# Math Review Sheet

The following things are the fundamentals on which the Quantitative section of the GMAT is built. You'll want to print this out and make several copies of it to prepare for your exam. Plan on going through it at least five times before taking the CAT. When you finish, click here for the answers. Good luck on your test!

- Circles
- Perfect Squares
- Odds and Evens
- Least Common Multiples
- Common Percent Equivalencies
- Distance Problems (Distance, Rate & Time)
- Triangles (30-60-90, 45-45-90, 3-4-5, 5-12-13)
- Prime Numbers
- Work Problems
- Percent Problems
- Number Properties
- Probability
- Inequalities
- Averages
- Divisibility Rules
- Ratios
- Exponents
- Parallelograms

1. Circles

Circumference =

Diameter =

Radius =

Area =

The area of a circle is 36. What is the diameter of the circle?

The radius of a circle is 10. What is the circumference of the circle?

What formula do you use to find the ratio of the arcs, sectors, etc. of a circle?

2. Perfect Squares

List all the perfect squares from 0 to 100

3. Odds and Evens

Odd + Odd =

Odd * Even =

Even - Even =

Even/Odd =

Even * Even =

Odd + Even =

Odd - Odd =

Odd/Odd =

4. Least Common Multiples

What is the least common multiple of 15 and 24?

What is the least common multiple of 12 and 30?

5. Common Percent Equivalencies

Decimals to Fractions

0.4 =

0.875 =

0.167 =

0.85 =

0.375 =

Fractions to Decimals

5/8 =

2/40 =

5/6 =

3/5 =

2/16 =

6. Distance Problems (Distance, Rate & Time)

Distance =

Rate =

Time =

7. Triangles (30-60-90, 45-45-90, 3-4-5, 5-12-13)

Draw a 30-60-90 triangle and label its sides and angles

Draw a 45-45-90 triangle and label its sides and angles

(Note: All of the following are right triangles)

If the leg opposite the 30-degree angle is 8, what is the hypotenuse of the triangle?

If one of the legs is 6 and the hypotenuse is 10, what is the other leg?

If the hypotenuse is 20, what is the length of the leg opposite the 45-degree angle?

If one of the legs is 10 and the other leg is 24, what is the length of the hypotenuse?

8. Prime Numbers

List all the prime numbers less than 22

9. Work Problems

What is the formula to use for work problems?

If Sue can do a job in 3 hours and Bob can do the same job in 6 hours, how long will it take them working together at their respective rates?

If Tom can do a job in 10 hours and Tom and Mary together can do the job in 6 hours working at their respective rates, how long will it take Mary to do the job by herself?

10. Percent Problems

What number should you always pick for percent problems?

What formula will give you the percent increase/decrease?

What formula will give you what percent the new quantity is of the old quantity?

11. Number Properties

What numbers get bigger when you square them?

What numbers stay the same when you square them?

What numbers get smaller when you square them?

What numbers get bigger when you cube them?

What numbers stay the same when you cube them?

What numbers get smaller when you cube them?

12. Probability

What formula will give you probability of an event occuring?

What method do you use to find the total number of events that could occur?

What is a popular shortcut to find the probability of "success"?

13. Inequalities

An inequality can be treated just like an equal sign with one exception. What is it?

If 6x < -18, what does x have to be?

If -10x + 120 > -2(40 + 15x), what does x have to be?

14. Averages

What is the formula used to find out the average of a group of numbers?

If a group contains five numbers and the average of the numbers is 17, what is the sum of the numbers?

If the average of a group of numbers is 24 and the sum of the numbers is 192, how many numbers are there?

15. Divisibility Rules

How do you know if a number is divisible by 3?

How do you know if a number is divisible by 4?

How do you know if a number is divisible by 5?

How do you know if a number is divisible by 6?

How do you know if a number is divisible by 7?

How do you know if a number is divisible by 9?

Is 47 a prime number?

Is 117 a prime number?

Is 981,495 a prime number?

16. Ratios

If three things are in a ratio of 5:9:11, what does the total number of things have to be a multiple of?

If the number of things represented by the 5 doubles, can you represent the new ratio as 10:9:11?

If you add 6 things to the the number of things represented by the 9, can you represent the new ratio as 5:15:11?

If the number of things represented by the 9 is reduced by one-third, can you represent the new ratio as 5:7:11?

17. Exponents

(xˆ2)*(xˆ3) =

(xˆ8)/(xˆ2) =

(xˆ3)ˆ2 =

xˆ(-6) =

18. Parallelograms

What is the formula for the area of parallelogram?

What things do you know to be true about a parallelogram?

What do you know about the area of a parallelogram versus the product of its sides?

Is a square always a parallelogram?

Is a parallelogram always a square?

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