# GRE Math : GRE Quantitative Reasoning

## Example Questions

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

Quantity A:

Quantity B: 11

The two quantities are equal.

Quantity A is greater

Quantity B is greater

The relationship cannot be determined.

Quantity B is greater

Explanation:

Expand  out into .

Since , it can be seen that

so Quantity B is greater.

### Example Question #11 : Equations / Inequalities

Quantity A:

Quantity B:

The two quantities are the same.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

Quantity A is greater.

Explanation:

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:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Quantity A is greater.

Explanation:

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?

Explanation:

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?

Explanation:

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

–1

–2

1

2

0

2

Explanation:

b/(m– 1)

–bm/(m+ 1)

bm/(m+ 1)

–b/(+ 1)

b/(m+ 1)

b/(m+ 1)

Explanation:

### Example Question #17 : Equations / Inequalities

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

Explanation:

### 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?

The answer cannot be determined from the information given.

Explanation:

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

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.

Quantity A and Quantity B are equal.

Explanation:

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

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