GMAT Math : Algebra

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #431 : Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, we need to combine like terms and then factor:

Example Question #432 : Algebra

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve this we must factor:

The first step is to recognize that all of the terms on the equation's left side contain 4x. Therefore we can pull 4x out:

Then we factor the inside of the parentheses, realizing that only -3, and -4 add to form -7, and multiply to form 12:

Now we can see that, for the left side of the equation to equal zero, x can only equal 0, 3, or 4.

Example Question #431 : Algebra

Solve the following by factoring:

Possible Answers:

Correct answer:

Explanation:

To solve, divide out a  and then factor.

Example Question #432 : Algebra

Simplify .

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Absolute Value

Solve \left | 3x - 7 \right |=8.

Possible Answers:

 or

or

 or

Correct answer:

or

Explanation:

\left | 3x - 7 \right |=8 really consists of two equations: 3x - 7 = \pm 8

We must solve them both to find two possible solutions.

3x - 7 = 8 \Rightarrow 3x = 15\Rightarrow x = 5

3x - 7 = - 8 \Rightarrow 3x = -1\Rightarrow x = -1/3

So  or  .

Example Question #2 : Absolute Value

Solve \left | 2x - 5 \right |\geq 3.

Possible Answers:

1 < x < 4

-2 \leq x\leq 5

x \leq 1, x\geq 4

x \leq -1, x\geq -4

x < 1, x > 4

Correct answer:

x \leq 1, x\geq 4

Explanation:

It's actually easier to solve for the complement first.  Let's solve \left | 2x-5 \right |<3.  That gives -3 < 2x - 5 < 3.  Add 5 to get 2 < 2x < 8, and divide by 2 to get 1 < x < 4.  To find the real solution then, we take the opposites of the two inequality signs.  Then our answer becomes x\leq 1 \textsc{ or } x\geq 4.

Example Question #3 : Absolute Value

Give the -intercept(s), if any, of the graph of the function  in terms of 

Possible Answers:

Correct answer:

Explanation:

Set  and solve for :

 

Rewrite as a compound equation and solve each part separately:

 

 

 

Example Question #4 : Absolute Value

A number is ten less than its own absolute value. What is this number?

Possible Answers:

No such number exists.

Correct answer:

Explanation:

We can rewrite this as an equation, where  is the number in question:

A nonnegative number is equal to its own absolute value, so if this number exists, it must be negative.

In thsi case, , and we can rewrite that equation as

This is the only number that fits the criterion.

Example Question #1 : Understanding Absolute Value

If , which of the following has the greatest absolute value?

Possible Answers:

Correct answer:

Explanation:

Since , we know the following:  

 ;

;

;

;

.

Also, we need to compare absolute values, so the greatest one must be either  or .

We also know that  when .

Thus, we know for sure that .

 

Example Question #6 : Absolute Value

Give all numbers that are twenty less than twice their own absolute value.

Possible Answers:

No such number exists.

Correct answer:

Explanation:

We can rewrite this as an equation, where  is the number in question:

If  is nonnegative, then , and we can rewrite this as 

Solve:

 

If  is negative, then , and we can rewrite this as 

 

The numbers  have the given characteristics.

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