Percent Change and Growth - GRE Quantitative Reasoning
Card 1 of 25
A value doubles. What is the percent increase?
A value doubles. What is the percent increase?
Tap to reveal answer
$100%$. Doubling corresponds to a multiplier of $2$, which is a $100%$ increase from the original.
$100%$. Doubling corresponds to a multiplier of $2$, which is a $100%$ increase from the original.
← Didn't Know|Knew It →
A value is halved. What is the percent decrease?
A value is halved. What is the percent decrease?
Tap to reveal answer
$50%$. Halving corresponds to losing half of the original value, which is a $50%$ decrease.
$50%$. Halving corresponds to losing half of the original value, which is a $50%$ decrease.
← Didn't Know|Knew It →
Find the overall multiplier for successive increases of $+20%$ and $+30%$.
Find the overall multiplier for successive increases of $+20%$ and $+30%$.
Tap to reveal answer
$1.56$. Multiplies the individual multipliers $1.2$ and $1.3$ for the successive increases.
$1.56$. Multiplies the individual multipliers $1.2$ and $1.3$ for the successive increases.
← Didn't Know|Knew It →
If a price increases by $15%$, what is the multiplier applied to the original price?
If a price increases by $15%$, what is the multiplier applied to the original price?
Tap to reveal answer
$1.15$. Adds $15%$ as a decimal to $1$ to scale the original price.
$1.15$. Adds $15%$ as a decimal to $1$ to scale the original price.
← Didn't Know|Knew It →
What is the percent decrease from $50$ to $40$?
What is the percent decrease from $50$ to $40$?
Tap to reveal answer
$20%$. The absolute difference of $10$ divided by the original $50$ yields $0.2$, or $20%$ decrease.
$20%$. The absolute difference of $10$ divided by the original $50$ yields $0.2$, or $20%$ decrease.
← Didn't Know|Knew It →
What is the percent increase from $80$ to $100$?
What is the percent increase from $80$ to $100$?
Tap to reveal answer
$25%$. The difference of $20$ divided by the original $80$ yields $0.25$, or $25%$.
$25%$. The difference of $20$ divided by the original $80$ yields $0.25$, or $25%$.
← Didn't Know|Knew It →
State the multiplier for a decrease of $p%$ (in terms of $p$).
State the multiplier for a decrease of $p%$ (in terms of $p$).
Tap to reveal answer
$1-\frac{p}{100}$. Subtracts the fractional percent decrease from 1 to form the scaling factor.
$1-\frac{p}{100}$. Subtracts the fractional percent decrease from 1 to form the scaling factor.
← Didn't Know|Knew It →
State the multiplier for an increase of $p%$ (in terms of $p$).
State the multiplier for an increase of $p%$ (in terms of $p$).
Tap to reveal answer
$1+\frac{p}{100}$. Adds the fractional percent increase to 1 to form the scaling factor.
$1+\frac{p}{100}$. Adds the fractional percent increase to 1 to form the scaling factor.
← Didn't Know|Knew It →
State the formula for percent change from an original value $A$ to a new value $B$.
State the formula for percent change from an original value $A$ to a new value $B$.
Tap to reveal answer
$\frac{B-A}{A}\times 100%$. Calculates the relative difference as a fraction of the original value, then converts to percent.
$\frac{B-A}{A}\times 100%$. Calculates the relative difference as a fraction of the original value, then converts to percent.
← Didn't Know|Knew It →
What is the net percent change for successive increases of $+20%$ and $+30%$?
What is the net percent change for successive increases of $+20%$ and $+30%$?
Tap to reveal answer
$56%$. The overall multiplier of $1.56$ indicates a $56%$ increase from the original.
$56%$. The overall multiplier of $1.56$ indicates a $56%$ increase from the original.
← Didn't Know|Knew It →
If a quantity decreases by $30%$, what is the multiplier applied to the original quantity?
If a quantity decreases by $30%$, what is the multiplier applied to the original quantity?
Tap to reveal answer
$0.70$. Subtracts $30%$ as a decimal from $1$ to scale the original quantity.
$0.70$. Subtracts $30%$ as a decimal from $1$ to scale the original quantity.
← Didn't Know|Knew It →
Find the overall multiplier for successive changes of $+10%$ then $-10%$.
Find the overall multiplier for successive changes of $+10%$ then $-10%$.
Tap to reveal answer
$0.99$. Multiplies the individual multipliers $1.1$ and $0.9$ for the successive changes.
$0.99$. Multiplies the individual multipliers $1.1$ and $0.9$ for the successive changes.
← Didn't Know|Knew It →
What is the net percent change for successive changes of $+10%$ then $-10%$?
What is the net percent change for successive changes of $+10%$ then $-10%$?
Tap to reveal answer
$-1%$. The overall multiplier of $0.99$ represents a $1%$ decrease from the original.
$-1%$. The overall multiplier of $0.99$ represents a $1%$ decrease from the original.
← Didn't Know|Knew It →
If a value is multiplied by $k$, what is the percent change in terms of $k$?
