# GRE Math : Evaluating Expressions

## Example Questions

### Example Question #381 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

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 #382 : Algebra

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

Possible Answers:

Correct answer:

Explanation:

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 #383 : Algebra

For any integer , let

Quantity A:

Quantity B:

Possible Answers:

Quantity B is greater.

The relationship cannot be determined.

Quantity A is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

Follow the condition given, namely  to evaluate each quantity:

Quantity A:

Quantity B:

Quantity B is greater.

### Example Question #384 : Algebra

For any positive integer

Quantity A:

Quantity B:

Possible Answers:

The relationship cannot be determined.

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

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

Quantity A:

Quantity B:

Quantity B is greater.

### Example Question #385 : Algebra

For any positive integer

Quantity A:

Quantity B:

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

Quantity A is greater.

Explanation:

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

Quantity A:

Quantity B:

Quantity A is greater.

### Example Question #386 : Algebra

For any integer

Quantity A:

Quantity B:

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

Correct answer:

The two quantities are equal.

Explanation:

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

Quantity A:

Quantity B:

The two quantities are equal.

### Example Question #387 : Algebra

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:

Explanation:

For group problems, we may use the group equation:

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

### Example Question #388 : Algebra

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:

Explanation:

For group problems, we may use the group equation:

### Example Question #389 : Algebra

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:

Explanation:

For group problems, we may use the group equation:

### Example Question #390 : Algebra

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:

Explanation:

For group problems, we may use the group equation:

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