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MathProblem-Solving and Data AnalysisHard

A store raises the price of a jacket by 20%. Later, it lowers the new price by 20%. The final price is what percent of the original price?

A80%
B96%Correct
C100%The trap
D104%

Check with $100: $100then$120then$96

  1. Turn each change into a multiplier.

    Up 20% means × 1.20. Down 20% means × 0.80.

  2. Apply them in order.

    1.20 × 0.80 = 0.96

  3. Read the answer.

    The final price is 96% of the original. That’s B.

  4. Why not 100%?

    The 20% cut is taken from the higher price, so it removes more than the 20% increase added.

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  1. Reading & Writing · Module 1

    27 questions32 min

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The Daily, plus 36 practice questions every day: 12 easy, 12 medium and 12 hard, each with a full explanation. Full-length Test A, Challenge Test 1 and all 1,023 vocabulary words are free too. No card needed.

Pro is $20 a month or $200 a year: unlimited practice with no daily limit, plus every full-length test and Challenge test. Peak is $29 a month or $280 a year: everything in Pro, plus the full Learn course and Peak Plan. Cancel anytime from your account.

98 questions across four modules, in the digital SAT’s order: Reading & Writing Module 1 and Module 2 (27 questions each), a 10-minute break, then Math Module 1 and Module 2 (22 questions each). On official timing that’s 2 hr 14 min of testing. You get estimated section scores and a total at the end.

Yes. In the standard full-length tests, Module 2 of each section is the harder version if you get 60% or more of Module 1 right, and the easier version if you don’t. Challenge tests use the hardest material throughout.

Official timing, extended 1.5× time, or untimed, on every test, including the free ones. Extended time allows 48 minutes for each Reading & Writing module and about 52 for each Math module. Untimed removes the clock so you can focus on accuracy.

A quick run with three hearts. Each right answer builds your streak: the questions get harder as it grows, and your points multiply (×2 from three in a row, ×3 from six). A miss costs a heart and drops you back to easy. Best is your longest streak.

Every day at midnight. You get a fresh 12 easy, 12 medium and 12 hard.

No. Peakscor is an independent SAT practice tool, not affiliated with the College Board. Scores shown are estimates.

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Percentages · Lesson 2

Increase, decrease and percent change

When a quantity grows by a percent rr (written as a decimal), the new amount is the old amount plus rr times the old amount: new = old × (1 + r). For a decrease: new = old × (1 − r). The number you multiply by is the multiplier.

A price of 60 dollars increased by 15% is 60⋅1.15=6960 \cdot 1.15 = 69 dollars. Decreased by 15%, it is 60⋅0.85=5160 \cdot 0.85 = 51 dollars. One multiplication does the whole job, and the multiplier tells you the new amount as a percent of the old: 1.15 means 115% of the original.

Percent change =new−oldold×100%= \frac{\text{new} - \text{old}}{\text{old}} \times 100\%. The base, the number you divide by, is the starting value, the one you change from.

From 40 to 52, the change is 12 and 1240=0.3\frac{12}{40} = 0.3: a 30% increase. From 52 to 40, the change is still 12, but the base is 52: 1252≈0.231\frac{12}{52} \approx 0.231, about a 23.1% decrease. Same gap, different base, different percent.

Comparisons work the same way. In A is 30% more than B, the base is B, the value after than, so A=1.3BA = 1.3B.

Worked example Easy

The price of a tent rose from 120 dollars to 150 dollars.

By what percent did the price of the tent increase?

  1. 20%20\%
  2. 25%25\%Answer
  3. 30%30\%
  4. 125%125\%

How to solve it

  1. Find the change: 150−120=30150 - 120 = 30 dollars.
  2. Divide by the starting price, the base: 30120=0.25\frac{30}{120} = 0.25.
  3. Write it as a percent: a 25% increase. Check: 120⋅1.25=150120 \cdot 1.25 = 150.

Why each choice is right or wrong

  • A. Incorrect. This divides the change by the new price: 30150=0.2\frac{30}{150} = 0.2, or 20%. The base for a percent change is the starting price, 120.
  • B. Correct. The price rose 30 dollars from a starting price of 120 dollars, and 30120=0.25\frac{30}{120} = 0.25, a 25% increase.
  • C. Incorrect. This reports the 30 dollar change as a percent. A change of 30 would be 30% only if the starting price were 100 dollars.
  • D. Incorrect. 150120=1.25\frac{150}{120} = 1.25 says the new price is 125% of the old price. The increase is 125%−100%=25%125\% - 100\% = 25\%.

Worked example Medium

The positive number nn is 50% greater than the positive number mm. The number mm is what percent less than nn?

  1. 3313%33\frac{1}{3}\%Answer
  2. 50%50\%
  3. 6623%66\frac{2}{3}\%
  4. 150%150\%

How to solve it

  1. Pick an easy value: let m=100m = 100. Then nn is 50% greater, so n=150n = 150.
  2. Now the question compares mm with nn: *less than nn* makes nn the base.
  3. The gap is 50, and 50150=13\frac{50}{150} = \frac{1}{3}. So mm is 3313%33\frac{1}{3}\% less than nn.

Why each choice is right or wrong

  • A. Correct. With m=100m = 100 and n=150n = 150, the gap of 50 is 13\frac{1}{3} of nn, so mm is 3313%33\frac{1}{3}\% less than nn.
  • B. Incorrect. This assumes the percent is the same in both directions. The gap of 50 is 50% of mm, but the question uses n=150n = 150 as the base, and 50150=3313%\frac{50}{150} = 33\frac{1}{3}\%.
  • C. Incorrect. 100150=6623%\frac{100}{150} = 66\frac{2}{3}\% is the percent mm is of nn. The question asks how much less, which is 100%−6623%=3313%100\% - 66\frac{2}{3}\% = 33\frac{1}{3}\%.
  • D. Incorrect. nn is 150% of mm. That compares nn to mm, the reverse direction, and it is not a percent less.

Trap Dividing by the new value

The base is the starting value. From 40 to 52 is a 30% increase, but dividing the change by 52 gives about 23.1%, which is the percent for the reverse trip, a decrease from 52 to 40. Both numbers can be among the choices.

Trap Multiplying by the change instead of the multiplier

Multiplying by 0.15 gives only the size of a 15% change. For the new amount after an increase, multiply by 1.15. For the new amount after a decrease, multiply by 0.85.

Desmos When Desmos isn’t faster

Percent change is one subtraction and one division, so a hand calculation is usually quickest. Desmos can check it: type (52 − 40)/40 and it shows 0.3, which is 30%.

Desmos computes whatever you type, so it can't catch a wrong base. Deciding which value is the starting value is the step that matters.

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Study the classic SAT vocabulary list. Browse, flip flashcards, or quiz yourself.

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