Percent Increase and Decrease - SSAT Middle Level Quantitative

1. Identify the multiplier for a $25\%$ increase.

   $1.25$. Converting $25\%$ to $0.25$ and adding to $1$ yields the growth factor.

2. What is the new value when $120$ is increased by $15\%$?

   $138$. Multiplying $120$ by the $15\%$ increase multiplier of $1.15$ gives the new value.

3. State the formula for the new value after a percent decrease of $r\%$ from original $O$.

   $N=O\left(1-\frac{r}{100}\right)$. The formula applies the decrease multiplier to the original value to find the new amount.

4. What is the multiplier for increasing a value by $r\%$?

   $1+\frac{r}{100}$. Adding the decimal form of the percentage to 1 gives the factor by which the original value grows.

5. What is the final price after a $25\%$ discount on $80$ dollars?

   $60$. Multiplying $80$ by the $25\%$ discount factor of $0.75$ gives the discounted price.

6. What is the percent increase from $40$ to $50$?

   $25\%$. The change of $10$ divided by the original $40$ equals $0.25$, or $25\%$.

7. What is the price before a $15\%$ discount if the sale price is $85$ dollars?

   $100$. Dividing $85$ by the remaining factor of $0.85$ after a $15\%$ discount recovers the original price.

8. What is the original value if the new value is $84$ after a $20\%$ decrease?

   $105$. Dividing $84$ by the remaining factor of $0.8$ after a $20\%$ decrease recovers the original.

9. Identify the multiplier for a $10\%$ decrease.

   $0.90$. Converting $10\%$ to $0.10$ and subtracting from $1$ yields the reduction factor.

10. Identify the percent increase from $60$ to $75$.

    $25\%$. The change of $15$ divided by the original $60$ equals $0.25$, or $25\%$.

11. What is the percent change from $30$ to $45$ (include the sign)?

    $+50\%$. The change of $15$ divided by the original $30$ equals $0.5$, or $+50\%$.

12. What is the percent decrease from $80$ to $60$?

    $25\%$. The change of $-20$ divided by the original $80$ equals $-0.25$, so a $25\%$ decrease.

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

    $\frac{N-O}{O}\times 100\%$. The formula computes the relative change by dividing the difference by the original value and converting to a percentage.

14. What is the percent change from $50$ to $40$ (include the sign)?

    $-20\%$. The change of $-10$ divided by the original $50$ equals $-0.2$, or $-20\%$.

15. What percent of the original remains after a $35\%$ decrease?

    $65\%$. Subtracting $35\%$ from $100\%$ leaves the portion of the original that remains.

16. What is the new value when $200$ is decreased by $30\%$?

    $140$. Multiplying $200$ by the $30\%$ decrease multiplier of $0.7$ gives the new value.

17. State the formula for the new value after a percent increase of $r\%$ from original $O$.

    $N=O\left(1+\frac{r}{100}\right)$. The formula applies the increase multiplier to the original value to find the new amount.

18. What percent of the original is the new value after a $12\%$ increase?

    $112\%$. Adding $12\%$ to $100\%$ gives the new value as a percentage of the original.

19. What is the multiplier for decreasing a value by $r\%$?

    $1-\frac{r}{100}$. Subtracting the decimal form of the percentage from 1 gives the factor by which the original value shrinks.

20. What is the original value if the new value is $132$ after a $10\%$ increase?

    $120$. Dividing $132$ by the growth factor of $1.1$ after a $10\%$ increase recovers the original.

21. Identify the multiplier for a $10\%$ increase.

    $1.10$. Converting $10\%$ to $0.10$ and adding to $1$ yields the growth factor.

22. Identify the multiplier for a $25\%$ decrease.

    $0.75$. Converting $25\%$ to $0.25$ and subtracting from $1$ yields the reduction factor.

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