (x/y) or with a colon (x:y), or in a word problems (“the ratio of apples to oranges”). Typically, whatever follows the word “of” is in the numerator, and whatever follows the word “to” is in the denominator.
A proportion is a set of ratios set equal to each other. Basically, an equation with two fractions, such as 4/x = y/7. You can always solve a proportion by cross-multiplying the numerator of one fraction by the denominator of the other. 4/x = y/7 would become 28 = xy after we cross-multiplied.
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Ratios are usually expressed as part: whole or part:part. Making that distinction is important, especially in complex GRE word problems. Ratios are always reduced to the simplest form, but you can multiply them by any integer to increase the numerator/denominator values, as long as you do the same thing to the top and the bottom of the fraction.
Remember: When given a part:whole ratio, at at least one “real-world” number, you can solve for the other “real-world” value. For example, if the ratio of girls to total students in a class is 3:5, and there are 8 boys in the class, how many girls are in the class?
We know the ratio of boys:total students must be 2:5, since there are 3 girls out of 5. Let’s set up a proportion to solve: 2/5 = 8/x. There are 20 students total in the class, so there must be 12 girls.
When working with proportions, make sure to carefully look for any change in units. This especially occurs in questions involving time. Don’t forget – there are 60 seconds in 1 minute, and 60 minutes in 1 hour. J
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