Percent Increase and Decrease - SSAT Upper Level Quantitative

1. State the formula for the percent change from an original value $O$ to a new value $N$.

   $\frac{N-O}{O}\times 100\%$. Calculates the relative change by dividing the difference by the original value and multiplying by 100 to express as a percentage.

2. A price is discounted $30\%$ and then discounted $20\%$. What single discount percent is equivalent?

   $44\%$. The equivalent single discount is $100\% - (0.7 \times 0.8) \times 100\%$, yielding 44%.

3. What percent decrease takes $120$ down to $96$?

   $20\%$. Divide the decrease by the original value and multiply by 100 to determine the percentage reduction.

4. State the multiplier for increasing a value by $p\%$.

   $1+\frac{p}{100}$. Represents the factor by which the original value is scaled to include the percentage increase.

5. A $35\%$ discount is followed by a $35\%$ markup on the discounted price. What is the net percent change?

   $-12.25\%$. The overall multiplier $0.65 \times 1.35 = 0.8775$ indicates a 12.25% decrease from the original.

6. What is the percent decrease from $90$ to $72$?

   $20\%$. Divide the decrease by the original value and multiply by 100 to find the percentage change.

7. What is the final value after increasing $200$ by $15\%$ and then increasing the result by $10\%$?

   $253$. Successive application of multipliers $1.15$ and $1.1$ to the original value gives the final result.

8. What discount percent from original price $O$ to sale price $S$? (Express in terms of $O$ and $S$.)

   $\frac{O-S}{O}\times 100\%$. Discount percentage is the reduction relative to the original price, computed as the difference over original times 100%.

9. What is the percent increase from $50$ to $65$?

   $30\%$. Divide the increase by the original value and multiply by 100 to find the percentage change.

10. What percent increase takes $40$ up to $50$?

    $25\%$. Divide the increase by the original value and multiply by 100 to determine the percentage growth.

11. A quantity decreases from $y$ to $0.6y$. What is the percent decrease?

    $40\%$. The decrease of $0.4y$ relative to the original $y$ corresponds to a 40% change.

12. A quantity increases from $x$ to $1.5x$. What is the percent increase?

    $50\%$. The increase of $0.5x$ relative to the original $x$ corresponds to a 50% change.

13. What is the new value if $80$ is increased by $25\%$?

    $100$. Apply the multiplier $1.25$ to the original value to compute the increased amount.

14. A shirt costs $48 after a $20\%$ discount. What was the original price?

    $60. Divide the discounted price by the retention rate $0.8$ to recover the original price.

15. What markup percent from cost $C$ gives selling price $S$? (Express in terms of $C$ and $S$.)

    $\frac{S-C}{C}\times 100\%$. Markup percentage is the profit relative to cost, computed as the difference over cost times 100%.

16. A price is increased by $10\%$ and then decreased by $10\%$. What is the net percent change?

    $-1\%$. The successive multipliers $1.1$ and $0.9$ yield an overall factor of $0.99$, indicating a 1% decrease.

17. After a $25\%$ decrease, a value is $150$. What was the original value?

    $200$. Divide the decreased value by the retention rate $0.75$ to find the original value.

18. A price is increased $30\%$ and then increased $20\%$. What single increase percent is equivalent?

    $56\%$. The equivalent single increase is $(1.3 \times 1.2 - 1) \times 100\%$, yielding 56%.

19. What is the overall percent change after increases of $20\%$ and $30\%$ applied successively?

    $56\%$. The combined multiplier $1.2 \times 1.3 = 1.56$ corresponds to a 56% increase from the original.

20. A value is multiplied by $1.2$ and then by $0.75$. What is the overall percent change?

    $-10\%$. The product of the multipliers $1.2$ and $0.75$ is $0.9$, representing a 10% decrease overall.

21. A number is decreased by $20\%$ and then increased by $25\%$. What is the net percent change?

    $0\%$. The multipliers $0.8$ and $1.25$ product to $1$, resulting in no net percentage change.

22. What is the new value if $60$ is decreased by $15\%$?

    $51$. Apply the multiplier $0.85$ to the original value to compute the decreased amount.

23. A value becomes $84$ after a $40\%$ increase. What was the original value?

    $60$. Divide the new value by the growth factor $1.4$ to find the original value before the increase.

24. State the multiplier for decreasing a value by $p\%$.

    $1-\frac{p}{100}$. Represents the factor by which the original value is scaled to account for the percentage decrease.

25. What is the overall percent change after decreases of $20\%$ and $30\%$ applied successively?

    $-44\%$. The combined multiplier $0.8 \times 0.7 = 0.56$ corresponds to a 44% decrease from the original.

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