# SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

## Example Questions

### Example Question #1 : How To Find Absolute Value

Define an operation  as follows:

For all real numbers ,

Evaluate: .

None of the other responses is correct.

The expression is undefined.

Explanation:

, or, equivalently,

### Example Question #1 : How To Find Absolute Value

Define .

Evaluate .

Explanation:

, or, equivalently,

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

Define an operation  as follows:

For all real numbers ,

Evaluate .

Explanation:

Define .

Evaluate .

Explanation:

### Example Question #61 : New Sat Math No Calculator

Define an operation  as follows:

For all real numbers ,

Evaluate

Both  and

Explanation:

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

Given:  are distinct integers such that:

Which of the following could be the least of the three?

, or

or  only

or  only

or  only

only

or  only

Explanation:

, which means that  must be positive.

If  is nonnegative, then . If  is negative, then it follows that . Either way, . Therefore,  cannot be the least.

We now show that we cannot eliminate  or  as the least.

For example, if , then  is the least;  we test both statements:

, which is true.

, which is also true.

If , then  is the least; we test both statements:

, which is true.

, which is also true.

Therefore, the correct response is  or  only.

### Example Question #11 : Absolute Value

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

only

only

None of the other responses is correct.

, or

only

only

Explanation:

, so  must be positive. Therefore, since , equivalently, , 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 greatest of the three.

### Example Question #32 : Algebra

Give the solution set:

Explanation:

If , then either  or . Solve separately:

or

The solution set, in interval notation, is .

### Example Question #12 : Absolute Value

Define an operation  on the real numbers as follows:

If , then

If , then

If , then

If , and

then which of the following is a true statement?

Explanation:

Since , evaluate

, setting  :

Since , then select the pattern

Since , evaluate

, setting :

, so the correct choice is that .

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

Given:  are distinct integers such that:

Which of the following could be the least of the three?

or  only

only

only

, or

only

only

Explanation:

, which means that  must be positive.

If  is nonnegative, then . If  is negative, then it follows that . Either way, . Therefore,  cannot be the least.

Now examine the statemtn . If , then  - but we are given that  and  are distinct. Therefore,  is nonzero, , and

and

.

cannot be the least either.