### All GMAT Math Resources

## Example Questions

### Example Question #11 : Solving Inequalities

What is the lowest value the integer can take?

**Possible Answers:**

**Correct answer:**

The lowest value n can take is 6.

### Example Question #111 : Algebra

What value of will make the following expression negative:

**Possible Answers:**

**Correct answer:**

Our first step is to simplify the expression. We need to remember our order of operations or PEMDAS.

First distribute the 0.4 to the binomial.

Now distribute the 10 to the binomial.

Now multiply 0.6 by 5

Remember to flip the sign of the inequation when multiplying or dividing by a negative number.

220 will make the expression negative.

### Example Question #12 : Inequalities

Solve for .

**Possible Answers:**

**Correct answer:**

To solve this problem all we need to do is solve for :

### Example Question #121 : Algebra

What value of satisfies both of the following inequalities?

**Possible Answers:**

**Correct answer:**

Solve for in both inequalities:

(1)

Subtract 9 from each side of the inequality:

Then, divide by . Remember to switch the direction of the sign from "less than or equal to" to "greater than or equal to."

(2)

Add to both sides of the inequality:

Subtract 7 from each side of the inequality:

Divide each side of the inequality by 3:

From solving both inequalities, we find such that:

Only is in that interval .

and are less than 1.33, so they are not in the interval.

and are more than 2, so they are not in the interval.

### Example Question #1 : How To Find The Solution To An Inequality With Division

Which of the following could be a value of , given the following inequality?

**Possible Answers:**

**Correct answer:**

The inequality that is presented in the problem is:

Start by moving your variables to one side of the inequality and all other numbers to the other side:

Divide both sides of the equation by . Remember to flip the direction of the inequality's sign since you are dividing by a negative number!

Reduce:

The only answer choice with a value greater than is .

### Example Question #14 : Inequalities

If and are two integers, which of the following inequalities would be true?

**Possible Answers:**

**Correct answer:**

First let's solve each of the inequalities:

Don't forget to flip the direction of the sign when dividing by a negative number:

is the correct answer. is an integer greater than 3 and is greater than 9. Therefore, the sum of and is greater than 12.

is not true. and are two positive integers as is greater than 3 and is greater than 9. The sum of two positive integers cannot be a negative number.

is not true. and are two positive integers as is greater than 3 and is greater than 9. The division of two positive numbers is positive and therefore cannot be less than 0.

is not true. is greater than 3 and is greater than 9. The product of and cannot be less than 3.

is not true. and are positive. Therefore, the product of and is negative and cannot be greater than 0.

### Example Question #123 : Algebra

If an integer satisfies both of the above inequalities, which of the following is true about ?

**Possible Answers:**

**Correct answer:**

First, we solve both inequalities:

If satisfies both inequalities, then is greater than 5 AND is greater than 11. Therefore is greater than 11.

is the correct answer.

### Example Question #124 : Algebra

Solve the following inequality:

**Possible Answers:**

**Correct answer:**

We start by simplifying our inequality like any other equation:

Now we must remember that when we divide by a negative, the inequality is flipped, so we obtain:

### Example Question #125 : Algebra

Solve the following inequality:

**Possible Answers:**

**Correct answer:**

Solving inequalities is very similar to solving equations, but we need to remember an important rule:

If we multiply or divide by a negative number, we must switch the direction of the inequality. So a "greater than" sign will become a "less than" sign and vice versa.

We are given

Start by moving the and the over:

Simplify to get the following:

Then, we will divide both sides of the equation by . Remember to switch the direction of the inequality sign!

So,

### Example Question #11 : Solving Inequalities

and . If the greatest number of the three, then what are the possible values of ?

**Possible Answers:**

**Correct answer:**

The question is equivalent to asking when and are both true statements.

We can solve for in the first equation:

Now use substitution to solve the inequality

Therefore, if and only if .

Similarly, we can solve for in the first equation:

Now use substitution to solve the inequality

Therefore, if and only if .

We combine these results, and conclude that *both * and hold - that is, is the greatest of the three - if and only if .