Percent Increase and Decrease - ISEE Upper Level: Quantitative Reasoning
Card 1 of 24
What is the new value after decreasing $90$ by $\frac{1}{3}$?
What is the new value after decreasing $90$ by $\frac{1}{3}$?
Tap to reveal answer
$60$. Decreasing by $\frac{1}{3}$ means multiplying by $\frac{2}{3}$, yielding $60$.
$60$. Decreasing by $\frac{1}{3}$ means multiplying by $\frac{2}{3}$, yielding $60$.
← Didn't Know|Knew It →
What is the percent decrease from $60$ to $45$?
What is the percent decrease from $60$ to $45$?
Tap to reveal answer
$25%$. The difference of $15$ divided by the original $60$ yields $0.25$, or $25%$.
$25%$. The difference of $15$ divided by the original $60$ yields $0.25$, or $25%$.
← Didn't Know|Knew It →
What is the percent of the original after a $p%$ increase?
What is the percent of the original after a $p%$ increase?
Tap to reveal answer
$(100+p)%$. The increased portion by adding $p%$ to $100%$ of the original.
$(100+p)%$. The increased portion by adding $p%$ to $100%$ of the original.
← Didn't Know|Knew It →
What is the percent of the original remaining after a $p%$ decrease?
What is the percent of the original remaining after a $p%$ decrease?
Tap to reveal answer
$(100-p)%$. The remaining portion after subtracting $p%$ from $100%$ of the original.
$(100-p)%$. The remaining portion after subtracting $p%$ from $100%$ of the original.
← Didn't Know|Knew It →
What is the final value after multiplying $150$ by a $0.9$ factor (a $10%$ decrease)?
What is the final value after multiplying $150$ by a $0.9$ factor (a $10%$ decrease)?
Tap to reveal answer
$135$. The factor $0.9$ reduces the original value by $10%$, yielding the new amount.
$135$. The factor $0.9$ reduces the original value by $10%$, yielding the new amount.
← Didn't Know|Knew It →
What percent decrease is needed to go from $100$ to $80$?
What percent decrease is needed to go from $100$ to $80$?
Tap to reveal answer
$20%$. The difference of $20$ divided by the original $100$ yields $0.2$, or $20%$.
$20%$. The difference of $20$ divided by the original $100$ yields $0.2$, or $20%$.
← Didn't Know|Knew It →
What percent increase is needed to go from $80$ to $100$?
What percent increase is needed to go 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 →
What is the overall multiplier for successive changes of $+a%$ then $+b%$?
What is the overall multiplier for successive changes of $+a%$ then $+b%$?
Tap to reveal answer
$\left(1+\frac{a}{100}\right)\left(1+\frac{b}{100}\right)$. Combines the individual growth factors for each successive percentage increase.
$\left(1+\frac{a}{100}\right)\left(1+\frac{b}{100}\right)$. Combines the individual growth factors for each successive percentage increase.
← Didn't Know|Knew It →
Identify the net percent change for a decrease of $20%$ followed by an increase of $25%$.
Identify the net percent change for a decrease of $20%$ followed by an increase of $25%$.
Tap to reveal answer
$0%$. The combined multipliers $0.8$ and $1.25$ yield $1.00$, resulting in no net change.
$0%$. The combined multipliers $0.8$ and $1.25$ yield $1.00$, resulting in no net change.
← Didn't Know|Knew It →
Identify the net percent change for an increase of $10%$ followed by a decrease of $10%$.
Identify the net percent change for an increase of $10%$ followed by a decrease of $10%$.
Tap to reveal answer
$-1%$. The combined multipliers $1.1$ and $0.9$ yield $0.99$, equivalent to a $-1%$ net change.
$-1%$. The combined multipliers $1.1$ and $0.9$ yield $0.99$, equivalent to a $-1%$ net change.
← Didn't Know|Knew It →
What is the percent change from $30$ to $45$?
What is the percent change from $30$ to $45$?
Tap to reveal answer
$50%$. The change of $15$ relative to the original $30$ results in a $50%$ increase.
$50%$. The change of $15$ relative to the original $30$ results in a $50%$ increase.
← Didn't Know|Knew It →
What is the percent increase from $45$ to $60$?
