Percent Increase and Decrease - ISEE Upper Level Quantitative Reasoning

1. What is the percent change from $30$ to $45$?

   $50\%$. The change of $15$ relative to the original $30$ results in a $50\%$ increase.

2. What is the final value after multiplying $150$ by a $0.9$ factor (a $10\%$ decrease)?

   $135$. The factor $0.9$ reduces the original value by $10\%$, yielding the new amount.

3. Identify the net percent change for a decrease of $20\%$ followed by an increase of $25\%$.

   $0\%$. The combined multipliers $0.8$ and $1.25$ yield $1.00$, resulting in no net change.

4. What is the original value if a $20\%$ increase gives a new value of $96$?

   $80$. Dividing $96$ by $1.2$ reverses the $20\%$ increase to find the original value.

5. What is the new value after increasing $120$ by $15\%$?

   $138$. Multiplying $120$ by the factor $1.15$ accounts for the $15\%$ increase.

6. State the formula for the percent change from original $O$ to new $N$.

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

7. What is the new value after decreasing $200$ by $12\%$?

   $176$. Multiplying $200$ by the factor $0.88$ accounts for the $12\%$ decrease.

8. Identify the multiplier for a $p\%$ decrease (in terms of $p$).

   $1-\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the decreased amount.

9. What is the percent decrease from $60$ to $45$?

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

10. What is the percent change from $50$ to $40$?

    $-20\%$. The change of $-10$ relative to the original $50$ results in a $-20\%$ change.

11. What is the percent of the original remaining after a $p\%$ decrease?

    $(100-p)\%$. The remaining portion after subtracting $p\%$ from $100\%$ of the original.

12. Identify the multiplier for a $p\%$ increase (in terms of $p$).

    $1+\frac{p}{100}$. Represents the factor by which the original value is multiplied to achieve the increased amount.

13. What is the overall multiplier for successive changes of $+a\%$ then $+b\%$?

    $\left(1+\frac{a}{100}\right)\left(1+\frac{b}{100}\right)$. Combines the individual growth factors for each successive percentage increase.

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

    $25\%$. The difference of $20$ divided by the original $80$ yields $0.25$, or $25\%$.

15. What is the percent increase from $45$ to $60$?

    $\frac{100}{3}\%$. The difference of $15$ divided by the original $45$ yields $\frac{1}{3}$, or $\frac{100}{3}\%$.

16. What is the original value if a $25\%$ decrease gives a new value of $75$?

    $100$. Dividing $75$ by $0.75$ reverses the $25\%$ decrease to find the original value.

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

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

18. State the formula for the new value after a $p\%$ increase of original $O$.

    $N=O\left(1+\frac{p}{100}\right)$. Applies the growth factor by multiplying the original value by 1 plus the percentage increase divided by 100.

19. What is the percent of the original after a $p\%$ increase?

    $(100+p)\%$. The increased portion by adding $p\%$ to $100\%$ of the original.

20. State the formula for the new value after a $p\%$ decrease of original $O$.

    $N=O\left(1-\frac{p}{100}\right)$. Applies the reduction factor by multiplying the original value by 1 minus the percentage decrease divided by 100.

21. What percent decrease is needed to go from $100$ to $80$?

    $20\%$. The difference of $20$ divided by the original $100$ yields $0.2$, or $20\%$.

22. What percent increase is needed to go from $80$ to $100$?

    $25\%$. The difference of $20$ divided by the original $80$ yields $0.25$, or $25\%$.

23. What is the new value after decreasing $90$ by $\frac{1}{3}$?

    $60$. Decreasing by $\frac{1}{3}$ means multiplying by $\frac{2}{3}$, yielding $60$.

24. Identify the net percent change for an increase of $10\%$ followed by a decrease of $10\%$.

    $-1\%$. The combined multipliers $1.1$ and $0.9$ yield $0.99$, equivalent to a $-1\%$ net change.

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