GMAT percentages strategies

Percent change equals the difference divided by the original, times 100: $\text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$. The denominator is always the original value, the starting point. If a price goes from 80 to 100, the change is 20 and the original is 80, so the percent increase is $\frac{20}{80} \times 100 = 25\%$. The formula is the same for increases and decreases. The only thing that changes is whether the new value is larger or smaller than the old.

When a value changes by two percents in sequence, each percent applies to the current value, not the original. A 20% increase followed by a 20% decrease is not zero. Starting from 100: a 20% increase gives 120. A 20% decrease from 120 gives 96. The net change is a 4% decrease. The shortcut is to multiply the multipliers: $(1 + 0.20)(1 - 0.20) = 1.20 \times 0.80 = 0.96$, which is a 4% decrease. Adding the percents (20 minus 20 equals 0) gives the wrong answer because each percent applies to a different base.

A stock price increases by 25% on Monday, then decreases by 20% on Tuesday. What is the net percent change from the original price? Step 1: Identify the base. The 25% increase applies to the original price. The 20% decrease applies to the price after Monday's increase. Step 2: Convert to multipliers. A 25% increase is 1.25. A 20% decrease is 0.80. Step 3: Multiply. The net multiplier is $1.25 \times 0.80 = 1.00$. Step 4: Interpret. A multiplier of 1.00 means no net change. The 25% increase and 20% decrease exactly cancel because the decrease acts on the larger (post-increase) value. The answer is 0%.