Quick: what's 35% of 80?
If your instinct was to grab a calculator and multiply 0.35 by 80, great. You'd get 28, and you'd be right. But what about this one:
28 is 35% of what number?
That's the version that slows students down. And the SAT knows it.
Percentage questions show up all over the math section, sometimes dressed up in word problems about sales tax, population growth, or discounts. The math itself isn't hard. The setup is where people lose points. So let's get the setup right.
The one formula you need
Every percentage problem, no matter how it's worded, comes down to this:
Part / Whole = Percent / 100
That's it. Three slots, and the SAT will always give you two of them. Your job is to find the missing one.
Let's run through each version.
"What is 35% of 80?"
You know the whole (80) and the percent (35). Solve for the part by cross-multiplying.
x / 80 = 35 / 100
35 * 80 = 100x
x = 28
"28 is what percent of 80?"
You know the part (28) and the whole (80). Solve for the percent.
28 / 80 = x / 100
28 * 100 = 80x
x = 35
"28 is 35% of what number?"
You know the part (28) and the percent (35). Solve for the whole.
28 / x = 35 / 100
28 * 100 = 35x
x = 80
Same formula every time. Just different slots filled in.
Where students actually lose points
The tricky part isn't the arithmetic. It's figuring out what's the "part" and what's the "whole" when the problem is buried in a word problem.
Here's an example:
A store marks up a jacket from $60 to $75. What is the percent increase?
A lot of students will write 15 / 75. That gives you 20%. Nope (and it will definitely be listed as a fake-out answer).
The correct denominator is the original value, which is $60. The increase is $15. So:
15 / 60 = 25%
The whole in a percent change problem is always where you started, not where you ended up. This is probably the single most common percentage mistake on the SAT, and it shows up constantly.
Percent change has its own shortcut
For any increase or decrease problem, you can use this:
Percent change = Change / Original x 100
Memorize this one. It'll save you time.
A word on calculator use
The SAT now allows a calculator for the entire math section, so feel free to use one on percentage problems. That said, the formula approach still matters. A calculator won't tell you which number is the "part" and which is the "whole." If you plug in the wrong values, you'll get a wrong answer very efficiently. Set up the equation first, then let the calculator do the arithmetic.
When you see those, slow down, identify your part and your whole, and plug into the formula before you do anything else.
If percentage problems still feel shaky, or you're not sure where else you might be leaving points on the table, that's exactly the kind of thing we work through at District Scholars. One-on-one SAT prep, real explanations, no worksheets that go straight in the recycling bin. Get started at www.districtscholars.com/contact.
