# GRE Math : How to evaluate algebraic expressions

## Example Questions

### Example Question #71 : How To Evaluate Algebraic Expressions

For any integer

Quantity A:

Quantity B:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Explanation:

To solve this problem, use the property  to evaluate each quantity:

Quantity A:

Quantity B:

Quantity A is greater.

### Example Question #72 : Evaluating Expressions

Jason can run  miles in  hours. How many miles will Jason run in  minutes?

Explanation:

First, create an expression for Jason's running speed. If he runs  miles in  hours, his speed is

Now convert the time spent running to hours  minutes:

Now to find the distance travelled, mutiply his speed by the time spent running:

### Example Question #73 : Evaluating Expressions

For any pair of numbers  and .

What is  ?

Explanation:

To solve this problem, utilize the property , starting with the terms in the parenthesis:

### Example Question #391 : Gre Quantitative Reasoning

For two numbers  and  . What is  ?

Explanation:

To solve this problem, use the  starting with the term in the parenthesis:

### Example Question #75 : Evaluating Expressions

Quantity A:

Quantity B:

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined.

The relationship cannot be determined.

Explanation:

Consider the condtions we're given:

Because neither of these are zero,

Now we must consider the signs of each variable.

Looking at

We know that as a square, , even if the sign of  is unknown.

This means that  as well. Although the signs of  and  are unknown, we know that they must share the same sign.

Now consider

So , meaning  and  have opposite signs. However, since we cannot make a definite statement about either, the signs remain unknown.

The relationship cannot be determined.

### Example Question #76 : Evaluating Expressions

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:

Consider the parameters

Since these are not zero,

Looking at

Squares of non-zero real values are positive, so

This means that

Now consider

Again,

This means that

Since

It must mean that

Quantity A is greater.

### Example Question #77 : Evaluating Expressions

Quantity A:

Quantity B:

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Quantity A is greater.

Explanation:

To solve this problem, solve for  and

We have the system of equations

Rewrite them so that the variables are on one side of the equation and the numbers are on the other:

Now, subtract the bottom equation from the top equation:

Plut this value back into the bottom equation:

Now consider the quantities:

Quantity A:

Quantity B:

Quantity A is greater.

### Example Question #391 : Algebra

Quantity A:

Quantity B:

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Quantity A is greater.

Explanation:

This problem essentially requires finding the value of Quantity A.

Do not trouble yourself with finding the individual values of  and .

Rather, multiply out the terms:

We're told that , therefore

Quantity A is greater.

### Example Question #79 : Evaluating Expressions

Take the expression  to be equivalent to the expression . What does the expression  represent?

Explanation:

To approach tihs problem, note that if   is equivalent to the expression , then

Let's replace that complex function with a single variable:

Now we can rewrite as

Now plug in the value for

### Example Question #80 : Evaluating Expressions

If the sum of two consecutive even integers is  and the difference of their squares is , what is the smaller integer?

Explanation:

In this problem we're given two pieces of information; however, consider how much we need to utilize.

We're told that the sum of two consecutive even integers is . Writing that in mathematical terms:

The two integers are  and .

Note that we could confirm this with the other piece of information regarding the difference of squares:

However, there is no need to do this; it's better to save time by only utilizing as much information is needed.

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