Useful GMAT

Quantitative Formulas

Introduction

• This presentation contains a collection of some quantitative formulas I found useful during my GMAT study

• While I’ve tried my best to make sure all formulas are correct, however I’m not a subject matter expert, so it is your responsibility to validate the accuracy of anything you read in the presentation.

• Please email me on garhy@garhy.com if you have any errors or fixes to report in this presentation.

• It is important to state that knowing the formulas contributes to 20% or even less of succeeding the GMAT exam, it is mainly about practice.

Golden Rule

This is based on my short experience during the last few months and two attempts to beat the GMAT.

The advice is mainly for those who have relatively strong math background.

• The Quantitative section of GMAT is not really about being able to solve math problems, it’s about being able to solve them on time.

• If you can solve it in 4+ minutes, then most probably the GMAT will beat you.

• The decision to solve or guess is the real challenge, please don’t take it personal, and feel free to guess if you are not sure you will be able to finish it on time.

• I’ve talked with people who scored 750+ and used guessing on at least 8 questions.

Study Resources

• I used two resources which I found very useful during GMAT preparation

period

• Magoosh (www.magoosh.com), it has videos describing all common topics and it also

has good bank of questions

• Manhattanprep (www.manhattanprep.com), it has an amazing bank of relatively

challenging questions

Counting

• For any given fraction 𝑥

𝑦whenever we add the same positive value to the numerator and denominator

𝑥+𝑎

𝑦+𝑎we move the

value of the fraction closer to 1

• If 𝑥

𝑦> 1 or (x>y) then

𝑥

𝑦>

𝑥+5

𝑦+5

• If 𝑥

𝑦< 1 or (x<y) then

𝑥

𝑦<

𝑥+5

𝑦+5

• Number of divisors for any number N

• Write Prime Factors in the form of 𝑋𝑎 ∗ 𝑌𝑏 ∗ 𝑍𝑐

• The number of divisors is (a+1) * (b+1) * (c+1)

• Combinations Rule “Order Doesn’t Matter”: 𝑛𝐶𝑟 =𝑛!

𝑟!∗ 𝑛−𝑟 !=

𝑛 ∗ 𝑛−1 …..∗ 𝑛−𝑟+1

𝑟!

• We use Combinations when order doesn’t matter

• We use Permutation when order matters

Counting

• 𝐷𝑒𝑐𝑖𝑚𝑎𝑙 𝑝𝑎𝑟𝑡 𝑜𝑓 𝑎 𝑑𝑒𝑐𝑖𝑚𝑎𝑙 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡 =𝑅𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟

𝐷𝑖𝑣𝑖𝑠𝑜𝑟

• 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 = 𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡 ∗ 𝐷𝑖𝑣𝑖𝑠𝑜𝑟 + 𝑅𝑒𝑚𝑎𝑖𝑛𝑑𝑒𝑟

• 𝑎 ÷ 𝑏 = 𝑐 𝑑 𝑡ℎ𝑒𝑛 𝑎 = 𝑐 ∗ 𝑏 + 𝑑

• Greatest Common Divisor (Greatest Common Factor) of two numbers = the product of common prime factors between the two numbers

• The Least Common Multiple between two numbers = the product of common prime factors between the two numbers * all other factors that are not common between the two numbers

• If X is the Greatest Common Divisor of A & B, and Y is the Least Common Multiple of A & B, then AB = XY

• Only squares of integers have odd number of positive divisors

• Only square of prime numbers have exactly 3 number of divisors

• Two is the only even prime number

Counting

• If an even integer is multiplied by any integer, the product is always even

• For any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.

• For example, the sum of 1, 2, and 3 (three consecutives -- an odd number) is 6, which is a multiple of 3.

• For any set of consecutive integers with an even number of terms, the sum of the integers is never a multiple of the number of terms.

• For example, the sum of 1, 2, 3, and 4 (four consecutives -- an even number) is 10, which is not a multiple of 4.

