### All GRE Math Resources

## Example Questions

### Example Question #61 : How To Evaluate Algebraic Expressions

When the integer is increased by , the result is less than times the integer . What is ?

**Possible Answers:**

**Correct answer:**

The trick for this problem is to translate "When the integer is increased by , the result is less than times the integer ." into mathematical terms. Let's do it piece by piece:

When the integer :

When the integer is increased by :

When the integer is increased by , the result is:

When the integer is increased by , the result is less than:

When the integer is increased by , the result is less than times the integer :

Now that we have this, solve for

Now plug this value in for the problem question:

### Example Question #62 : How To Evaluate Algebraic Expressions

When the integer is mulitplied by , the result is greater than the product of and the integer . What is ?

**Possible Answers:**

**Correct answer:**

To solve this problem, translate "When the integer is mulitplied by , the result is greater than the product of and the integer " into mathematical terms. Step-by-step it is:

When the integer :

When the integer is mulitplied by :

When the integer is mulitplied by , the result is:

When the integer is mulitplied by , the result is greater than:

When the integer is mulitplied by , the result is greater than the product:

When the integer is mulitplied by , the result is greater than the product of and the integer :

Now, solve for

Now, plug this value into the problem question:

### Example Question #61 : Evaluating Expressions

For any integer , let

Quantity A:

Quantity B:

**Possible Answers:**

Quantity A is greater.

The two quantities are equal.

The relationship cannot be determined.

Quantity B is greater.

**Correct answer:**

Quantity B is greater.

Follow the condition given, namely to evaluate each quantity:

Quantity A:

Quantity B:

Quantity B is greater.

### Example Question #64 : How To Evaluate Algebraic Expressions

For any positive integer ,

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

**Correct answer:**

Quantity B is greater.

To solve this problem, follow the operation given for each quantity:

,

Quantity A:

Quantity B:

Quantity B is greater.

### Example Question #65 : How To Evaluate Algebraic Expressions

For any positive integer ,

Quantity A:

Quantity B:

**Possible Answers:**

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

**Correct answer:**

Quantity A is greater.

To perform this problem, simply perform the operation , for each quantity:

Quantity A:

Quantity B:

Quantity A is greater.

### Example Question #62 : Evaluating Expressions

For any integer ,

Quantity A:

Quantity B:

**Possible Answers:**

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

**Correct answer:**

The two quantities are equal.

To solve this problem, evaluate each quantity using the property :

Quantity A:

Quantity B:

The two quantities are equal.

### Example Question #67 : How To Evaluate Algebraic Expressions

A counselor found that in a group of students, were taking a foreign language, were taking math, and were taking neither. How many students were taking both?

**Possible Answers:**

**Correct answer:**

For group problems, we may use the group equation:

Our unknown value is the number of students in both groups:

### Example Question #65 : How To Evaluate Algebraic Expressions

In a group of employees, can use the cash register, can use the price gun, and can use both. How many employees cannot use either?

**Possible Answers:**

**Correct answer:**

For group problems, we may use the group equation:

### Example Question #69 : How To Evaluate Algebraic Expressions

In a group of artists, are able to use traditional media, can use both traditional and digital media, and cannot use either (they work with novel and untraditional methods.) How many artists can only use digital media?

**Possible Answers:**

**Correct answer:**

For group problems, we may use the group equation:

### Example Question #70 : How To Evaluate Algebraic Expressions

In a group of high school athletes, can play baseball, can play soccer, and can play neither (playing American football instead). How many athletes can play both baseball and soccer?

**Possible Answers:**

**Correct answer:**

For group problems, we may use the group equation: