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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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Example Questions

Example Question #241 : Rational Numbers

Define an operation $\blacklozenge$ $\displaystyle \blacklozenge$ as follows:

For all real numbers a,b $\displaystyle a,b$:

$a\blacklozenge b = a^{2} - b^{2}$ $\displaystyle a\blacklozenge b = a^{2} - b^{2}$

Which of the following is closest to $\frac{1}{2} \blacklozenge \frac{1}{3}$ $\displaystyle \frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Possible Answers:

0.3 $\displaystyle 0.3$

0.2 $\displaystyle 0.2$

0.1 $\displaystyle 0.1$

0.15 $\displaystyle 0.15$

0.25 $\displaystyle 0.25$

Correct answer:

0.15 $\displaystyle 0.15$

Explanation:

$a\blacklozenge b = a^{2} - b^{2}$ $\displaystyle a\blacklozenge b = a^{2} - b^{2}$

$\frac{1}{2} \blacklozenge \frac{1}{3} =\left ( \frac{1}{2} \right ) ^{2} - \left ( \frac{1}{3} \right )^{2}= \frac{1}{4} - \frac{1}{9}= \frac{9}{36} - \frac{4}{36}= \frac{5}{36}$ $\displaystyle \frac{1}{2} \blacklozenge \frac{1}{3} =\left ( \frac{1}{2} \right ) ^{2} - \left ( \frac{1}{3} \right )^{2}= \frac{1}{4} - \frac{1}{9}= \frac{9}{36} - \frac{4}{36}= \frac{5}{36}$

$= 5 \div 36 = 0.13888...$ $\displaystyle = 5 \div 36 = 0.13888...$

The correct choice is 0.15.

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Example Question #1371 : Ssat Upper Level Quantitative (Math)

Let $a =1 \frac{4}{9}$ $\displaystyle a =1 \frac{4}{9}$, $b = 1\frac{3}{8}$ $\displaystyle b = 1\frac{3}{8}$, and $c= \frac{1}{2}$ $\displaystyle c= \frac{1}{2}$.

Which of the following is closest to a bc $\displaystyle a bc$ ?

Possible Answers:

$\displaystyle 1$

1.3 $\displaystyle 1.3$

1.4 $\displaystyle 1.4$

1.2 $\displaystyle 1.2$

1.1 $\displaystyle 1.1$

Correct answer:

$\displaystyle 1$

Explanation:

$a bc=1 \frac{4}{9} \times 1\frac{3}{8} \times \frac{1}{2}= \frac{13}{9} \times \frac{11}{8} \times \frac{1}{2}= \frac{143}{144}= 143 \div 144 \approx 0.99$ $\displaystyle a bc=1 \frac{4}{9} \times 1\frac{3}{8} \times \frac{1}{2}= \frac{13}{9} \times \frac{11}{8} \times \frac{1}{2}= \frac{143}{144}= 143 \div 144 \approx 0.99$

The correct response is 1.

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Example Question #4 : Decimals With Fractions

Simplify and express as a decimal:

$\frac{4\frac{2}{3}}{5\frac{3}{5}}$ $\displaystyle \frac{4\frac{2}{3}}{5\frac{3}{5}}$

Possible Answers:

$0.\overline{8}$ $\displaystyle 0.\overline{8}$

0.8 $\displaystyle 0.8$

$0.8\overline{3}$ $\displaystyle 0.8\overline{3}$

0.875 $\displaystyle 0.875$

0.9 $\displaystyle 0.9$

Correct answer:

$0.8\overline{3}$ $\displaystyle 0.8\overline{3}$

Explanation:

$\frac{4\frac{2}{3}}{5\frac{3}{5}} = 4\frac{2}{3} \div 5\frac{3}{5} = \frac{14}{3} \div \frac{28}{5} = \frac{14}{3} \times \frac{5} {28} = \frac{1}{3} \times \frac{5} {2} = \frac{5}{6}$ $\displaystyle \frac{4\frac{2}{3}}{5\frac{3}{5}} = 4\frac{2}{3} \div 5\frac{3}{5} = \frac{14}{3} \div \frac{28}{5} = \frac{14}{3} \times \frac{5} {28} = \frac{1}{3} \times \frac{5} {2} = \frac{5}{6}$

$\frac{5}{6}= 5 \div 6 = 0.8333...$ $\displaystyle \frac{5}{6}= 5 \div 6 = 0.8333...$,

so the correct response is $0.8\overline{3}$ $\displaystyle 0.8\overline{3}$.

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Example Question #11 : Decimals With Fractions

Define an operation $\blacklozenge$ $\displaystyle \blacklozenge$ as follows:

For all real numbers a,b $\displaystyle a,b$:

$a\blacklozenge b = \frac{ab}{a+b}$ $\displaystyle a\blacklozenge b = \frac{ab}{a+b}$

Which of the following is equal to $\frac{1}{2} \blacklozenge \frac{1}{3}$ $\displaystyle \frac{1}{2} \blacklozenge \frac{1}{3}$ ?

