All GMAT Math Resources
Example Questions
Example Question #465 : Algebra
If , then how many possible values of are there?
Four
Zero
Two
One
Three
Two
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 #31 : Absolute Value
Solve for :
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 #467 : Algebra
True or false: is a positive number.
Statement 1:
Statement 2:
BOTH STATEMENTS TOGETHER do 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.
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.
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.
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 #461 : Algebra
How many values of make
a true statement?
None
Two
One
Four
Three
Two
, 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 #469 : Algebra
How many values of make
a true statement?
Three
None
Four
Two
One
None
, 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.