# GMAT Math : Understanding absolute value

## Example Questions

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### Example Question #31 : Understanding Absolute Value  If , then how many possible values of are there?

Zero

Four

Two

Three

One

Two

Explanation: can be rewritten as  , so .

If , then , or, equivalently, either or .

Solve separately:  or   , so the above two statements can be rewritten as and  has no solution, since the absolute value of a number cannot be negative. can be rewritten as and It is not necessary to solve these statements, as we can determine that the correct response is two solutions.

### Example Question #32 : Absolute Value

Solve for        Explanation:

To solve absolute value equations, we must set up two equations: one where the solution is negative, and one where the solution is positive.       ### Example Question #33 : Absolute Value

True or false: is a positive number.

Statement 1: Statement 2: STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

Explanation:

Assume Statement 1 alone. can be rewritten as   Therefore, is positive.

Assume Statement 2 alone. The sign of cannot be determined. For example, if , which is positive, then .

If , which is not positive, then .

### Example Question #34 : Absolute Value  How many values of make a true statement?

Four

Two

Three

One

None

Two

Explanation: , so we want the number of values of for which . , so Therefore, if , then    Either , in which case , or , in which case .

The correct choice is therefore two.

### Example Question #35 : Absolute Value  How many values of make a true statement?

Two

None

One

Three

Four

None

Explanation: , so we want the number of values of for which   , so either or If the first equation is true, then  and .

If the second equation is true, then  and .

In each situation, the absolute value of an expression would be negative; since the absolute value of an expression cannot be negative, no solution is yielded.

There are no values of that make true; the correct response is zero.

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