Percent Increase and Decrease - SSAT Upper Level: Quantitative
Card 1 of 25
What discount percent from original price $O$ to sale price $S$? (Express in terms of $O$ and $S$.)
What discount percent from original price $O$ to sale price $S$? (Express in terms of $O$ and $S$.)
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$\frac{O-S}{O}\times 100%$. Discount percentage is the reduction relative to the original price, computed as the difference over original times 100%.
$\frac{O-S}{O}\times 100%$. Discount percentage is the reduction relative to the original price, computed as the difference over original times 100%.
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What markup percent from cost $C$ gives selling price $S$? (Express in terms of $C$ and $S$.)
What markup percent from cost $C$ gives selling price $S$? (Express in terms of $C$ and $S$.)
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$\frac{S-C}{C}\times 100%$. Markup percentage is the profit relative to cost, computed as the difference over cost times 100%.
$\frac{S-C}{C}\times 100%$. Markup percentage is the profit relative to cost, computed as the difference over cost times 100%.
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A $35%$ discount is followed by a $35%$ markup on the discounted price. What is the net percent change?
A $35%$ discount is followed by a $35%$ markup on the discounted price. What is the net percent change?
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$-12.25%$. The overall multiplier $0.65 \times 1.35 = 0.8775$ indicates a 12.25% decrease from the original.
$-12.25%$. The overall multiplier $0.65 \times 1.35 = 0.8775$ indicates a 12.25% decrease from the original.
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A price is increased $30%$ and then increased $20%$. What single increase percent is equivalent?
A price is increased $30%$ and then increased $20%$. What single increase percent is equivalent?
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$56%$. The equivalent single increase is $(1.3 \times 1.2 - 1) \times 100%$, yielding 56%.
$56%$. The equivalent single increase is $(1.3 \times 1.2 - 1) \times 100%$, yielding 56%.
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A price is discounted $30%$ and then discounted $20%$. What single discount percent is equivalent?
A price is discounted $30%$ and then discounted $20%$. What single discount percent is equivalent?
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$44%$. The equivalent single discount is $100% - (0.7 \times 0.8) \times 100%$, yielding 44%.
$44%$. The equivalent single discount is $100% - (0.7 \times 0.8) \times 100%$, yielding 44%.
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A value becomes $84$ after a $40%$ increase. What was the original value?
A value becomes $84$ after a $40%$ increase. What was the original value?
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$60$. Divide the new value by the growth factor $1.4$ to find the original value before the increase.
$60$. Divide the new value by the growth factor $1.4$ to find the original value before the increase.
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After a $25%$ decrease, a value is $150$. What was the original value?
After a $25%$ decrease, a value is $150$. What was the original value?
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$200$. Divide the decreased value by the retention rate $0.75$ to find the original value.
$200$. Divide the decreased value by the retention rate $0.75$ to find the original value.
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A price is increased by $10%$ and then decreased by $10%$. What is the net percent change?
A price is increased by $10%$ and then decreased by $10%$. What is the net percent change?
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$-1%$. The successive multipliers $1.1$ and $0.9$ yield an overall factor of $0.99$, indicating a 1% decrease.
$-1%$. The successive multipliers $1.1$ and $0.9$ yield an overall factor of $0.99$, indicating a 1% decrease.
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What percent increase takes $40$ up to $50$?
What percent increase takes $40$ up to $50$?
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$25%$. Divide the increase by the original value and multiply by 100 to determine the percentage growth.
$25%$. Divide the increase by the original value and multiply by 100 to determine the percentage growth.
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What percent decrease takes $120$ down to $96$?
What percent decrease takes $120$ down to $96$?
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$20%$. Divide the decrease by the original value and multiply by 100 to determine the percentage reduction.
$20%$. Divide the decrease by the original value and multiply by 100 to determine the percentage reduction.
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What is the overall percent change after decreases of $20%$ and $30%$ applied successively?
What is the overall percent change after decreases of $20%$ and $30%$ applied successively?
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$-44%$. The combined multiplier $0.8 \times 0.7 = 0.56$ corresponds to a 44% decrease from the original.
$-44%$. The combined multiplier $0.8 \times 0.7 = 0.56$ corresponds to a 44% decrease from the original.
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What is the overall percent change after increases of $20%$ and $30%$ applied successively?
