Percent Change Problems on the SAT

Every percent change question compares a new number to an old one. Before touching anything, figure out which value is the starting point and which is the result. Mix those up and the whole answer flips, no matter how clean the rest of the work is.

Say a jacket costs $40 and goes on sale for 25% off. Working it in two steps means finding 25% of $40, which is $10, then subtracting: $40 minus $10 leaves $30. That's fine. There's a faster route, though, one that matters once a module clock is running down: a 25% decrease is the same as keeping 75% of the price, so $40 times 0.75 lands on $30 in one move.

An increase works the mirror way. A 25% increase multiplies by 1.25, not 0.25. Add the percent onto 100%, turn the result into a decimal, and multiply straight through. Once that habit sets in, a question that used to take two lines takes one.

This is the whole engine behind percent change on the SAT. Everything else in this topic, the successive changes, the backward questions, the wording traps, is this same multiplier idea applied under slightly different disguises. Get comfortable building the multiplier in your head before you reach for Desmos, and most of these questions stop feeling like separate problems.

A price goes up 20%, then comes back down 20%. Does it return to where it started? No. Plenty of students assume it does, and the SAT counts on exactly that assumption.

Walk it through. Start at $100. Up 20% means multiply by 1.20, giving $120. Down 20% from there means multiplying by 0.80, but 0.80 of $120, not of the original $100. That comes out to $96. The price ends up below where it began, since the decrease was calculated off a bigger number than the increase was.

The same thing happens with two increases back to back. Two separate 10% raises don't add up to 20%. Multiply instead: 1.10 times 1.10 is 1.21, a 21% increase overall. The gap between 20% and 21% looks tiny on paper. On a test built around catching that exact shortcut, it's the whole question.

Mixed changes work the same way, just with different multipliers stacked on top of each other. A value up 30% and then down 20% isn't a net 10% gain. Multiply: 1.30 times 0.80 is 1.04, so the real result is a 4% increase, nowhere close to the number you'd get from just subtracting the two percentages.

Some questions flip the setup entirely. Instead of giving the starting value and asking for the result, they give the result and ask what the starting value was. The fix: divide by the multiplier. Don't subtract the percent from the final number.

A shirt costs $68 after a 15% discount. That $68 is 85% of the original price, not the whole thing, so the move is division: 68 divided by 0.85 equals $80. Subtracting 15% of $68 from $68 gives a different, wrong number, because that treats the discount as if it applied to the sale price instead of the original one.

The same logic runs in reverse for an increase. If a number is the result of a 12% increase, divide by 1.12 to recover the starting value. Multiplying by 0.88 instead is the trap, and it's a popular one on this test.

Percentage points and percent change measure two different things, and mixing them up is an easy way to miss an otherwise simple question. Say a rate moves from 5% to 8%. That's a jump of 3 percentage points, but the percent change is 60%, since 8 minus 5 divided by 5 works out to 0.60. A question can ask for either one, so check which word it actually uses before picking a number.

"20 percent of 60" and "20 percent more than 60" aren't the same question either. The first is just 0.20 times 60, which is 12. The second tacks that 12 back onto the 60, which puts it at 72. One extra word changes the entire setup. Read the sentence twice before writing anything down, especially under time pressure.

Percent change shows up constantly across the Math section, tucked inside word problems about prices, populations, and survey data. It's worth practicing on its own rather than hoping it sorts itself out inside mixed sets. StudyPebble's practice by skill groups percent and ratio questions together, with an explanation after each one.

Already sitting on a pile of missed percent questions from a Bluebook test? Screenshot them and upload them at /mistakes/upload. It sorts the misses by skill, so a cluster of percent change mistakes lands in one place instead of scattering across a results page where it's easy to ignore.