### All GRE Math Resources

## Example Questions

### Example Question #1 : Number Line

The range of the earnings for architecture graduates is , and the range of the salaries for engineering graduates is .

Which of the following statements individually provide(s) sufficient additional information to determine the range of the salaries of all graduates between the two professions?

**A**: The median salary for the engineers is greater than that of the architects.

**B**: The average (arithmetic mean) of the engineers is greater than that of the architects.

**C**: The lowest salary of the engineers is less than the lowest of the architects.

**Possible Answers:**

B only

A and C only

A, B, and C

A only

C only

**Correct answer:**

C only

The provision of the bottom-end of the engineering range is the only additional information that provides us a fixed endpoint from which we can build off of by supplementing with the ranges provided in the question, to give us the full range between both engineering and achitecture graduates. See the diagram provided to understand how this can be done.

Even if the mean and medians were provided, these additional values give us no information on the endpoints of the salaries, and the question only asks for the range.

### Example Question #2 : How To Find Value With A Number Line

What's the distance between and on a number line?

**Possible Answers:**

**Correct answer:**

Let's draw a number line.

Since a number line is straight and contains the numbers consecutively, we just subtract from to get .

### Example Question #3 : How To Find Value With A Number Line

Which of the following answer best fits in the picture below?

**Possible Answers:**

**Correct answer:**

Open circles mean the values are excluded from the set.

The number line shows the set is between and exclusive.

The only value in that set would be .

### Example Question #4 : How To Find Value With A Number Line

If , then where on the number line lies ?

**Possible Answers:**

**Correct answer:**

Because a number line contains both positive and negative integers, we need to consider both possibilities.

is and that value is the same as . Therefore we eliminate the choice because will always be greater than those values raised to the power.

Next is . We elminate both the positive and negative range of . If we look at the difference between and , it's over .

Then, we should guess that will definitely be greater than so therefore answer is .

Remember, a negative value raised to an even power will always have a positive value.

### Example Question #51 : Integers

If perimeter of equilateral triangle is , what is the height of the triangle?

**Possible Answers:**

**Correct answer:**

Since perimeter of equilateral triangle is and we have three equal sides, we just divide that vaue by to get . To find height, we can set-up a proportion.

The height is opposite the angle . Side opposite is and the side of equilateral triangle which is opposite is .

Cross multiply.

Divide both sides by

Let's simplify by factoring out to get a final answer of .

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