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SSAT Upper Level Math : Number Concepts and Operations

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Number Concepts And Operations

Define a function as follows:

$g(x)=\left | x^{5}-x^{2}\right |$

Evaluate g(2) - g(-2) .

Possible Answers:

Correct answer:

Explanation:

$g(x)=\left | x^{5}-x^{2}\right |$

$g(2)=\left | 2^{5}-2^{2}\right | = \left | 32-4\right | = \left | 28\right | = 28$

$g(-2)=\left |( -2)^{5}-\left (-2 \right )^{2}\right | = \left | -32-4\right | = \left | -36\right | = 36$

g(2) - g(-2) = 28 - 36 = -8

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Example Question #5 : How To Subtract

Define a function as follows:

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

Evaluate f(-1) .

Possible Answers:

The correct answer is not among the other responses.

The expression is undefined.

Correct answer:

Explanation:

$f(x) = 10 - \sqrt[3]{x} - \sqrt[5]{x}$

$f(-1) = 10 - \sqrt[3]{-1} - \sqrt[5]{-1} = 10 - (-1)- (-1)= 10+1+1 = 12$

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Example Question #21 : Basic Addition, Subtraction, Multiplication And Division

Define a function on the real numbers as follows:

$f(x) = 100 -\left ( \sqrt{x} - \sqrt[4]{x} \right )$

Evaluate f(-1) .

Possible Answers:

The correct answer is not among the other responses.

The expression is undefined.

100

102

Correct answer:

The expression is undefined.

Explanation:

$f(x) = 100 -\left ( \sqrt{x} - \sqrt[4]{x} \right )$

$f(-1) = 100 -\left ( \sqrt{-1} - \sqrt[4]{-1} \right )$

Since even-numbered roots of negative numbers are not defined for real-valued functions, the expression is undefined.

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Example Question #11 : How To Subtract

Define an operation $\bigtriangleup$ on the real numbers as follows:

For all real numbers a, b :

$a \bigtriangleup b = \sqrt[3]{a} - \sqrt[4]{b}$ .

Evaluate $(-1) \bigtriangleup (-1)$ .

Possible Answers:

The expression is undefined on the real numbers.

Correct answer:

The expression is undefined on the real numbers.

Explanation:

$a \bigtriangleup b = \sqrt[3]{a} - \sqrt[4]{b}$

$(-1) \bigtriangleup (-1) = \sqrt[3]{-1} - \sqrt[4]{-1}$

However, $\sqrt[4]{-1}$ is undefined in the real numbers; subsequently, so is $(-1) \bigtriangleup (-1)$ .

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Example Question #1 : How To Multiply

$\dpi{100} \frac{\frac{1}{2}\times \frac{1}{3}}{\frac{1}{9}}=$

Possible Answers:

$\dpi{100} \frac{1}{9}$

$\dpi{100} \frac{3}{2}$

$\dpi{100} \frac{1}{54}$

$\dpi{100} \frac{2}{3}$

Correct answer:

$\dpi{100} \frac{3}{2}$

Explanation:

First multiply the fraction in the numerator.

$\dpi{100} \frac{1}{2}\times \frac{1}{3}=\frac{1\times 1}{2\times 3}=\frac{1}{6}$

Now we have $\dpi{100} \frac{\frac{1}{6}}{\frac{1}{9}}$

Never divide fractions. We multiply the numerator by the reciprocal of the denominator.

$\dpi{100} \frac{\frac{1}{6}}{\frac{1}{9}}=\frac{1}{6}\div \frac{1}{9}=\frac{1}{6}\times \frac{9}{1}=\frac{1\times 9}{6\times 1}=\frac{9}{6}=\frac{3}{2}$

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Example Question #2 : How To Multiply

Which of these expressions is the greatest?

Possible Answers:

All of these expressions are equivalent

One fourth of 0.2

Twenty percent of one fourth

Twenty-five percent of one fifth

One fifth of 0.25

Correct answer:

All of these expressions are equivalent

Explanation:

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to 0.2 , and twenty-five percent and one fourth are equal to 0.25 .