Possible Answers:

0.25 $\displaystyle 0.25$

The correct answer is not among the other choices.

$0.\overline{2}$ $\displaystyle 0.\overline{2}$

0.2 $\displaystyle 0.2$

$0.1\overline{6}$ $\displaystyle 0.1\overline{6}$

Correct answer:

0.2 $\displaystyle 0.2$

Explanation:

$a\blacklozenge b = \frac{ab}{a+b}$ $\displaystyle a\blacklozenge b = \frac{ab}{a+b}$

$\frac{1}{2} \blacklozenge \frac{1}{3}=\frac{\frac{1}{2} \times \frac{1}{3}}{\frac{1}{2} +\frac{1}{3}}=\frac{\frac{1}{6} }{\frac{5}{6} } = \frac{1}{6} \div \frac{5}{6} = \frac{1}{6} \times \frac{6} {5} = \frac{1}{1} \times \frac{1} {5} = \frac{1}{5}$ $\displaystyle \frac{1}{2} \blacklozenge \frac{1}{3}=\frac{\frac{1}{2} \times \frac{1}{3}}{\frac{1}{2} +\frac{1}{3}}=\frac{\frac{1}{6} }{\frac{5}{6} } = \frac{1}{6} \div \frac{5}{6} = \frac{1}{6} \times \frac{6} {5} = \frac{1}{1} \times \frac{1} {5} = \frac{1}{5}$

$\frac{1}{5} = 1 \div 5 = 0.2$ $\displaystyle \frac{1}{5} = 1 \div 5 = 0.2$,

is the correct response.

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Example Question #1371 : Ssat Upper Level Quantitative (Math)

Which of the following is a true statement?

Possible Answers:

$0.54 < \frac{7}{13} < 0.55$ $\displaystyle 0.54 < \frac{7}{13} < 0.55$

$0.55 < \frac{7}{13} < 0.56$ $\displaystyle 0.55 < \frac{7}{13} < 0.56$

$0.52 < \frac{7}{13} < 0.53$ $\displaystyle 0.52 < \frac{7}{13} < 0.53$

$0.56 < \frac{7}{13} < 0.57$ $\displaystyle 0.56 < \frac{7}{13} < 0.57$

$0.53 < \frac{7}{13} < 0.54$ $\displaystyle 0.53 < \frac{7}{13} < 0.54$

Correct answer:

$0.53 < \frac{7}{13} < 0.54$ $\displaystyle 0.53 < \frac{7}{13} < 0.54$

Explanation:

Divide 7 by 13. The result is as follows:

Division

The correct choice is that $0.53 < \frac{7}{13} < 0.54$ $\displaystyle 0.53 < \frac{7}{13} < 0.54$.

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Example Question #1372 : Ssat Upper Level Quantitative (Math)

Which of the following is closest to the sum of two thirds and four fifths?

Possible Answers:

1.6 $\displaystyle 1.6$

1.55 $\displaystyle 1.55$

1.45 $\displaystyle 1.45$

1.4 $\displaystyle 1.4$

1.5 $\displaystyle 1.5$

Correct answer:

1.45 $\displaystyle 1.45$

Explanation:

$\frac{2}{3} + \frac{4}{5} = \frac{2 \cdot 5}{3\cdot 5} + \frac{3\cdot 4}{3\cdot 5} = \frac{10}{15} + \frac{12}{15} =\frac{22}{15}$ $\displaystyle \frac{2}{3} + \frac{4}{5} = \frac{2 \cdot 5}{3\cdot 5} + \frac{3\cdot 4}{3\cdot 5} = \frac{10}{15} + \frac{12}{15} =\frac{22}{15}$

Divide 22 by 15:

Division

Of the five choices, the closest is 1.45.

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Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Which of the following is a true statement?

Possible Answers:

$-0.72< -\frac{19}{27}< -0.71$ $\displaystyle -0.72< -\frac{19}{27}< -0.71$

$-0.73< -\frac{19}{27}< -0.72$ $\displaystyle -0.73< -\frac{19}{27}< -0.72$

$-0.75< -\frac{19}{27}< -0.74$ $\displaystyle -0.75< -\frac{19}{27}< -0.74$

$-0.71< -\frac{19}{27}< -0.70$ $\displaystyle -0.71< -\frac{19}{27}< -0.70$

$-0.74< -\frac{19}{27}< -0.73$ $\displaystyle -0.74< -\frac{19}{27}< -0.73$

Correct answer:

$-0.71< -\frac{19}{27}< -0.70$ $\displaystyle -0.71< -\frac{19}{27}< -0.70$

Explanation:

Divide 19 by 27:

Division

$0.70 < \frac{19}{27}< 0.71$ $\displaystyle 0.70 < \frac{19}{27}< 0.71$,

$-0.71< -\frac{19}{27}< -0.70$ $\displaystyle -0.71< -\frac{19}{27}< -0.70$.

