GRE Quantitative Flashcards: Percent Change Growth

What this deck covers

This deck focuses on Percent Change Growth, giving you a quick way to review the definitions, rules, and examples that matter most for GRE Quantitative.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: If a value decreases by $p\%$ each period for $n$ periods, state the decay formula from $A$.

Answer: $A\left(1-\frac{p}{100}\right)^n$. Applies the decay multiplier compounded over $n$ periods to the initial value $A$.

Flashcard 2: State the relationship between percent change and the ratio $\frac{B}{A}$.

Answer: $\text{percent change}=\left(\frac{B}{A}-1\right)\times 100\%$. Subtracts $1$ from the ratio $\frac{B}{A}$ and multiplies by $100$ to get percent change.

Flashcard 3: A value is halved. What is the percent decrease?

Answer: $50\%$. Halving corresponds to losing half of the original value, which is a $50\%$ decrease.

Flashcard 4: What is the percent change from $40$ to $50$?

Answer: $25\%$. The difference of $10$ divided by the original $40$ yields $0.25$, or $25\%$.

Flashcard 5: Find the overall multiplier for successive increases of $+20\%$ and $+30\%$.

Answer: $1.56$. Multiplies the individual multipliers $1.2$ and $1.3$ for the successive increases.

Flashcard 6: A value increases by $25\%$; by what percent must it then decrease to return to the original value?

Answer: $20\%$. To reverse a $25\%$ increase, the subsequent decrease is relative to the higher value, requiring $20\%$.

Flashcard 7: A value decreases by $20\%$; by what percent must it then increase to return to the original value?

Answer: $25\%$. To reverse a $20\%$ decrease, the subsequent increase is relative to the lower value, requiring $25\%$.

Flashcard 8: If a value is multiplied by $k$, what is the percent change in terms of $k$?

Answer: $(k-1)\times 100\%$. Subtracts $1$ from $k$ to find the relative change, then multiplies by $100$ for percent.

Flashcard 9: A store marks an item $20\%$ off, then raises the discounted price by $20\%$. What is the net percent change?

Answer: $-4\%$. The overall multiplier of $0.8 \times 1.2 = 0.96$ represents a $4\%$ decrease.

Flashcard 10: State the multiplier for a decrease of $p\%$ (in terms of $p$).

Answer: $1-\frac{p}{100}$. Subtracts the fractional percent decrease from 1 to form the scaling factor.

Flashcard 11: A value doubles. What is the percent increase?

Answer: $100\%$. Doubling corresponds to a multiplier of $2$, which is a $100\%$ increase from the original.

Flashcard 12: State the formula for percent change from an original value $A$ to a new value $B$.

Answer: $\frac{B-A}{A}\times 100\%$. Calculates the relative difference as a fraction of the original value, then converts to percent.

Flashcard 13: State the percent change from $A$ to $B$ when $A=0$.

Answer: Undefined (division by $0$). The percent change formula involves division by $A$, which is zero, making it undefined.

Flashcard 14: If a value increases by $p\%$ each period for $n$ periods, state the growth formula from $A$.

Answer: $A\left(1+\frac{p}{100}\right)^n$. Applies the growth multiplier compounded over $n$ periods to the initial value $A$.

Flashcard 15: If a price increases by $15\%$, what is the multiplier applied to the original price?

Answer: $1.15$. Adds $15\%$ as a decimal to $1$ to scale the original price.

Flashcard 16: Find the overall multiplier for successive changes of $+10\%$ then $-10\%$.

Answer: $0.99$. Multiplies the individual multipliers $1.1$ and $0.9$ for the successive changes.

Flashcard 17: What is the percent change from $50$ to $40$?

Answer: $-20\%$. The difference of $-10$ divided by the original $50$ yields $-0.2$, or $-20\%$.

Flashcard 18: What is the net percent change for successive changes of $+10\%$ then $-10\%$?

Answer: $-1\%$. The overall multiplier of $0.99$ represents a $1\%$ decrease from the original.

Flashcard 19: What is the percent decrease from $50$ to $40$?

Answer: $20\%$. The absolute difference of $10$ divided by the original $50$ yields $0.2$, or $20\%$ decrease.

Flashcard 20: An investment of $200$ decreases $10\%$ each year for $2$ years. What is the final value?

Answer: $162$. Compounds the $10\%$ decrease by multiplying $200$ by $0.9^2$.

Flashcard 21: What is the net percent change for successive increases of $+20\%$ and $+30\%$?

Answer: $56\%$. The overall multiplier of $1.56$ indicates a $56\%$ increase from the original.

Flashcard 22: If a quantity decreases by $30\%$, what is the multiplier applied to the original quantity?

Answer: $0.70$. Subtracts $30\%$ as a decimal from $1$ to scale the original quantity.

Flashcard 23: What is the percent increase from $80$ to $100$?

Answer: $25\%$. The difference of $20$ divided by the original $80$ yields $0.25$, or $25\%$.

Flashcard 24: State the multiplier for an increase of $p\%$ (in terms of $p$).

Answer: $1+\frac{p}{100}$. Adds the fractional percent increase to 1 to form the scaling factor.

Flashcard 25: A population is $1000$ and grows $5\%$ for $2$ years. What is the final population?

Answer: $1102.5$. Compounds the $5\%$ growth by multiplying $1000$ by $1.05^2$.