Not a child genius? Not a problem. My name is Corey and I’m here to guide you through an interactive course on quantitative problem solving for mastering the math section of the GRE and GMAT exams. These problems are not duplicates of the long, tedious, subpar GRE and GMAT course books that you’ve already purchased (such as the Barron’s or Manhattan series which deviate from the actual GRE given by ETS and assume that you have infinite preparation time to work through their long lists of questions), so you will be getting brand new problems modeled after REAL GRE and GMAT questions that will challenge you in a unique way. This course is vitally important for anyone planning to apply to most graduate programs and the GRE and GMAT math questions come fully annotated solutions. This course is also ideal for high school students preparing for the SAT, as many of the harder math questions on the SAT will seem simple after mastering these questions. Feel free to preview sample solutions so that you have an idea of what to expect in the rest of the course. Thank you for your time and I look forward to helping you maximize your math proficiency.

Feel free submit questions through the course or directly to my email (hokiesalum[AT_symbol]]gmail[DOT]com ; include Udemy in the subject line). Also feel free to contact me if you need additional help with your math prep. I want to do my best to make sure that you succeed! 🙂

### Introduction

### Teaching Lectures

This lecture will cover the derivation of the formulas for permutations and combinations. Permutations represent selecting objects from a set of objects and the order of selection IS important. Combinations represent selecting objects from a set of objects and the order of selection is NOT important.

n Permutation x = n! / (n-x)!

n Choose x = n! / ( (n-x)! * x! )

A prime number is a number that is only divisible by 1 and itself. 2 is defined as the first prime number.

The factors of a number are the numbers that evenly divide into that number. For example, the factors of 10 are 1, 2, 5, and 10.

The prime factorization can be used to find the greatest common factor (GCF) or the least common multiple (LCM) of two or more numbers.

The GCF can be used to simplify fractions.

The LCM can be used to find a common denominator to add or subtract fractions.

The most important exponent rules are covered in this lecture. The most important rules are:

1. Add the exponents when you have two numbers with the same base multiplied together.

2. Subtract the exponents when you have two numbers with the same base divided by each other.

3. Multiply the exponents when you have an exponent raised to an exponent.

4. Negative exponents can be made positive by moving the number from the numerator to the denominator or vice versa.

5. Radicals can be changed into fractional exponents and vice versa.

Remember that when you add or subtract the fractions, the time component has to be in the denominator, on the bottom. For example, 5 miles per hour + 10 miles per hour = 15 miles per hour. Do NOT do: 1 hour per 5 miles + 1 hour per 10 miles = 3 hours per 15 miles.

This lecture covers the most important subtopics for dealing with triangles.

1. A triangle has three sides and the sum of its angles is 180 degrees.

2. The area of a triangle is 1/2 * base * height.

3. Pythagorean's Theorem for right triangles: c^2 = a^2 + b^2.

4. An exterior angle for a triangle is equal to the sum of the other two angles.

5. There are two special triangles in terms of angles:

45:45:90 triangle = x : x : x*sqrt(2)6. Any side of a triangle must be less than the sum of the other two sides of the triangle and more than the absolute value of the difference between the other two sides of the triangle.

30:60:90 triangle = x : x*sqrt(3) : 2x

1. To multiply fractions, multiply the numerators and denominators straight across.

2. To divide fractions, change the fraction being divided into its inverse, and then multiply the fractions straight across.

3. To add and/or subtract fractions, find the LCM (least common multiple) of the denominators, change all fractions so that they share this LCM, then perform the addition and subtraction operations only on the numerators, not the denominators.

This lecture will cover divisibility rules.

2: The number is even; the number ends in 0, 2, 4, 6, or 8.

3: The sum of the digits of the number is divisible by 3.

4: The last two digits is divisible by 4.

5: The last digit is either 5 or 0.

6: The number is divisible by both 2 and 3.

9: The sum of the digits is divisible by 9.

10: The number ends in 0.

