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SSAT Upper Level Math : Basic Addition, Subtraction, Multiplication and Division

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 #1 : How To Subtract

$\dpi{100} 4593-1296=$

Possible Answers:

$\dpi{100} 3497$

$\dpi{100} 3397$

$\dpi{100} 3297$

$\dpi{100} 497$

Correct answer:

$\dpi{100} 3297$

Explanation:

Subtract the two numbers, being careful not to forget to remove the borrowed number.

You can also add the solution back to 1296 to check your work, as addition is easier than subtraction.

$\dpi{100} 1296+3297=4593$

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Example Question #2 : How To Subtract

$\dpi{100} 4.8-\frac{9}{2}$

Possible Answers:

$\dpi{100} 0.3$

$\dpi{100} \frac{5}{2}$

$\dpi{100} -5.2$

$\dpi{100} 2$

Correct answer:

$\dpi{100} 0.3$

Explanation:

First convert $\dpi{100} \frac{9}{2}$ into a decimal.

$\dpi{100} 9\div 2=4\ remainder\ of\ 1$

So we are left with $\dpi{100} 4\frac{1}{2}$ , which is 4.5 in decimal form.

Now subtract:

$\dpi{100} 4.8-4.5=0.3$

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Example Question #3 : How To Subtract

Subtract $\left ( 2a-3b+7c\right )$ from $\left ( 5a-4b-3c\right )$

Possible Answers:

-3a+b+10c

7a+b+4c

3a-7b+4c

7a-7b+4c

3a-b-10c

Correct answer:

3a-b-10c

Explanation:

You set up the expression with $\left ( 5a-4b-3c\right )$ on the top and $\left ( 2a-3b+7c\right )$ on the bottom. Because this is subtraction, remember to distribute the negative sign to the expression on the bottom, and then add, so

you get 3a-b-10c .

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Example Question #21 : Number Concepts And Operations

and are prime integers. 65 < K < 75 and 45 < L < 55 .

How many possible values of K - L are there?

Possible Answers:

Four

Eight

Seven

Six

Five

Correct answer:

Five

Explanation:

The prime integers between 65 and 75 are 67, 71, and 73, so assumes one of those values; the prime integers between 45 and 55 are 47 and 53, so assumes one of those values. Therefore, one of the following holds true:

K - L = 73 - 53 = 20

K - L = 73 - 47 = 26

K - L = 71 - 53 = 18

K - L = 71 - 47 = 24

K - L = 67 - 53 = 14

K - L = 67 - 47 = 20

There are five possible values for K - L (20 appears twice here).

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Example Question #5 : How To Subtract

and are prime integers. 55< K < 65 and 85 < L < 95 . What is the greatest possible value of L - K ?

Possible Answers:

Correct answer:

Explanation:

The greatest possible value of L - K is the least possible value of subtracted from the greatest possible value of . The least prime between 55 and 65 is 59, and the greatest prime between 85 and 95 is 89, so L = 89 and K = 59 give the greatest possible value of L - K , which is equal to 89-59 = 30

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Example Question #22 : Number Concepts And Operations

Define an operation $\Upsilon$ as follows:

For all real numbers a, b ,

$a \Upsilon b = a^{5} - b^{4}$ .

Evaluate: $\frac{1}{2}\; \Upsilon\; \frac{1}{2}$ .

Possible Answers:

$-\frac{1}{32}$

$-\frac{1}{16}$

$\frac{1}{16}$

$\frac{1}{32}$

Correct answer:

$-\frac{1}{32}$

Explanation:

$a \Upsilon b = a^{5} - b^{4}$

$\frac{1}{2}\; \Upsilon\; \frac{1}{2} =\left ( \frac{1}{2} \right )^{5} - \left ( \frac {1}{2} \right )^{4}$

$= \frac{1}{32} - \frac{1}{16}$

$= \frac{1}{32} - \frac{2}{32}$

$= -\frac{1}{32}$

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Example Question #7 : How To Subtract

Define a function as follows:

$g(x)=\left | x^{2} - \frac{1}{x^{2}}\right |$

Evaluate $g(2) - g \left ( \frac{1}{2} \right )$ .

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

$7\frac{1}{2}$

$-7\frac{1}{2}$

Correct answer:

Explanation:

$g(x)=\left | x^{2} - \frac{1}{x^{2}}\right |$

$g(2)=\left | 2^{2} - \frac{1}{2^{2}}\right | = \left | 4- \frac{1}{4}\right | = \left | 3 \frac{3}{4}\right |= 3 \frac{3}{4}$

$g\left ( \frac{1}{2} \right )=\left | \left ( \frac{1}{2} \right )^{2} - \frac{1}{\left ( \frac{1}{2} \right )^{2}}\right | = \left | \frac{1}{4}- \frac{1}{ \frac{1}{4}} \right | = \left | 3 \frac{3}{4}\right | = \left | \frac{1}{4}- 4 \right | = \left | - 3 \frac{3}{4} \right | = 3 \frac{3}{4}$

$g(2) - g \left ( \frac{1}{2} \right ) = 3 \frac{3}{4} - 3 \frac{3}{4} = 0$

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Example Question #6 : How To Subtract

Define an operation $\forall$ as follows:

For all real numbers a ,b :

$a \forall b = a^{4} + \frac{1}{b^{4}}$ .

Evaluate $\frac{1}{2} \forall (-2 )$ .

Possible Answers:

The correct answer is not among the other responses.

$-15\frac{15}{16}$

$\frac{1}{8}$

$16\frac{1}{16}$

Correct answer:

$\frac{1}{8}$

Explanation:

$a \forall b = a^{4} + \frac{1}{b^{4}}$

$\frac{1}{2} \forall (-2 ) = \left (\frac{1}{2} \right )^{4} + \frac{1}{(-2)^{4}}= \frac{1}{16} + \frac{1}{16} = \frac{2}{16} = \frac{1}{8}$

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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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Basic Addition, Subtraction, Multiplication and Division

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Subtract

Example Question #2 : How To Subtract

Example Question #3 : How To Subtract

Example Question #21 : Number Concepts And Operations

Example Question #5 : How To Subtract

Example Question #22 : Number Concepts And Operations

Example Question #7 : How To Subtract

Example Question #6 : How To Subtract

Example Question #31 : Number Concepts And Operations

Example Question #5 : How To Subtract

All SSAT Upper Level Math Resources

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