Absolute Value

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SSAT Upper Level Quantitative › Absolute Value

Questions 1 - 10

Evaluate: $\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}$

Explanation

$\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}=\begin{vmatrix}; ; \left | 5- 12\right |-8 \right ;\end{vmatrix}=\begin{vmatrix}; ; \left | -7\right |-8 \right ;\end{vmatrix}=| 7 - 8| = | -1| = 1$

Evaluate: $\begin{vmatrix}; ; \left | 5- 3 \cdot 4\right |-8 \right ;\end{vmatrix}$

Explanation

$-\left |-8- 2 (5-2)^{2} \right |$

Explanation

Step One: Order of Operations

$-\left |-8 - 2 x 3^{2} \right |$

$-\left | -8-2x9\right |$

$-\left | -8-18\right |$

$-\left | -26\right |$

The absolute value of is However, because there is a negative sign outside the Absolute value bars, you would multiply the by to get the solution.

The correct answer is

Which of the following sentences is represented by the equation

The absolute value of the sum of a number and seven is three less than the number.

The absolute value of the sum of a number and seven is three greater than the number.

The sum of three and the absolute value of the sum of a number is three greater than the number.

The sum of three and the absolute value of the sum of a number is three less than the number.

None of the other responses are correct.

Explanation

is the absolute value of , which in turn is the sum of a number and seven and a number. Therefore, can be written as "the absolute value of the sum of a number and seven". Since it is equal to , it is three less than the number, so the equation that corresponds to the sentence is

"The absolute value of the sum of a number and seven is three less than the number."

Give the solution set:

Explanation

When dealing with absolute value bars, it is important to understand that whatever is inside of the absolute value bars can be negative or positive. This means that an inequality can be made.

In this particular case if , then, equivalently,

From here, isolate the variable by adding seven to each side.

In interval notation, this is .

$-\left |-8- 2 (5-2)^{2} \right |$

Explanation

Step One: Order of Operations

$-\left |-8 - 2 x 3^{2} \right |$

$-\left | -8-2x9\right |$

$-\left | -8-18\right |$

$-\left | -26\right |$

The absolute value of is However, because there is a negative sign outside the Absolute value bars, you would multiply the by to get the solution.

The correct answer is

Give the solution set:

$(-\infty, -11) \cup (23, \infty)$

$(-\infty, -23) \cup (23, \infty)$

$(-\infty,-23 ) \cup (11, \infty)$

$(-\infty, -11) \cup (11, \infty)$

$(-\infty,-23 ) \cup (-11, \infty)$

Explanation

If , then either or . Solve separately:

The solution set, in interval notation, is $(-\infty, -11) \cup (23, \infty)$ .

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

If , then $a \bigstar b = |a + b-1|$

If , then $a \bigstar b = 4$

If , then $a \bigstar b = |a - b+1|$

If $p = 0 \bigstar 5$ , $q = 0 \bigstar 0$ , and $r=0 \bigstar( -5)$

then which of the following is a true statement?

Explanation

$p = 0 \bigstar 5$

Since , evaluate

$a \bigstar b = |a - b+1|$ , setting :

$0 \bigstar 5 = |0 - 5+1|$

$0 \bigstar 5 = |-4| = 4$

$q = 0 \bigstar 0$

Since , then select the pattern

$0 \bigstar 0 = 4$

$r=0 \bigstar( -5)$

Since , evaluate

$a \bigstar b = |a + b-1|$ , setting :

$0 \bigstar (-5) = |0 + (-5)-1|$

$0 \bigstar (-5) = |-6| = 6$

, so the correct choice is that .

Which of the following sentences is represented by the equation

The absolute value of the sum of a number and seven is three less than the number.

The absolute value of the sum of a number and seven is three greater than the number.

The sum of three and the absolute value of the sum of a number is three greater than the number.

The sum of three and the absolute value of the sum of a number is three less than the number.

None of the other responses are correct.

Explanation

"The absolute value of the sum of a number and seven is three less than the number."

Give the solution set:

Explanation

When dealing with absolute value bars, it is important to understand that whatever is inside of the absolute value bars can be negative or positive. This means that an inequality can be made.

In this particular case if , then, equivalently,

From here, isolate the variable by adding seven to each side.

In interval notation, this is .

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