SAT percentage changes: a worked lesson for Riyadh students

Successive percentage changes use different starting amounts. A 25% increase followed by a 20% reduction does not mean a 5% increase. The second change applies to the amount after the first change.

Original practice example: markup followed by discount

A shop buys an item for SAR 80, marks it up by 25%, then reduces the marked price by 20%. What percentage of the original cost is the final sale price?

1. After the markup: 80 × 1.25 = SAR 100.
2. After the discount: 100 × 0.80 = SAR 80.
3. Final price as a percentage of original cost: 80 ÷ 80 × 100 = 100%.

The 25% markup adds SAR 20. The 20% discount removes SAR 20 because it applies to the larger SAR 100 marked price. Equal currency changes can correspond to different percentages.

Use multipliers to keep the bases straight

An increase of p% multiplies the current amount by 1 + p/100. A decrease of p% multiplies it by 1 − p/100. Here the combined multiplier is 1.25 × 0.80 = 1. That checks the result without assuming the percentages cancel.

Compare a 20% increase followed by a 20% reduction: 1.20 × 0.80 = 0.96. The result is 96% of the original amount, a 4% decrease.

Try it yourself

A subscription costs SAR 200. Its price rises by 10% and later falls by 15%. Find its final price and percentage change from the original.

Practise inside the correct SAT timing

SAT Math has two modules of 22 questions and 35 minutes each. Reading and Writing comes first, followed by the break and Math. The second module in each section follows a higher- or lower-difficulty route based on first-module performance. Do not assign a fixed score loss to a particular mistake; College Board’s scoring explanation describes a more complex model.

First solve several percentage problems accurately without a timer. Then practise mixed questions so you must identify the method yourself. Record the wrong base or multiplier in your error log and retry a different example later.

Use the SAT Math Skills Check and free study planner for the next practice step. Riyadh candidates should confirm dates and centres through official SAT registration; the Riyadh tutoring page explains the online service.