What is the overall percent change after increases of $20%$ and $30%$ applied successively?
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$56%$. The combined multiplier $1.2 \times 1.3 = 1.56$ corresponds to a 56% increase from the original.
$56%$. The combined multiplier $1.2 \times 1.3 = 1.56$ corresponds to a 56% increase from the original.
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What is the final value after increasing $200$ by $15%$ and then increasing the result by $10%$?
What is the final value after increasing $200$ by $15%$ and then increasing the result by $10%$?
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$253$. Successive application of multipliers $1.15$ and $1.1$ to the original value gives the final result.
$253$. Successive application of multipliers $1.15$ and $1.1$ to the original value gives the final result.
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A number is decreased by $20%$ and then increased by $25%$. What is the net percent change?
A number is decreased by $20%$ and then increased by $25%$. What is the net percent change?
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$0%$. The multipliers $0.8$ and $1.25$ product to $1$, resulting in no net percentage change.
$0%$. The multipliers $0.8$ and $1.25$ product to $1$, resulting in no net percentage change.
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A quantity decreases from $y$ to $0.6y$. What is the percent decrease?
A quantity decreases from $y$ to $0.6y$. What is the percent decrease?
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$40%$. The decrease of $0.4y$ relative to the original $y$ corresponds to a 40% change.
$40%$. The decrease of $0.4y$ relative to the original $y$ corresponds to a 40% change.
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A quantity increases from $x$ to $1.5x$. What is the percent increase?
A quantity increases from $x$ to $1.5x$. What is the percent increase?
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$50%$. The increase of $0.5x$ relative to the original $x$ corresponds to a 50% change.
$50%$. The increase of $0.5x$ relative to the original $x$ corresponds to a 50% change.
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A shirt costs $\$48$ after a $20%$ discount. What was the original price?
A shirt costs $\$48$ after a $20%$ discount. What was the original price?
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$\$60$. Divide the discounted price by the retention rate $0.8$ to recover the original price.
$\$60$. Divide the discounted price by the retention rate $0.8$ to recover the original price.
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A value is multiplied by $1.2$ and then by $0.75$. What is the overall percent change?
A value is multiplied by $1.2$ and then by $0.75$. What is the overall percent change?
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$-10%$. The product of the multipliers $1.2$ and $0.75$ is $0.9$, representing a 10% decrease overall.
$-10%$. The product of the multipliers $1.2$ and $0.75$ is $0.9$, representing a 10% decrease overall.
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State the formula for the percent change from an original value $O$ to a new value $N$.
State the formula for the percent change from an original value $O$ to a new value $N$.
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$\frac{N-O}{O}\times 100%$. 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.
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State the multiplier for decreasing a value by $p%$.
State the multiplier for decreasing a value by $p%$.
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$1-\frac{p}{100}$. Represents the factor by which the original value is scaled to account for the percentage decrease.
$1-\frac{p}{100}$. Represents the factor by which the original value is scaled to account for the percentage decrease.
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What is the new value if $80$ is increased by $25%$?
What is the new value if $80$ is increased by $25%$?
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$100$. Apply the multiplier $1.25$ to the original value to compute the increased amount.
$100$. Apply the multiplier $1.25$ to the original value to compute the increased amount.
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What is the new value if $60$ is decreased by $15%$?
What is the new value if $60$ is decreased by $15%$?
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$51$. Apply the multiplier $0.85$ to the original value to compute the decreased amount.
$51$. Apply the multiplier $0.85$ to the original value to compute the decreased amount.
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What is the percent increase from $50$ to $65$?
What is the percent increase from $50$ to $65$?
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$30%$. Divide the increase by the original value and multiply by 100 to find the percentage change.
$30%$. Divide the increase by the original value and multiply by 100 to find the percentage change.
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What is the percent decrease from $90$ to $72$?
What is the percent decrease from $90$ to $72$?
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$20%$. Divide the decrease by the original value and multiply by 100 to find the percentage change.
$20%$. Divide the decrease by the original value and multiply by 100 to find the percentage change.
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State the multiplier for increasing a value by $p%$.
State the multiplier for increasing a value by $p%$.
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$1+\frac{p}{100}$. Represents the factor by which the original value is scaled to include the percentage increase.
$1+\frac{p}{100}$. Represents the factor by which the original value is scaled to include the percentage increase.
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