• Odd exponents as well as odd roots preserve the sign of the number inside

Algebra

• The equation |x| = (negative value) has no solution since |x| must be

positive

• Solving equations that involve square roots or absolute values require testing

final values to make sure they don’t lead to impossible equations (square root

of a number can’t equal negative value)

• Cube of a sum formula: 𝐴 + 𝐵 3 = 𝐴3 + 3𝐴2𝐵 + 3𝐴𝐵2 + 𝐵3

Statistics

• Standard Deviation of a set of numbers roughly equals the average distance between each number in the set and the average value of the set

• The range of numbers in a set = the difference between the largest and smallest numbers in the set

• The median of a set is the number positioned in the middle of the set (or the average of the 2 middle numbers) after arranging them in order

• Standard Deviation of a set doesn’t change if we add or subtract any number to all of the numbers in the set

Statistics

• Standard Deviation of a set increases when we multiply all numbers in the set by x where |x| > 1

• Standard Deviation of a set decreases when we multiply all numbers in the set by x where |x| < 1

• We can determine the standard deviation of a set of consecutive integers just by knowing the number of items in the set (without knowing the actual values)

• Same applies to a set of consecutive odd or even integers or any set with a given linear pattern

• We can NOT determine the standard deviation of a set of consecutive integers if we only know the mean of the set (we still need to know the number of items in the set)

Geometry

• Sides of base 30-60-90 triangle are 1, 3, 2

• Sides of base 45-45-90 triangle (isosceles right triangle) are 1, 1, 2

• Area of equilateral triangle =3

4∗ 𝑆𝑖𝑑𝑒2

• The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles

• For any triangle, we can determine all sides and angles if we know the lengths of any two sides and the included angle between them (SAS Triangle: Side-Angle-Side Triangle)

• A quadrilateral is a square if all sides are equal and …

• The two diagonals are equal

• All angles are equal (right angles)

• Deluxe Pythagorean Theory: d2 = x2 + y2 + z2 (for space problems instead of using Pythagorean twice)

• The sum of interior angles of a polygon with n sides = 180 ∗ n − 2

Probabilities

• 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑠𝑐𝑒𝑛𝑎𝑟𝑖𝑜 =# 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑡ℎ𝑎𝑡 𝑠𝑎𝑡𝑖𝑠𝑓𝑦 𝑡ℎ𝑖𝑠 𝑠𝑐𝑒𝑛𝑎𝑟𝑖𝑜

𝑡𝑜𝑡𝑎𝑙 # 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

Simple and Compound Interest

• Simple Interest: Total Amount = Principle * ( 1 + (Interest Rate * Period))

• Compound Interest: 𝑃𝑟𝑖𝑛𝑐𝑖𝑝𝑙𝑒 ∗ 1 + 𝑟 𝑛

• r = Interest for each compounding period

• n = Number of compounding periods

Mixture Questions

• Typical solution steps

• Draw the problem

• Using given concentrations (C1, C2), identify variables (V1, S1, V2, S2)

• S1 = C1 * V1

• S2 = C2 * V2

• In most cases, we are solving for V2, and we already know V1, and S1

• 𝑁𝑒𝑤 𝑆𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 =Total Volume of Solid

Total Volume=

𝑆1+𝑆2

𝑉1+𝑉2=

𝑆1+ 𝑉2∗𝐶2

𝑉1+𝑉2

General Rules

• In real life problems, always make sure to test “Real Life Boundaries” like

• Certain numbers that can only be integers

• Numbers that must fall within a certain maximum or minimum limit

• Numbers that can only be positive or negative or fractions (less than one)

• Line equation

• 𝑦 = 𝑚𝑥 + 𝑐(m is the slope, and c is the Y-intersect)

• Slopes of parallel lines are equal

• Slopes of perpendicular lines are negative reciprocals

Good to know values

•1

9= 0.1111111

•1

6= 0.1666667

•1

8= 0.125

•1

11= 0.0909091

• 2 = 1.4

• 3 = 1.7

• 6 = 2.45

Best of Luck

Thank You