Ratios and Proportions Review Problem Video Solutions

**This lecture covers GRE quantitative comparison strategies.**

1. Always use your pencil and paper.

2. Add or subtract any number from both sides to simplify the problem. Usually this is useful if you have the same number, variable, or equivalent expression on both sides.

3. Multiply of divide any positive number, variable, or expression from both sides to simplify the problem. Sometimes this is optional, but other times this is essential for solving a problem. Remember that it must be a positive number, variable, or expression, as doing this with a negative number change the problem being asked.

4. Have confidence. The GRE test is also a psychological test of your math ability and confidence level. Not being confident in your math skills leads to double and triple checking answers, thereby taking away time from the other questions in the test.1. Always use your pencil and paper.

2. Add or subtract any number from both sides to simplify the problem. Usually this is useful if you have the same number, variable, or equivalent expression on both sides.

3. Multiply of divide any positive number, variable, or expression from both sides to simplify the problem. Sometimes this is optional, but other times this is essential for solving a problem. Remember that it must be a positive number, variable, or expression, as doing this with a negative number change the problem being asked.

4. Have confidence. The GRE test is also a psychological test of your math ability and confidence level. Not being confident in your math skills leads to double and triple checking answers, thereby taking away time from the other questions in the test.

### Math Problems

Problem List

Translating Words Into Equations

Solving Algebraic Equations

Translating Words into Equations

Age Problems

Integer Problems

Percentages

Translating Words Into Equations

Permutations

Probability

Two-Way Tables

Combining Algebraic Equations

Exponents

Work / Rate Problems

Unit Conversions

Algebraic Factoring

Solving Algebraic Equations

Averages

Ratios

Ratios

(Correction: $20 should be added at the end to give $420 as the correct answer)

Interest Rate Problems

Distance, Rate, Time Problems

Ratio Problems

Probability

Geometry

Ratios

Sum and Average Problems

Area

Perimeter

Optimization

Permutations

Mixture Problems

Distance, Rate, Time Problems

Matching Pairs

Combined Work / Rate Problems

Combined Work / Rate Problems

Averages

Medians

Probability

Probability

Translating Words Into Equations

Probability

Topics:

Probability

Two-Way Tables

Geometry

Angles

Polygons

Geometry

Inscribed Polygons

Areas

Perimeters

Percentages

Translating Words Into Equations

Solving Algebraic Equations

Triangles

Statistics

Normal Distribution

Means and Standard Deviations

Averages

Sums

Numerical Factors

Prime Numbers

Factorials

Divisibility

Numerical Factors

Ratios

Unit Conversions

Inequalities

Translating Words Into Equations

Proportionality

Solving Algebraic Equations

Translating Words Into Equations

Solving Algebraic Equations

Coin Problems

Translating Words Into Equations

Solving a System of Linear Equations

Topics:

Solving Algebraic Equations with Radicals

Solving algebraic equations with absolute value signs

Prime Numbers

Divisibility Rules

Translating Words Into Equations

Combined Work / Rate Problems

Ratios and Proportions

Factorials

Multiplication Factors

Mixture Problems

Translating Words Into Equations

Solving Algebraic Equations

Translating words into equations

Right triangles

Pythagorean triples

Perimeters

Solving a system of equations

Geometry

Combinations

Multiplication rules

Divisibility rules

Combinations

Divisibility rules

Sequences

Time Problems

Circles

Special Triangles

Areas

Angles

Equations of Lines

Slopes

Perpendicular Lines

System of Equations

Factoring Quadratic Equations

Ratios and Proportions

Squares

Circles

Areas

Perimeters

Sequences and Series

Averages

Sums

Permutations and Combinations

Digits

Ratios and Proportions

Topics:

Exponents

Topics: Inequalities

Systems of Equations

Topics: Translating Words Into Equations

Fraction Arithmetic

Solving an Equation for a Variable

Topics: Translating Words Into Equations

Fraction Arithmetic

Solving an Equation for a Variable