Problem Solving & Data Analysis • 15% of test
Percentages
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Percentages?
Percentage questions test percent calculations, percent change, and interpreting percentages in context. They appear in various forms including discounts, tax, tips, and data interpretation.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
How do I calculate percent change?
(New - Original) / Original × 100. Always divide by the ORIGINAL value.
If price increases 20% then decreases 20%, is it back to original?
No! It's 0.96 of original (1.2 × 0.8 = 0.96). You must multiply, not add/subtract percentages.
How do I find the original after a percent change?
If final = original × factor, then original = final / factor. Work backwards.
What does 'percent of' mean?
'Of' means multiply. 25% of 80 = 0.25 × 80 = 20.
How do I convert between decimals and percents?
Multiply by 100 to get percent (0.35 → 35%). Divide by 100 to get decimal (35% → 0.35).
Are percentage word problems common?
Yes! They appear in taxes, discounts, and population change. Focus on these in our <a href='/math'>Problem Solving modules</a>.
How do I calculate 'Tax and Tip' together?
Multiply the price by (1 + tax_rate + tip_rate) if they apply to the subtotal, or factor them sequentially if tip is charged on the taxed total.
What is 'Simple Interest'?
I = Prt. Interest is calculated ONLY on the principal amount, unlike compound interest which earns interest on interest.
How do I find 'Percent of a Percent'?
Multiply the decimals. For example, 20% of 50% is 0.20 × 0.50 = 0.10, which is exactly 10%.
What does 'Percentage Point' mean vs 'Percent'?
A change from 10% to 15% is a 5 'percentage point' increase, but it represents a 50 'percent' increase over the original value.
How do I handle 'Mixture' problems?
Set up an equation based on the substance amount: (vol1 × %1) + (vol2 × %2) = total_vol × final_%. Ensure units match.
What is 'Margin of Error' in percentages?
It's the range around a sample result (e.g., 45% ± 3%) within which the true population percentage likely falls.
How do I calculate 'Net Price' after multiple discounts?
Multiply the original by the 'remainders'. If discounts are 10% and 15%, net price = original × 0.90 × 0.85.
What if the numerator is larger than the denominator?
The percentage will simply be greater than 100%. For example, 150/100 = 1.5, which is 150%.
Why do I divide by 'Original' in percent change?
Because 'change' is measured relative to your starting point, not the ending result. (New - Old) / Old is the standard.