What is the percent increase from $45$ to $60$?
Tap to reveal answer
$\frac{100}{3}%$. The difference of $15$ divided by the original $45$ yields $\frac{1}{3}$, or $\frac{100}{3}%$.
$\frac{100}{3}%$. The difference of $15$ divided by the original $45$ yields $\frac{1}{3}$, or $\frac{100}{3}%$.
← Didn't Know|Knew It →
State the formula for the percent change from original $O$ to new $N$.
State the formula for the percent change from original $O$ to new $N$.
Tap to reveal answer
$\frac{N-O}{O}\times 100%$. Calculates the relative change by dividing the difference by the original value and multiplying by 100 to express as a percentage.
$\frac{N-O}{O}\times 100%$. Calculates the relative change by dividing the difference by the original value and multiplying by 100 to express as a percentage.
← Didn't Know|Knew It →
Identify the multiplier for a $p%$ decrease (in terms of $p$).
Identify the multiplier for a $p%$ decrease (in terms of $p$).
Tap to reveal answer
$1-\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the decreased amount.
$1-\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the decreased amount.
← Didn't Know|Knew It →
What is the percent increase from $40$ to $50$?
What is the percent increase 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 decrease from $80$ to $60$?
What is the percent decrease from $80$ to $60$?
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 →
What is the new value after increasing $120$ by $15%$?
What is the new value after increasing $120$ by $15%$?
Tap to reveal answer
$138$. Multiplying $120$ by the factor $1.15$ accounts for the $15%$ increase.
$138$. Multiplying $120$ by the factor $1.15$ accounts for the $15%$ increase.
← Didn't Know|Knew It →
What is the new value after decreasing $200$ by $12%$?
What is the new value after decreasing $200$ by $12%$?
Tap to reveal answer
$176$. Multiplying $200$ by the factor $0.88$ accounts for the $12%$ decrease.
$176$. Multiplying $200$ by the factor $0.88$ accounts for the $12%$ decrease.
← Didn't Know|Knew It →
What is the original value if a $20%$ increase gives a new value of $96$?
What is the original value if a $20%$ increase gives a new value of $96$?
Tap to reveal answer
$80$. Dividing $96$ by $1.2$ reverses the $20%$ increase to find the original value.
$80$. Dividing $96$ by $1.2$ reverses the $20%$ increase to find the original value.
← Didn't Know|Knew It →
What is the original value if a $25%$ decrease gives a new value of $75$?
What is the original value if a $25%$ decrease gives a new value of $75$?
Tap to reveal answer
$100$. Dividing $75$ by $0.75$ reverses the $25%$ decrease to find the original value.
$100$. Dividing $75$ by $0.75$ reverses the $25%$ decrease to find the original value.
← Didn't Know|Knew It →
Identify the multiplier for a $p%$ increase (in terms of $p$).
Identify the multiplier for a $p%$ increase (in terms of $p$).
Tap to reveal answer
$1+\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the increased amount.
$1+\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the increased amount.
← Didn't Know|Knew It →
State the formula for the new value after a $p%$ decrease of original $O$.
State the formula for the new value after a $p%$ decrease of original $O$.
Tap to reveal answer
$N=O\left(1-\frac{p}{100}\right)$. Applies the reduction factor by multiplying the original value by 1 minus the percentage decrease divided by 100.
$N=O\left(1-\frac{p}{100}\right)$. Applies the reduction factor by multiplying the original value by 1 minus the percentage decrease divided by 100.
← Didn't Know|Knew It →
State the formula for the new value after a $p%$ increase of original $O$.
State the formula for the new value after a $p%$ increase of original $O$.
Tap to reveal answer
$N=O\left(1+\frac{p}{100}\right)$. Applies the growth factor by multiplying the original value by 1 plus the percentage increase divided by 100.
$N=O\left(1+\frac{p}{100}\right)$. Applies the growth factor by multiplying the original value by 1 plus the percentage increase divided by 100.
← 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 change of $-10$ relative to the original $50$ results in a $-20%$ change.
$-20%$. The change of $-10$ relative to the original $50$ results in a $-20%$ change.
← Didn't Know|Knew It →