### All GRE Math Resources

## Example Questions

### Example Question #1 : Linear / Rational / Variable Equations

Quantity A:

Quantity B: 11

**Possible Answers:**

The two quantities are equal.

Quantity A is greater

Quantity B is greater

The relationship cannot be determined.

**Correct answer:**

Quantity B is greater

Expand out into .

Since , it can be seen that

so Quantity B is greater.

### Example Question #11 : Equations / Inequalities

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are the same.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

**Correct answer:**

Quantity A is greater.

To solve this problem, expand each function described by Quantities A and B:

Quantity A:

Quantity B:

Now note that Quantities A and B only differ in that Quantity A is greater by .

Since we are told that is greater than and thus always positive, Quantity A must be greater than Quantity B for all possible values of .

### Example Question #12 : Equations / Inequalities

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

**Correct answer:**

Quantity A is greater.

Rather than manually finding common denominators and adding the fractions together, realize that

Since

Quantity A must be greater, and this can be seen without actually calculating its value.

### Example Question #13 : Equations / Inequalities

Approximately, what was the percent growth of Beetleton's GDP from 2009 to 2010?

**Possible Answers:**

**Correct answer:**

Percent growth is given as:

For Beetleton, this can be expressed as (in terms of billions of US dollars):

### Example Question #14 : Equations / Inequalities

The sum of two integers is . The larger integer is greater than the smaller integer. What is the positive difference between the two?

**Possible Answers:**

**Correct answer:**

Let us write down what we are told in mathematical terms, designating the smaller integer as and the larger integer as .

The sum of the two integers is :

And the larger integer is % greater than the smaller integer:

Writing the first equation in terms of gives:

Which allows us to find :

Thus, the positive difference between the two is found as

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

**Possible Answers:**

–1

–2

1

2

0

**Correct answer:**

2

### Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

**Possible Answers:**

–*b*/(*m*^{2 }– 1)

*–bm*/(*m*^{2 }+ 1)

*bm*/(*m*^{2 }+ 1)

*–b*/(*m *+ 1)

*b*/(*m*^{2 }+ 1)

**Correct answer:**

*b*/(*m*^{2 }+ 1)

### Example Question #17 : Equations / Inequalities

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

**Possible Answers:**

**Correct answer:**

### Example Question #18 : Equations / Inequalities

Four less than three times a certain number is equivalent to five plus four times this same number. What is three less than three times this number?

**Possible Answers:**

The answer cannot be determined from the information given.

**Correct answer:**

The key to solving this problem is deciphering the language and translating it into a numerical representation. The first part can be written as an equaltiy as follows:

Rearranging terms allows us to solve for this mystery number:

From there we can address the problem's question:

### Example Question #19 : Equations / Inequalities

The arithmetic mean of , , , and is 14.

Quantity A: 32

Quantity B: The arithmetic mean of and

**Possible Answers:**

Quantity B is greater.

Quantity A and Quantity B are equal.

Quantity A is greater.

The relationship between Quantity A and Quantity B cannot be determined.

**Correct answer:**

Quantity A and Quantity B are equal.

The definition of an arithmetic mean of a set of values is given as the sum of all the values divided by the total count of values:

Where represents the value in a set, and is the number of values in the set.

Quantity B can thus be defined as follows:

Which simplifies to:

or, simplifying:

We are told that the mean of , , , and is 14, which can be written as:

and then as

Plugging this value into our definition of Quantity B, we can find its numerical value:

So