One fourth of 0.2: $\frac{1}{4}*0.2=\frac{1}{4}*\frac{2}{10}=\frac{2}{40}=\frac{1}{20}$

One fifth of 0.25: $\frac{1}{5}*0.25=\frac{1}{5}*\frac{25}{100}=\frac{25}{500}=\frac{5}{100}=\frac{1}{20}$

Twenty-five percent of one fifth: $*\frac{1}{5}=\frac{25}{100}*\frac{1}{5}=\frac{25}{500}=\frac{1}{20}$

Twenty percent of one fourth: $*\frac{1}{4}=\frac{20}{100}*\frac{1}{4}=\frac{20}{400}=\frac{1}{20}$

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Example Question #3 : How To Multiply

Write .007341 in scientific notation.

Possible Answers:

$7.341\times10^{-1}$

$7.341\times10^{^{-3}}$

$7.341\times10^{^{3}}$

$73.41\times10^{^{-2}}$

$7.341\times10^{-2}$

Correct answer:

$7.341\times10^{^{-3}}$

Explanation:

The answer is $7.341\times10^{^{-3}}$ .

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Example Question #4 : How To Multiply

If X, Y, Z are consecutive negative numbers, which of the following is false?

Possible Answers:

$\left ( xyz^{}\right )^{2}>0$

xyz<0

xyz>0

x+y+z<0

xy>0

Correct answer:

xyz>0

Explanation:

When three negative numbers are multiplied together, the product will be negative as well. All the other expressions are true.

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Example Question #3 : How To Multiply

Fill in the circle to yield a true statement:

$5 \times \bigcirc \equiv 3 \mod 6$

Possible Answers:

Correct answer:

Explanation:

The problem is asking for a number whose product with 5 yields a number congruent to 3 in modulo 6 arithmetic - that is, a number which, when divided by 6, yields remainder 3. We multiply 5 by each choice and look for a product with this characteristic.

$5 \times 1 = 5$ ; $5 \div 6 = 0 \textrm{ R } 5$

$5 \times 2 = 10$ ; $10 \div 6 = 1 \textrm{ R } 4$

$5 \times 3= 15$ ; $15 \div 6 = 2 \textrm{ R } 3$

$5 \times 4=20$ ; $20 \div 6 = 3 \textrm{ R } 2$

$5 \times 5 = 25$ ; $25 \div 6 = 4 \textrm{ R } 1$

The only choice whose product with 5 yields a number congruent to 3 modulo 6 is 3, so this is the correct choice.

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Example Question #6 : How To Multiply

You are asked to fill in all three circles in the statement

$\bigcirc \times \bigcirc \times \bigcirc \equiv 9 \mod 10$

with the same number from the set

$\left \{ 0, 1, 2, 3,...9\right \}$

to make a true statement.

How many ways can you do this?

Possible Answers:

Five

One

Three

Four

Two

Correct answer:

One

Explanation:

The problem is asking for a number whose cube is a number congruent to 9 in modulo 10 arithmetic - that is, a number whose cube, when divided by 10, yields remainder 9. If the quotient of a number and 10 has remainder 9, then it is an integer that ends with the digit "9". Since this makes the cube odd, the number that is cubed must also be odd, so we need only test the five odd integers:

$1 ^{3} = 1$

$3^{3}= 27$

$5^{3} = 125$

$7 ^{3} = 343$

$9^{3} = 729$

Only 9 fits the criterion, so "one" is the correct response.

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #31 : Number Concepts And Operations

Example Question #5 : How To Subtract

Example Question #21 : Basic Addition, Subtraction, Multiplication And Division

Example Question #11 : How To Subtract

Example Question #1 : How To Multiply

Example Question #2 : How To Multiply

Example Question #3 : How To Multiply

Example Question #4 : How To Multiply

Example Question #3 : How To Multiply

Example Question #6 : How To Multiply

All SSAT Upper Level Math Resources

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