SSAT (Secondary School Admission Test) Quantitative Reasoning: Number Sense and Arithmetic Flashcards

24 sample cards from the Quantitative Reasoning: Number Sense and Arithmetic deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. What is the formula to find a percent of a number, and what is $30\%$ of $80$?

   Percent of a number $=$ (percent as a decimal) $\times$ number. $0.30 \times 80 = 24$.

2. How do you find what percent one number is of another, e.g. what percent is $15$ of $60$?

   Divide the part by the whole and multiply by $100$: $\frac{15}{60}\times 100 = 25\%$.

3. How do you calculate percent increase or percent decrease?

   $\text{percent change} = \dfrac{\text{amount of change}}{\text{original amount}} \times 100\%$. Example: from $40$ to $50$ is $\frac{10}{40}\times 100\% = 25\%$ increase.

4. What is a ratio, and what are the three common ways to write the ratio of $3$ to $5$?

   A ratio compares two quantities. It can be written as $3:5$, as $3 \text{ to } 5$, or as the fraction $\frac{3}{5}$.

5. How do you simplify the ratio $18:24$?

   Divide both terms by their GCF ($6$): $18:24 = 3:4$.

6. What is a proportion, and what method solves it?

   A proportion states two ratios are equal, $\frac{a}{b}=\frac{c}{d}$. Solve by cross-multiplication: $a\cdot d = b\cdot c$.

7. Solve the proportion $\frac{x}{12} = \frac{3}{4}$.

   Cross-multiply: $4x = 36$, so $x = 9$.

8. What is a unit rate, and what is the unit rate for $150$ miles in $3$ hours?

   A unit rate is a rate with a denominator of $1$. $\frac{150 \text{ miles}}{3 \text{ hours}} = 50$ miles per hour.

9. How do you use unit pricing to find the better buy between two package sizes?

   Divide the price by the quantity for each option to get the price per unit, then choose the lower unit price. Example: $\$4$ for $2$ lb is $\$2/\text{lb}$; $\$9$ for $5$ lb is $\$1.80/\text{lb}$, so the $5$ lb is the better buy.

10. State the relationship among speed, distance, and time.

    $\text{distance} = \text{speed} \times \text{time}$, which rearranges to $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ and $\text{time} = \dfrac{\text{distance}}{\text{speed}}$.

11. A car travels $180$ miles at $60$ mph. How long does the trip take?

    $\text{time} = \dfrac{\text{distance}}{\text{speed}} = \dfrac{180}{60} = 3$ hours.

12. What is a scale (or scale factor) in a scale drawing or map?

    It is the ratio of a length in the drawing to the corresponding actual length, e.g. $1 \text{ inch} : 50 \text{ miles}$, telling how much the real object has been reduced or enlarged.

13. On a map with scale $1 \text{ inch} = 25$ miles, how far apart are two cities that are $4$ inches apart?

    Set up a proportion: $\frac{1}{25}=\frac{4}{x}$, so $x = 100$ miles.

14. State the product and quotient rules for exponents with the same base.

    Product: $a^{m}\cdot a^{n} = a^{m+n}$. Quotient: $\dfrac{a^{m}}{a^{n}} = a^{m-n}$.

15. State the power-of-a-power rule and the value of any nonzero base raised to the zero power.

    Power of a power: $(a^{m})^{n} = a^{mn}$. Zero exponent: $a^{0} = 1$ for any $a \neq 0$.

16. What does a negative exponent mean, e.g. $2^{-3}$?

    A negative exponent means the reciprocal of the positive power: $2^{-3} = \dfrac{1}{2^{3}} = \dfrac{1}{8}$.

17. What is a square root, and what is $\sqrt{49}$?

    A square root of a number is a value that, when multiplied by itself, gives that number. $\sqrt{49} = 7$ because $7^{2} = 49$.

18. List the perfect squares from $1$ to $144$.

    $1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144$ (the squares of $1$ through $12$).

19. Between which two consecutive whole numbers does $\sqrt{50}$ lie?

    Between $7$ and $8$, because $7^{2}=49$ and $8^{2}=64$, and $50$ is between them (closer to $7$).

20. How do you simplify $\sqrt{72}$?

    Factor out the largest perfect square: $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36}\,\sqrt{2} = 6\sqrt{2}$.

21. What is a cube root, and what is $\sqrt[3]{27}$?

    A cube root of a number is a value that, multiplied by itself three times, gives that number. $\sqrt[3]{27} = 3$ because $3^{3} = 27$.

22. List the perfect cubes from $1$ to $125$.

    $1, 8, 27, 64, 125$ (the cubes of $1, 2, 3, 4, 5$).

23. Evaluate $\sqrt[3]{-64}$ and explain why a cube root of a negative number is defined.

    $\sqrt[3]{-64} = -4$ because $(-4)^{3} = -64$. Odd roots of negative numbers are real because an odd number of negative factors stays negative.

24. What does the index $n$ in the radical $\sqrt[n]{x}$ tell you, and what is $\sqrt[4]{81}$?

    The index $n$ tells which root to take (what power gives $x$). $\sqrt[4]{81} = 3$ because $3^{4} = 81$.

What this deck covers

Quantitative Reasoning: Number Sense and Arithmetic flashcards FAQ