SSAT Upper Level Math : Number Concepts and Operations

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

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Example Questions

Example Question #3 : Decimals With Fractions

Let \displaystyle a = \frac{3}{5}\displaystyle b= \frac{2}{3}\displaystyle c = \frac{4}{7}

Which of the following is closest to \displaystyle a + b + c ?

Possible Answers:

\displaystyle 1.6

\displaystyle 1.9

\displaystyle 1.7

\displaystyle 1.5

\displaystyle 1.8

Correct answer:

\displaystyle 1.8

Explanation:

\displaystyle a + b + c

\displaystyle = \frac{3}{5}+ \frac{2}{3}+ \frac{4}{7}

\displaystyle = \frac{3 \times 21}{5 \times 21}+ \frac{2\times 35}{3 \times 35}+ \frac{4\times 15}{7 \times 15}

\displaystyle = \frac{63}{105}+ \frac{70}{105}+ \frac{60}{105} = \frac{193}{105}

\displaystyle = 193 \div 105 \approx 1.84

The correct choice is 1.8.

Example Question #7 : Decimals With Fractions

Let \displaystyle a =3 \frac{3}{5} and \displaystyle b=1 \frac{5}{6}

Which of the following is closest to \displaystyle a - b ?

Possible Answers:

\displaystyle 1.6

\displaystyle 1.4

\displaystyle 1.5

\displaystyle 1.7

\displaystyle 1.8

Correct answer:

\displaystyle 1.8

Explanation:

\displaystyle a - b = 3\frac{3}{5} - 1\frac{5}{6}

\displaystyle = \frac{18}{5} - \frac{11}{6}

\displaystyle = \frac{18\times 6 }{5 \times 6} - \frac{11\times 5}{6\times 5}

\displaystyle = \frac{108}{30} - \frac{55}{30}

\displaystyle = \frac{53}{30}

\displaystyle = 53 \div 30 \approx 1.77

The correct choice is 1.8.

 

Example Question #241 : Rational Numbers

Define an operation  as follows:

For all real numbers \displaystyle a,b:

 

Which of the following is closest to  ?

Possible Answers:

\displaystyle 0.3

\displaystyle 0.2

\displaystyle 0.1

\displaystyle 0.15

\displaystyle 0.25

Correct answer:

\displaystyle 0.15

Explanation:

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

The correct choice is 0.15.

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

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

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

Possible Answers:

\displaystyle 1

\displaystyle 1.3

\displaystyle 1.4

\displaystyle 1.2

\displaystyle 1.1

Correct answer:

\displaystyle 1

Explanation:

\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.

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

Simplify and express as a decimal:

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

Possible Answers:

\displaystyle 0.875

\displaystyle 0.9

\displaystyle 0.8

\displaystyle 0.8\overline{3}

\displaystyle 0.\overline{8}

Correct answer:

\displaystyle 0.8\overline{3}

Explanation:

\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}

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

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

Example Question #11 : Decimals With Fractions

Define an operation  as follows:

For all real numbers \displaystyle a,b:

 

Which of the following is equal to  ?

Possible Answers:

\displaystyle 0.25

The correct answer is not among the other choices.

\displaystyle 0.\overline{2}

\displaystyle 0.2

\displaystyle 0.1\overline{6}

Correct answer:

\displaystyle 0.2

Explanation:

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

is the correct response.

Example Question #301 : Number Concepts And Operations

Which of the following is a true statement?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Divide 7 by 13. The result is as follows:

Division

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

Example Question #302 : Number Concepts And Operations

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

Possible Answers:

\displaystyle 1.5

\displaystyle 1.4

\displaystyle 1.6

\displaystyle 1.45

\displaystyle 1.55

Correct answer:

\displaystyle 1.45

Explanation:

\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.

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

Which of the following is a true statement?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Divide 19 by 27:

Division

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

so

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

Example Question #13 : Decimals With Fractions

Which of the following falls between 0.32 and 0.33?

Possible Answers:

\displaystyle \frac{25}{77}

\displaystyle \frac{23}{77}

\displaystyle \frac{26}{77}

\displaystyle \frac{27}{77}

\displaystyle \frac{24}{77}

Correct answer:

\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

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

Multiply each expression by \displaystyle 77:

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

\displaystyle 24.64 < N < 25.41

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

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