ResourcesSAT (Digital SAT)Percent Change & Ratios

Percent Change & Ratios

How this shows up on the SAT

Percents and ratios show up everywhere in SAT Math's Problem-Solving & Data Analysis section. The three most-missed question types are: (1) reversing a percent change ('after a 25% raise, the salary is $62,500 — what was it before?'), (2) compound percents that don't cancel ('marked up 30% then marked down 30%'), and (3) ratio traps where students confuse the ratio a:b with the fraction a/(a+b). The SAT's favorite trick: a problem that sounds symmetric but isn't. 'Price went up 20%, then down 20% — what's the net change?' Most students say 0%; the correct answer is a 4% decrease. Always multiply the factors (1.20 × 0.80 = 0.96), never add or subtract the percents. Strategy: when you see 'by what percent', you're computing percent change — (new − old) / old × 100%. The denominator is ALWAYS the original. When the question asks you to reverse a percent change, divide by the multiplier, never subtract the percent of the new value.

The Intuition

Percents are fractions in disguise. 20% means 20/100 = 0.20. The tricky part is identifying the 'whole'. When you raise

00 by 20%, the whole is
00 (→
20). When you then LOWER that by 20%, the whole is now
20 — not
00 — so the decrease is larger than the original increase. You end at $96, not
00. This is why compound percents don't cancel.

Concept Refresher

Percent basics: p% means p/100. To find p% of a number, multiply by p/100 (or p ÷ 100). For example, 15% of 80 = 0.15 × 80 = 12. Percent change formula: (new − old) / old × 100%. The denominator is ALWAYS the original (old) value, not the new one. This is the single most common SAT mistake on percents. Reversing a percent change: if a value increased by r% to become N, the original was N ÷ (1 + r/100). NEVER subtract r% of N — the percent was taken from the original, not from N. Same logic applies to reversing a decrease: divide by (1 − r/100). Compound percents: multiply the factors, don't add the percents. A 30% markup followed by a 30% markdown gives 1.30 × 0.70 = 0.91 of the original — a 9% net decrease, not 0%. Ratios: a ratio a : b is the same as the fraction a/b. But if a question asks 'what fraction of the total is a', the answer is a/(a+b) — you need the WHOLE in the denominator. Cross-multiplying solves proportions: a/b = c/d → ad = bc. Unit rates: dividing gives you 'per one' — if 12 pens cost $9, each pen costs $9/12 = $0.75, and 20 pens cost 20 × $0.75 =

5.

Percent Change & Ratios — Practice Quiz

20 SAT-styled questions. Pick an answer to see the explanation immediately.

  1. 1.A product that cost $80 is now on sale for $60. What is the percent decrease?

  2. 2.A store marks up a

00 item by 30%, then marks the new price down by 30%. What is the final price?

00
60

  • 3.The ratio of red to blue marbles is 3:7. If there are 42 blue marbles, how many red?

  • 4.After a 15% raise, Jordan's salary is $57,500. What was it before the raise?

  • 5.A recipe calls for flour and sugar in a 5:2 ratio. If a baker uses 15 cups of flour, how many total cups are used?

  • 6.What is 15% of 240?

  • 7.A jacket originally costs

    20 and is marked up by 25%. What is the new price?

  • 8.If 8 apples cost $6, how much do 20 apples cost at the same rate?

  • 9.The ratio of adults to children at a park is 2:5. If there are 140 people in total, how many are children?

  • 10.A $75 dinner receives an 18% tip. What is the total amount paid?

  • 11.A number is increased by 40%, giving 112. What was the original number?

  • 12.In a survey of 400 people, 65% said they exercise daily. How many people said they exercise daily?

  • 13.A store offers successive discounts of 20% and then an additional 10% off the reduced price. What is the total percent discount?

  • 14.If x : y = 3 : 4 and y : z = 2 : 5, what is x : z?

  • 15.A map scale is 1 inch : 25 miles. How many miles apart are two cities that are 4.5 inches apart on the map?

  • 16.A company's profit rose from $40,000 to $50,000. What is the percent increase?

  • 17.Anna saves 15% of her ,400 monthly paycheck. How much does she save per month?

    40

  • 18.A solution is 25% salt by weight. How many grams of salt are in 400 grams of solution?

  • 19.If 3 workers can complete a job in 8 hours, how long will it take 6 workers (working at the same rate)?

  • 20.A store has 50 customers on Monday and 65 customers on Tuesday. What is the percent increase from Monday to Tuesday?

    • Frequently Asked Questions

    Why doesn't a 20% increase and 20% decrease cancel out?
    Because the 20% decrease is taken from the already-increased amount, which is larger.
    00 →
    20 → $96.
    How do I reverse a percent increase quickly?
    If something increased by r% to become N, the original was N / (1 + r/100). Always divide, never subtract.
    In a ratio a:b, is a/(a+b) or a/b the right fraction?
    Depends on the question. a/b is the ratio of a to b. a/(a+b) is the fraction of the TOTAL that is a.

    More SAT Practice