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When you take the test, you need a strategy for GRE percentage problems that works every time. Here’s that strategy, in four easy steps.
Step 1: Identify your problem as a “percent of” problem.
Specifically, this isn’t a strategy for “percent change” problems. Make sure the problem is asking you to calculate a percent of some value:
What is 80% of 120?
If x is 1/3 of y, and y is 120% of z, what percent of x is z?
What percent of 15x is 12y, in terms of x and y?
Step 2: Rephrase the question.
At the heart of every “percent of” problem, no matter how complex, is a basic question. It looks like this:
_____ is _____ percent of _____?
Sometimes, the problem will already be written in this form:
What is 80 percent of 120?
Sometimes, you’ll need to manipulate the terms slightly to make them fit:
z is what percent of x?
12y is what percent of 15x?
If you’re uncertain, look for the ‘of’ in the original problem—it always goes right before the value you’re calculating a percent of. By the way, you’re allowed to use exactly one ‘what’ in your rephrase! It can appear in any of the three positions.
Step 3: Turn it into math.
Translate your sentence into a mathematical equation by working from left to right. What translates into a variable, and I like to use w, as long as it hasn’t already been used elsewhere in the problem. Percent always translates into “/100”. Of translates into multiplication. Here are those three sentences again, this time in mathematical form:
w = 80/100 * 120
z = w/100 * x
12y = w/100 * 15x
Step 4: Isolate w.
w is the value that the problem asks you to solve for. So, use algebra to isolate it. This might take only a single step, as in the first problem:
w = (80/100) * 120
w = 96
You may have to incorporate other equations while solving, as in the second problem. In that case, isolate w first.
z = (w/100) * x
w = 100z / x
Then, use the other equations to eliminate the remaining variables.
x = (1/3)y
y = (120/100)z
w = 100z / ((1/3)y) = 300z/y
w = 300z / ((120/100)z) = 300/(120/100)
w = 250
If you need to solve in terms of another variable or variables, as in the third problem, isolate w while putting all of the other variables on the other side of the equation.
12y = (w/100) * 15x
w = 1200y/15x
w = 80y/x
This approach does require a decent amount of algebra, but it has one huge advantage. Have you ever noticed that many GRE percentage problems have answer choices like these?
The folks who write GRE problems do this intentionally. Once you’ve come up with a solution, they want you to waste time wondering, was I supposed to multiply by 100? Or was I supposed to divide? Or is this number actually the right answer by itself? The strategy in this article sidesteps that problem entirely, because there isn’t any step where you have to decide whether to multiply or divide by 100. That makes it useful for anyone who sometimes finds GRE percentage problems confusing and stressful. As long as you set everything up as shown and do the algebra correctly, the result you get will be exactly the right answer, with no conversion between percents and decimals required.
Try it out on this super-tough problem, and share your process in the comments:
xy is 20% of z. In terms of y, what percent of x is z? ?
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Chelsey Cooley is a Manhattan Prep instructor based in Seattle, Washington. Chelsey always followed her heart when it came to her education. Luckily, her heart led her straight to the perfect background for GMAT and GRE teaching: she has undergraduate degrees in mathematics and history, a master’s degree in linguistics, a 790 on the GMAT, and a perfect 170Q/170V on the GRE. Check out Chelsey’s upcoming GRE prep offerings here.