Quantitative Skills & Data Analysis - Complete Interactive Lesson
Part 1: Percent Change, Ratios & Fold-Change
MCAT Quantitative Skills
Part 1 of 1 - Percent Change, Ratios & Fold-Change
Many MCAT science questions look like biology, chemistry, or physics — but the real hurdle is a quick mental-math calculation. If you cannot rapidly compute a percent increase, a fold-change, or a ratio from a table or graph, you will lose time and pick trap answers.
The Three Core Formulas
| Calculation | Formula | When to Use |
|---|---|---|
| Percent change | (new − old) / old × 100% | "What is the approximate percent increase/decrease?" |
| Fold-change | new / old | "How many times greater is condition B than condition A?" |
| Ratio | A / B | "What is the ratio of X to Y?" |
Key insight: Percent change and fold-change use the same denominator (the reference/old value). Percent change = (fold-change − 1) × 100%.
Worked Example: Percent Increase
A table shows enzyme activity of 12 units at pH 6 and 54 units at pH 8. What is the approximate percent increase?
- Old = 12, New = 54
- (54 − 12) / 12 × 100% = 42/12 × 100% = 350%
- Sanity check: fold-change = 54 / 12 = 4.5×. Percent increase = (4.5 − 1) × 100% = 350% ✓
Common Trap: Students sometimes divide by the new value instead of the old value. That gives 42/54 ≈ 78% — a wrong answer that will appear as a distractor.
Quick Reference Table
| Fold-change | Percent increase | Percent decrease (if reversed) |
|---|---|---|
| 2× | 100% | 50% |
| 3× | 200% | 67% |
| 4× | 300% | 75% |
| 5× | 400% | 80% |
| 10× | 900% | 90% |
If a value triples, the percent increase is 200%, not 300%. Many students make this off-by-one error.
Percent Change & Ratios Drill
Key Takeaways
- Percent change = (new − old) / old × 100%. Always divide by the reference value.
- Fold-change = new / old. Percent increase = (fold − 1) × 100%.
- A 3× increase is a 200% increase, not 300%. Watch for this MCAT trap.
- For percent decrease, the formula is (old − new) / old × 100%.
- Sanity-check every calculation: if a value quadruples, that is a 300% increase and 4× fold-change.
Practice recognizing these patterns in tables and graphs — MCAT science sections frequently embed quantitative-reasoning hurdles within biology and chemistry questions.