If a value is multiplied by $k$, what is the percent change in terms of $k$?
Tap to reveal answer
$(k-1)\times 100%$. Subtracts $1$ from $k$ to find the relative change, then multiplies by $100$ for percent.
$(k-1)\times 100%$. Subtracts $1$ from $k$ to find the relative change, then multiplies by $100$ for percent.
← Didn't Know|Knew It →
If a value increases by $p%$ each period for $n$ periods, state the growth formula from $A$.
If a value increases by $p%$ each period for $n$ periods, state the growth formula from $A$.
Tap to reveal answer
$A\left(1+\frac{p}{100}\right)^n$. Applies the growth multiplier compounded over $n$ periods to the initial value $A$.
$A\left(1+\frac{p}{100}\right)^n$. Applies the growth multiplier compounded over $n$ periods to the initial value $A$.
← Didn't Know|Knew It →
If a value decreases by $p%$ each period for $n$ periods, state the decay formula from $A$.
If a value decreases by $p%$ each period for $n$ periods, state the decay formula from $A$.
Tap to reveal answer
$A\left(1-\frac{p}{100}\right)^n$. Applies the decay multiplier compounded over $n$ periods to the initial value $A$.
$A\left(1-\frac{p}{100}\right)^n$. Applies the decay multiplier compounded over $n$ periods to the initial value $A$.
← Didn't Know|Knew It →
A population is $1000$ and grows $5%$ for $2$ years. What is the final population?
A population is $1000$ and grows $5%$ for $2$ years. What is the final population?
Tap to reveal answer
$1102.5$. Compounds the $5%$ growth by multiplying $1000$ by $1.05^2$.
$1102.5$. Compounds the $5%$ growth by multiplying $1000$ by $1.05^2$.
← Didn't Know|Knew It →
An investment of $200$ decreases $10%$ each year for $2$ years. What is the final value?
An investment of $200$ decreases $10%$ each year for $2$ years. What is the final value?
Tap to reveal answer
$162$. Compounds the $10%$ decrease by multiplying $200$ by $0.9^2$.
$162$. Compounds the $10%$ decrease by multiplying $200$ by $0.9^2$.
← Didn't Know|Knew It →
A value increases by $25%$; by what percent must it then decrease to return to the original value?
A value increases by $25%$; by what percent must it then decrease to return to the original value?
Tap to reveal answer
$20%$. To reverse a $25%$ increase, the subsequent decrease is relative to the higher value, requiring $20%$.
$20%$. To reverse a $25%$ increase, the subsequent decrease is relative to the higher value, requiring $20%$.
← Didn't Know|Knew It →
A value decreases by $20%$; by what percent must it then increase to return to the original value?
A value decreases by $20%$; by what percent must it then increase to return to the original value?
Tap to reveal answer
$25%$. To reverse a $20%$ decrease, the subsequent increase is relative to the lower value, requiring $25%$.
$25%$. To reverse a $20%$ decrease, the subsequent increase is relative to the lower value, requiring $25%$.
← Didn't Know|Knew It →
State the percent change from $A$ to $B$ when $A=0$.
State the percent change from $A$ to $B$ when $A=0$.
Tap to reveal answer
Undefined (division by $0$). The percent change formula involves division by $A$, which is zero, making it undefined.
Undefined (division by $0$). The percent change formula involves division by $A$, which is zero, making it undefined.
← Didn't Know|Knew It →
What is the percent change from $40$ to $50$?
What is the percent change from $40$ to $50$?
Tap to reveal answer
$25%$. The difference of $10$ divided by the original $40$ yields $0.25$, or $25%$.
$25%$. The difference of $10$ divided by the original $40$ yields $0.25$, or $25%$.
← Didn't Know|Knew It →
What is the percent change from $50$ to $40$?
What is the percent change from $50$ to $40$?
Tap to reveal answer
$-20%$. The difference of $-10$ divided by the original $50$ yields $-0.2$, or $-20%$.
$-20%$. The difference of $-10$ divided by the original $50$ yields $-0.2$, or $-20%$.
← Didn't Know|Knew It →
A store marks an item $20%$ off, then raises the discounted price by $20%$. What is the net percent change?
A store marks an item $20%$ off, then raises the discounted price by $20%$. What is the net percent change?
Tap to reveal answer
$-4%$. The overall multiplier of $0.8 \times 1.2 = 0.96$ represents a $4%$ decrease.
$-4%$. The overall multiplier of $0.8 \times 1.2 = 0.96$ represents a $4%$ decrease.
← Didn't Know|Knew It →
State the relationship between percent change and the ratio $\frac{B}{A}$.
State the relationship between percent change and the ratio $\frac{B}{A}$.
Tap to reveal 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.
$\text{percent change}=\left(\frac{B}{A}-1\right)\times 100%$. Subtracts $1$ from the ratio $\frac{B}{A}$ and multiplies by $100$ to get percent change.
← Didn't Know|Knew It →