### All GMAT Math Resources

## Example Questions

### Example Question #152 : Algebra

What value must take in order for the following expression to be greater than zero?

**Possible Answers:**

**Correct answer:**

is such that:

Add to each side of the inequality:

Multiply each side of the inequality by :

Multiply each side of the inequality by :

Divide each side of the inequality by :

You can now change the fraction on the right side of the inequality to decimal form.

The correct answer is , since k has to be less than for the expression to be greater than zero.

### Example Question #361 : Arithmetic

**Possible Answers:**

**Correct answer:**

In order to add these fractions, we must first find a common denominator for all three. Looking at our three different denominators, we can see that their lowest common denominator is 12. Therefore, we need to rewrite each fraction with a denominator of 12:

Now that the fractions all have a common denominator, we can simply add them together and then simplify the result, recognizing that 27 and 12 have a common factor of 3:

### Example Question #11 : Fractions

Which of the following is less than ?

**Possible Answers:**

**Correct answer:**

In order to determine which fractions are less than , it's best to convert them to decimals and compare:

Therefore, is the only choice that is less than .

### Example Question #362 : Arithmetic

Define an operation as follows:

For all real numbers ,

Evaluate .

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

### Example Question #12 : Fractions

Casius has of a liter of water. Olivar has of the amount Casius has. How many liters of water does Olivar have?

**Possible Answers:**

**Correct answer:**

This question tests your ability to read word problems and multiply fractions. Because we know that Olivar has of what Casius has, we can see that we need to multiply. Perform the following operation to find the answer.

### Example Question #11 : Fractions

Define an operation as follows:

For all real numbers ,

Evaluate , and round to the nearest whole number.

**Possible Answers:**

**Correct answer:**

This rounds to 3.

### Example Question #11 : Fractions

Seven thirds of eighteen seventieths is what?

**Possible Answers:**

Seven sixths

Five thirds

Seven fifths

Three sevenths

Three fifths

**Correct answer:**

Three fifths

Seven thirds of eighteen seventieths is

### Example Question #14 : Fractions

One orange yields cup of juice; one gallon is equal to 16 cups. How many oranges are needed to yield one half gallon of orange juice?

**Possible Answers:**

**Correct answer:**

One half gallon comprises 8 cups. To find the number of oranges needed, divide:

### Example Question #11 : Fractions

Raise to the fourth power and express the result in lowest terms.

**Possible Answers:**

**Correct answer:**

reduces to . Raise this to the fourth power:

### Example Question #18 : Fractions

Evaluate:

**Possible Answers:**

**Correct answer:**

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