Why start from 100 in a percent change question?

Because a percentage is an amount out of 100. Starting from 100 means every result reads directly as a percentage of the original: 102 is 102% of it, a 2% increase. Any starting number gives the same answer; 100 is the one that needs no conversion at the end.

Why don't a 20% increase and a 20% decrease cancel out?

The decrease is 20% of the raised amount, which is larger than the amount the increase was worked out on. From 100, a 20% increase gives 120, and 20% of 120 is 24, so the result is 96, not 100.

Can I just add the two percentages?

No. Adding 20% and -15% gives 5%, but the true change is 2%. Adding leaves out the second change applied to the first: (20 x -15) / 100 = -3 percentage points.

When should I not use 100?

When the question gives a real starting amount, use that amount: the answer has to be in real units. And when a question is about percentage points, the difference between two percentages, there is no change to follow at all.

Percent change questions: start from 100 and follow it through

When a percentage question names no starting amount, call it 100. Every later percentage then becomes a number you can read.

1.If no starting amount is given, start with 100.
2.Apply each change in turn to what the last change left, never to the original.
3.Read the result against 100: 108 is an 8% increase, and 72 is a 28% decrease.
4.In a comparison, the thing named after "than" or "of" is the 100.

Try it on a question

Work it below before you open the working. The steps say what to do, and you can do each one yourself.

The price of a jacket is increased by 20%, and the new price is then reduced by 15%. The final price is what percent of the original price?

Choice A: 92%
Choice B: 102%
Choice C: 105%
Choice D: 135%

1
Drag the start down to 100.
2
Set the first change to +20% and the second change to -15%.
3
Read the final amount: 102. Against a start of 100 that is 102% of the original. The line marked "Adding the percents instead" shows the +5% the trap gives.

Two percent changes in a row

Every percent change is one multiplication, so two changes collapse into a single multiplier. Watch the third bar against the dashed start line: a rise and an equal fall never cancel, because the fall is a percentage of a different amount than the rise was.

start500

first change+20%

second change-20%

Multipliers: x1.20 then x0.80
Combined multiplier: x0.96
Final amount: 480
Overall change: -4%
Adding the percents instead: 0%

500 x 1.20 = 600, and then 600 x 0.80 = 480. The two steps collapse into one multiplier, because multiplication does not care about the order or the stopping point: 1.20 x 0.80 = 0.96, so the whole journey is 500 x 0.96 = 480, an overall change of -4%.

Adding the two percentages gives 0%, and it is wrong by exactly (20 x -20) / 100 = -4 percentage points. That term is the second change applied to the first change, and it only vanishes when one of the changes is 0%. An equal rise and fall is the case worth memorising: x1.20 times x0.80 is x0.96, never x1.00, so 500 comes back as 480 — short by 20, a loss of 4%. The rise was 20% of 500; the fall was 20% of the larger 600.

The full working, and why each wrong choice is there

No starting price is given, so call it 100. A 20% increase gives 120. The 15% reduction is 15% of 120, which is 18, so the final price is 102.

Against a start of 100, that is 102% of the original: a 2% rise, not the 5% that adding the percentages suggests. The reduction was taken from a larger amount than the rise was added to, so it removed more.

Choice A: 92%
This applies the changes the wrong way round: down by 20%, then up by 15%. The question raises the price first.
Choice B: 102%the answer
Starting from 100: a 20% increase gives 120, and 15% off 120 takes away 18, leaving 102.
Choice C: 105%
This adds the two percentages: up 20, down 15. The 15% is taken from the raised price, not from the original, so it removes more than 15.
Choice D: 135%
This adds both percentages to 100. The second change is a reduction.

Use it when

Two or more percentage changes in a row, with no actual amount given.
The question asks what single percentage change is equivalent to the changes together.
A comparison that has to be turned round: A is 40% greater than B, so B is what percent of A?

Do not use it when

A real starting amount is given. Use it: the question wants a real answer, and swapping in 100 adds a step.
The question is about percentage points, such as a share moving from 40% to 46%. That is a gap of 6 points, not a 6% change.
One change, with the amount given. Multiply once and finish.

Five questions on this move

Untimed, and nothing is saved. A wrong first answer gets one more try before the working is shown.

Question 1 of 5

A town's population fell by 10% in one year and rose by 10% in the next. Compared with its size at the start of the two years, the population at the end was

Five is a start

In your account there is a focused set of ten on Percentages from the question bank, with the same one more try. And after each practice test, the drills your plan sets for the skills you missed name the moves for them.

Practise Percentages in your account

How this page was checked

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The answer to each of the 6 questions on this page is worked out again by our calculator engine in an automated test, which fails when a key disagrees with the engine.
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Not yet. Every question and every item of its lab was worked through in a browser by Claude, an AI assistant, on 14 October 2026. The page was published on 14 October 2026 before a person had read it. If something here is wrong, tell us and it is put right.

The questions were drafted with AI and are original: none is a College Board question, and none comes from the question bank behind our practice tests.

Where this comes from

“Start from 100” is one card from the Preptics lesson Percentage traps: four right answers to the wrong question, which sits under the Digital SAT skill Percentages. The lesson has the other cards around it, and its questions come back for review on a schedule. The lessons are part of the Digital SAT track.

Common questions

Why start from 100 in a percent change question?: Because a percentage is an amount out of 100. Starting from 100 means every result reads directly as a percentage of the original: 102 is 102% of it, a 2% increase. Any starting number gives the same answer; 100 is the one that needs no conversion at the end.
Why don't a 20% increase and a 20% decrease cancel out?: The decrease is 20% of the raised amount, which is larger than the amount the increase was worked out on. From 100, a 20% increase gives 120, and 20% of 120 is 24, so the result is 96, not 100.
Can I just add the two percentages?: No. Adding 20% and -15% gives 5%, but the true change is 2%. Adding leaves out the second change applied to the first: (20 x -15) / 100 = -3 percentage points.
When should I not use 100?: When the question gives a real starting amount, use that amount: the answer has to be in real units. And when a question is about percentage points, the difference between two percentages, there is no change to follow at all.

Keep going

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