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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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Every Peakscor full test follows this order. In the standard tests, the second module of each section adapts to how you did on the first.

  1. Reading & Writing · Module 1

    27 questions32 min

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    22 questions35 min

  5. Math · Module 2

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98 questions · 2 hr 14 min of testing, plus the break

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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 1

Percent of a quantity

Percent means per hundred. 35% means 35 out of every 100, so 35% is 35100\frac{35}{100}, or 0.35. To turn a percent into a decimal, divide by 100: move the decimal point two places to the left.

Most percent questions come down to one equation: part = (percent as a decimal) × whole. In a word problem, of usually means multiply and is means equals. The whole is the amount the percent is of.

Find the part. What is 35% of 140? 0.35⋅140=490.35 \cdot 140 = 49.

Find the whole. 24 is 75% of what number? 0.75w=240.75w = 24, so w=240.75=32w = \frac{24}{0.75} = 32. The whole is bigger than the part whenever the percent is under 100%.

Find the percent. 18 is what percent of 225? Divide the part by the whole: 18225=0.08\frac{18}{225} = 0.08, which is 8%.

When a percent describes part of a group that is itself a percent of something larger, take one percent at a time, each of its own whole.

Worked example Easy

If 18% of a number is 36, what is the number?

  1. 6.486.48
  2. 2020
  3. 200200Answer
  4. 2,0002{,}000

How to solve it

  1. Write 18% as a decimal: 0.18. Call the number nn. 18% of a number is 36 becomes 0.18n=360.18n = 36.
  2. Divide both sides by 0.18: n=360.18=200n = \frac{36}{0.18} = 200.
  3. Check: 0.18⋅200=360.18 \cdot 200 = 36. The number is bigger than 36, as it must be, because 36 is only 18% of it.

Why each choice is right or wrong

  • A. Incorrect. This finds 18% of 36: 0.18⋅36=6.480.18 \cdot 36 = 6.48. But 36 is the part, not the whole. The number you want is larger than 36.
  • B. Incorrect. This writes 18% as 1.8, moving the decimal point only one place, so n=361.8=20n = \frac{36}{1.8} = 20. 18% is 0.18.
  • C. Correct. 0.18n=360.18n = 36, so n=360.18=200n = \frac{36}{0.18} = 200. Check: 18% of 200 is 36.
  • D. Incorrect. This writes 18% as 0.018, moving the decimal point three places, so n=360.018=2,000n = \frac{36}{0.018} = 2{,}000. 18% is 0.18.

Worked example Medium

A school has 600 students. Of these students, 45% take a language class, and 20% of the students who take a language class study Mandarin.

How many students at the school study Mandarin?

  1. 5454Answer
  2. 120120
  3. 270270
  4. 390390

How to solve it

  1. The 45% is of the whole school: 0.45⋅600=2700.45 \cdot 600 = 270 students take a language class.
  2. The 20% is of the language students, not of the school: 0.2⋅270=540.2 \cdot 270 = 54.
  3. In one step: 0.2⋅0.45=0.090.2 \cdot 0.45 = 0.09, so 9% of the school studies Mandarin, and 0.09⋅600=540.09 \cdot 600 = 54.

Why each choice is right or wrong

  • A. Correct. 45% of 600 is 270 language students, and 20% of those 270 is 54.
  • B. Incorrect. This takes 20% of the whole school, 0.2⋅600=1200.2 \cdot 600 = 120. The 20% is of the students who take a language class.
  • C. Incorrect. 270 is the number of students who take a language class. The question asks how many of them study Mandarin, so take 20% of 270.
  • D. Incorrect. This adds the percents, 45%+20%=65%45\% + 20\% = 65\%, and takes 65% of 600 to get 390. The two percents have different wholes, so they can't be added.

Trap Moving the decimal point the wrong number of places

A percent becomes a decimal when you divide by 100: 4% is 0.04, 40% is 0.4, and 0.4% is 0.004. Writing 0.4% as 0.4 makes an answer off by a factor of 100: too big when you multiply by the percent, too small when you divide by it. A choice built from a one-place or three-place slip can appear among the options, so count the places.

Trap Using the wrong whole

In the Mandarin example, 20% is a percent of the language students, not of the whole school. Before you multiply, ask: percent of what? Two percents with different wholes can't be added.

Desmos When Desmos isn’t faster

These are one- or two-step calculations, and the real work is deciding which number is the part and which is the whole. Desmos can't make that choice for you.

Desmos can still do the arithmetic. Type 27/0.18 on a line and it shows 150. If you'd rather not rearrange the equation, graph y=0.18xy = 0.18x and y=27y = 27, zoom out until you see where they cross, and click the intersection, (150,27)(150, 27). Its xx-coordinate is the whole.

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Each test mirrors the digital SAT: 98 questions across four modules, 2 hr 14 min on official timing.

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