### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #11 : Absolute Value

, , and are distinct integers. and . Which of the following could be the least of the three?

**Possible Answers:**

or only

or only

or only

, , or

None of the other responses is correct.

**Correct answer:**

None of the other responses is correct.

, so must be positive. Therefore, since , it follows that , so must be positive, and

If is negative or zero, it is the least of the three. If is positive, then the statement becomes

,

and is still the least of the three. Therefore, *must* be the least of the three, and the correct choice is "None of the other responses is correct."

### Example Question #11 : How To Find Absolute Value

Give the solution set:

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #12 : How To Find Absolute Value

Solve the following expression for when .

**Possible Answers:**

**Correct answer:**

First you plug in for and squre it.

This gives the expression which is equal to .

Since the equation is within the absolute value lines, you must make it the absolute value which is the amount of places the number is from zero.

This makes your answer .

### Example Question #11 : Absolute Value

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

The absolute value of a number is its distance from zero. Absolute value is represented with or absolute value bars . To solve this absolute value equation remove the absolute value bars and set the equation equal to positive and negative eleven.

and are the two values of which make this statement true.

and

Remember, because Absolute Value measures the distance from zero, the absolute value of a number whether negative or positive is* always* non-negative.

### Example Question #41 : Algebra

**Possible Answers:**

There is no solution.

**Correct answer:**

Absolute value measures distance from that number to the point of origin or zero.

However, there is a negative sign outside the Absolute value bars, which indicates the multiplication by

becomes

Therefore is the correct solution.

### Example Question #41 : Ssat Upper Level Quantitative (Math)

**Possible Answers:**

**Correct answer:**

The first step to solving is to use the Order of Operations.

The absolute value of a real number x is the non-negative value of x without regard to its sign. The absolute value of a number is the distance of that number from the point of origin or zero on a number line.

### Example Question #21 : How To Find Absolute Value

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

To solve this Absolute Value inequality, remove the Absolute Value bars and create two linear inequalities.

Then, using the Order of Operations and the method for solving multi-step equations solve.

First inequality:

Second inequality:

The solution to consists of the two intervals and . This pair of inequalities is the solution.

### Example Question #22 : How To Find Absolute Value

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

To solve this Absolute Value inequality, remove the Absolute Value bars and create two linear inequalities.

and

Then solve each of the inequalities.

First inequality:

Second inequality:

The solution to consists of the two intervals and . This pair of inequalities is the solution.

### Example Question #42 : Ssat Upper Level Quantitative (Math)

**Possible Answers:**

and

and

and

and

**Correct answer:**

and

To solve this Absolute value inequality, remove the absolute value bars and create two linear inequalities and solve.

The solution to consists of the two intervals and .

This pair of inequalities is the solution.

### Example Question #43 : Ssat Upper Level Quantitative (Math)

**Possible Answers:**

**Correct answer:**

Step One: Order of Operations

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