Step 1: Identify your problem as a “percent of” problem. <\/strong><\/h4>\nSpecifically, this <\/span>isn’t<\/span><\/i> a strategy for “percent change” problems. Make sure the problem is asking you to calculate a percent <\/span>of<\/span><\/i> some value:<\/span><\/p>\nWhat is 80% of 120?<\/span><\/p>\nIf <\/span>x<\/span><\/i> is 1\/3 of <\/span>y<\/span><\/i>, and <\/span>y<\/span><\/i> is 120% of <\/span>z<\/span><\/i>, what percent of <\/span>x<\/span><\/i> is <\/span>z<\/span><\/i>? <\/span><\/p>\nWhat percent of 15<\/span>x<\/span><\/i> is 12<\/span>y<\/span><\/i>, in terms of<\/span> x<\/span><\/i> and <\/span>y<\/span><\/i>?<\/span><\/p>\nStep 2: Rephrase the question.<\/strong><\/h4>\nAt the heart of every “percent of” problem, no matter how complex, is a basic question. It looks like this: <\/span><\/p>\n_____ is _____ percent of _____?<\/span><\/p>\nSometimes, the problem will already be written in this form:<\/span><\/p>\nWhat <\/span>is <\/span>80<\/span> percent of <\/span>120<\/span>? <\/span><\/p>\nSometimes, you’ll need to manipulate the terms slightly to make them fit:<\/span><\/p>\nz<\/span><\/i> is <\/span>what<\/span> percent of <\/span>x<\/span><\/i>?<\/span><\/p>\n12<\/span>y<\/span><\/i> is <\/span>what<\/span> percent of <\/span>15<\/span>x<\/span><\/i>?<\/span><\/p>\nIf you’re uncertain, look for the ‘of’ in the original problem\u2014it 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.<\/span><\/p>\nStep 3: Turn it into math. <\/strong><\/h4>\nTranslate your sentence into a mathematical equation by working from left to right. <\/span>What<\/span><\/i> translates into a variable, and I like to use <\/span>w<\/span><\/i>, as long as it hasn’t already been used elsewhere in the problem. <\/span>Percent<\/span><\/i> always translates into “\/100”. <\/span>Of<\/span><\/i> translates into multiplication. Here are those three sentences again, this time in mathematical form: <\/span><\/p>\nw<\/span><\/i> = 80\/100 * 120<\/span><\/p>\nz<\/span><\/i> = <\/span>w<\/span><\/i>\/100 * <\/span>x<\/span><\/i><\/p>\n12<\/span>y<\/span><\/i> = <\/span>w<\/span><\/i>\/100 * 15<\/span>x<\/span><\/i><\/p>\nStep 4: Isolate w<\/i>.<\/strong><\/h4>\nw<\/span><\/i> 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:<\/span><\/p>\nw<\/span><\/i> = (80\/100) * 120
\n<\/span>w<\/i><\/b> = 96<\/b><\/p>\nYou may have to incorporate other equations while solving, as in the second problem. In that case, isolate <\/span>w<\/span><\/i> first.<\/span><\/p>\nz<\/span><\/i> = (<\/span>w<\/span><\/i>\/100) * <\/span>x
\n<\/span><\/i>w<\/span><\/i> = 100<\/span>z<\/span><\/i> \/ <\/span>x<\/span><\/i><\/p>\nThen, use the other equations to eliminate the remaining variables.<\/span><\/p>\nx<\/span><\/i> = (1\/3)<\/span>y
\n<\/span><\/i>y<\/span><\/i> = (120\/100)<\/span>z
\n<\/span><\/i>w<\/span><\/i> = 100<\/span>z<\/span><\/i> \/ ((1\/3)<\/span>y<\/span><\/i>)<\/span> \u00a0= 300<\/span>z<\/span><\/i>\/<\/span>y
\n<\/span><\/i>w<\/span><\/i> = 300<\/span>z<\/span><\/i> \/ ((120\/100)<\/span>z<\/span><\/i>) = 300\/(120\/100)
\n<\/span>w <\/i><\/b>= 250<\/b><\/p>\nIf you need to solve <\/span>in terms of <\/span><\/i>another variable or variables, as in the third problem, isolate <\/span>w<\/span><\/i> while putting all of the other variables on the other side of the equation. <\/span><\/p>\n12<\/span>y<\/span><\/i> = (<\/span>w<\/span><\/i>\/100) * 15<\/span>x
\n<\/span><\/i>w<\/span><\/i> = 1200<\/span>y<\/span><\/i>\/15<\/span>x
\n<\/span><\/i>w<\/i><\/b> = 80<\/b>y<\/i><\/b>\/<\/b>x<\/i><\/b><\/p>\nThis 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?<\/span><\/p>\n(A) 0.4%
\n<\/span>(B) 4%
\n<\/span>(C) 40%
\n<\/span>(D) 400% <\/span><\/p>\nThe folks who write GRE problems do this intentionally. Once you’ve come up with a solution, they want you to waste time wondering, w<\/em><\/span>as I supposed to multiply by 100? Or was I supposed to divide? Or is this number actually the right answer by itself?<\/span><\/i> 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 <\/span>exactly the right answer<\/span><\/i>, with no conversion between percents and decimals required. <\/span><\/p>\nTry it out on this super-tough problem, and share your process in the comments:<\/span><\/p>\nxy<\/span><\/i> is 20% of <\/span>z<\/span><\/i>. In terms of <\/span>y<\/span><\/i>, what percent of <\/span>x<\/span><\/i>
![\"Blog-Percentage\"](\"\/\/www.manhattanprep.com\/gre\/wp-content\/uploads\/sites\/19\/2015\/12\/blog-percentage.png\")
<\/p>\n