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Example Question #13 : Decimals With Fractions

Which of the following falls between 0.32 and 0.33?

Possible Answers:

$\frac{25}{77}$ $\displaystyle \frac{25}{77}$

$\frac{23}{77}$ $\displaystyle \frac{23}{77}$

$\frac{26}{77}$ $\displaystyle \frac{26}{77}$

$\frac{27}{77}$ $\displaystyle \frac{27}{77}$

$\frac{24}{77}$ $\displaystyle \frac{24}{77}$

Correct answer:

$\frac{25}{77}$ $\displaystyle \frac{25}{77}$

Explanation:

Since all of the fractions have 77 as a denominator, one way to solve this problem is to let $\displaystyle N$ be the numerator of the correct fraction. Therefore, the equivalent problem is to find integer $\displaystyle N$ such that

$0.32 < \frac{N}{77} < 0.33$ $\displaystyle 0.32 < \frac{N}{77} < 0.33$

Multiply each expression by $\displaystyle 77$:

$0.32 \cdot 77 < \frac{N}{77} \cdot 77 < 0.33 \cdot 77$ $\displaystyle 0.32 \cdot 77 < \frac{N}{77} \cdot 77 < 0.33 \cdot 77$

$\displaystyle 24.64 < N < 25.41$

Therefore, N = 25 $\displaystyle N = 25$, making $\frac{25}{77}$ $\displaystyle \frac{25}{77}$ the correct choice.

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Example Question #1373 : Ssat Upper Level Quantitative (Math)

Which of the following fractions is closest to 0.6?

Possible Answers:

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

$\frac{9}{16}$ $\displaystyle \frac{9}{16}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

$\frac{13}{20}$ $\displaystyle \frac{13}{20}$

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

Correct answer:

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$

Explanation:

For each fraction, divide each numerator by its denominator to get its decimal representation, then subtract to find its difference from 0.6.

$\frac{4}{7} \approx 0.5714 ; 0.6 - 0.5714 =0.0286$ $\displaystyle \frac{4}{7} \approx 0.5714 ; 0.6 - 0.5714 =0.0286$

$\frac{5}{8}=0.625; 0.625-0.6 = 0.025$ $\displaystyle \frac{5}{8}=0.625; 0.625-0.6 = 0.025$

$\frac{9}{16} = 0.5625; 0.6-0.5625=0.0375$ $\displaystyle \frac{9}{16} = 0.5625; 0.6-0.5625=0.0375$

$\frac{2}{3}\approx 0.6667; 0.6667-0.6=0.0667$ $\displaystyle \frac{2}{3}\approx 0.6667; 0.6667-0.6=0.0667$

$\frac{13}{20} = 0.65; 0.65-0.6=0.05$ $\displaystyle \frac{13}{20} = 0.65; 0.65-0.6=0.05$

$\frac{5}{8}$ $\displaystyle \frac{5}{8}$ is the closest to 0.6 of the five.

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Example Question #1374 : Ssat Upper Level Quantitative (Math)

Give the decimal equivalent of $\frac{1}{6}$ $\displaystyle \frac{1}{6}$.

Possible Answers:

0.16 $\displaystyle 0.16$

$0.\overline{16}$ $\displaystyle 0.\overline{16}$

$0.1\overline{6}$ $\displaystyle 0.1\overline{6}$

0.167 $\displaystyle 0.167$

0.166 $\displaystyle 0.166$

Correct answer:

$0.1\overline{6}$ $\displaystyle 0.1\overline{6}$

Explanation:

Divide 1 by 6; the result is

$\frac{1}{6}= 1 \div 6 = 0.166666...$ $\displaystyle \frac{1}{6}= 1 \div 6 = 0.166666...$ .

That is, the 6 is repeated infinitely. This is equal to $0.1\overline{6}$ $\displaystyle 0.1\overline{6}$.

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #241 : Rational Numbers

Example Question #1371 : Ssat Upper Level Quantitative (Math)

Example Question #4 : Decimals With Fractions

Example Question #11 : Decimals With Fractions

Example Question #1371 : Ssat Upper Level Quantitative (Math)

Example Question #1372 : Ssat Upper Level Quantitative (Math)

Example Question #11 : How To Find The Decimal Equivalent Of A Fraction

Example Question #13 : Decimals With Fractions

Example Question #1373 : Ssat Upper Level Quantitative (Math)

Example Question #1374 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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