# Muhammad Ali Tariq’s GMAT Quant Mastery PLAN

### (3 MONTHS with 4 SESSIONS PER WEEK)

Note:

I am, along with my core team of GMAT Experts, a huge believer in creating the plan and following the plan diligently.

Without a plan, you are like a ship set sailing without a destination.

Without a plan, you are at the mercy of luck and luck can be ruthless—

more so when you require it the most to strike.

## Summary

Week 1: Algebra Core

Week 2: InEqualities and Absolute Values

Week 3 and 4: Number Theory

Week 5 and 6: Word Problems

(Ratios, %s, Weighted Averages, Rate, Time/Distance/Speed, Set Theory/Venn Diagrams)

Week 7: Statistics

Week 8: REST

Week 9 and 10: Counting(PnC and Probability)

Week 11: 2D and 3D Geometry

Week 12: Coordinate Geometry

DETAILED STUDY PLAN BREAKDOWN

MODULE I: ALGEBRA COMPREHENSIVE

WEEK I

Session # 1

1. ARITHMETIC/Algebraic Prerequisites for GMAT Quant
• Fundamentals
• The Four Basic Operations (PEMDAS)(Note: GMAT used to test Order of Operations, but hasn’t been tested for several years now).
• One Specialized Technique: (Note: Difference of Squares Factorization (a^2-b^2). It is the only “fast Calculation technique that you’ll ever require on the GMAT. If you search YouTube, you’ll find a lot of Fast calculation techniques that you almost never require on the GMAT since GMAT is not interested in your calculation prowess but is interested in your conceptual understanding).

• Negative Numbers andThe Number Line
• Arithmetic with Negative Numbers

(Note: Thorough understanding of how the negative numbers operates is absolutely critical to beat Data Sufficiency. Also, negative numbers are the basis of many ‘traps’ in equation-based algebra questions and Inequalities—questions typically known as “Negative Numbers trap questions”).

• Fractions
• Arithmetic with Fractions
• Fractions Within Fractions
• Comparing Fractions
• Labeling Digits and Decimals and Arithmetic
• Rounding
• Exponents
• Exponent Rules (The 4 Exponents Rules)
• Roots
• The Square Root Rules (3 Rules to combine roots)
• Simplifying Roots
• Rationalizing Denominators and Mandatory Simplifications
• Factorials

SESSION # 2 AND 3

1. ALGEBRA CORE
• Algebraic Techniques
• Simple Factoring
• Expressions
• Simple Equations
• Solving Equations
• Traps
• Guidelines
• Substitution
• Two Equations, Two Unknowns: Among The MOST Common Algebraic Situations in GMAT Algebra. Also the essence of many Word Problems. Immediate recognition is very important.
• Method #1 to solve Two Equations, Two Unknowns: Substitution with Two Equations
• Method #2 to solve Two Equations, Two Unknowns Adding and Subtracting Equations
• Comparing the Two Methods
• Nonlinear Equations
• Three Equations in Three Unknowns
• Multiplying Factors
• Factoring
• FOIL
• The Difference of Squares and Other Factoring Patterns
• Factoring with Larger Coefficients
• Limits

Session # 4

• Functions, Operations AND SEQUENCES
• Functions
• Functions: Miscellaneous Topics
• Operations
• Sequences
• Definition and Notation
• Functional Definitions
• Recursive Definitions
• Infinity
• Arithmetic Sequences and Series
• Geometric Sequences

WEEK 2

Session # 1 and 2

1. INEQUALITIES Mastery
• Introduction
• Simplifying
• Transitivity
• Negatives and Positives
• Products
• Thinking Conceptually
• Two inequalities, two unknowns
• Exponential Functions
• Equations, Non-Strict Inequalities
• Data Sufficiency Strategies

Session # 3 and 4

1. ABSOLUTE VALUE Mastery
• Definition
• Fundamental Principles
• Absolute Value in Equations or Inequalities
• The Distance Method
• The Cases Method
• Cases and Inequalities
• Absolute Value and Square Roots

Detailed Algebra Quiz comprising the trickiest 700-800 level Questions

WEEK 3 and 4

MODULE II: NUMBER THEORY

Session # 1

1. Even and Odd Integers
• Rules
• Even and Odd Arithmetic: Advanced Techniques
1. Units Digits

Session # 2

• Primes and Divisibility: Basic Properties
• Fundamental Properties
• Divisibility Tests
• Prime Testing
1. Prime Factorization

Session # 3 and 4

1. Applications of Prime Factorization
• Least Common Multiples
• Greatest Common Divisors
• The Relationship Between LCM and GCD
• Numbers, Exponents and Arithmetic
• Algebraic Factoring I
• Algebraic Factoring II
• Algebraic Factoring III
• Terminating Decimals
• Counting Divisors
• Powers and Divisibility
• Factorials and Divisibility
• Factorials and Prime Factorizations
• Trailing Zeros

WEEK 4(2 Sessions)

Session # 1

1. Number Properties Questions
• Number Theory and Word Problems

Session # 2

• Remainders
• Definitions
• Remainders Tests
• Remainders by the Same Divisor
• Remainders by Different Divisors
• Remainders by Related Numbers
• Remainders and Decimals
• Remainders and Word Problems

Detailed Number Theory Quiz comprising the trickiest 700-800 level Questions

…BREAK…

WEEK 5 and 6

MODULE III: WoRd Problems

Ratios, Percentages,

Complex Translations,

Compound Interest

Weighted Averages, RaTe Work Problems,

Time-Distance-Speed,

Set Theory & Misc.

Session # 1

1. Ratios and Percentages: Introduction
• Ratios Fundamentals
• Ratios and Divisibility
• Increase and Decrease by a Ratio
1. Ratio Strategies
• Pure Ratio Questions
• Algebraic Strategies
• Ratios: Typical Questions
• Compounded Ratios
• Ratio-based 2 Equation/2 Unknown Problems
• Ratios and Differences
• Three Part Ratios
• Ratios of Distances

Session # 2 and 3

1. Percentages, Percent Increase and Percent Decrease
• Percentages,Percent Increase, Percent Decrease
• Percent Profit, Percent Loss
• Sequences of Percent Changes
• Compound Interest,Simple Interest
• Ratios, Percentages, and Inequalities
• Ratios and Percentages in Data Sufficiency

Session # 4

1. Word Problems: Basic Techniques
• Units Conversion
• Estimation
1. Translating words into equations
• Word Translation in Problem Solving: General Principles
• Complex Translations
• Generating Formulas
• Word Translation in Data Sufficiency: General Principles

WEEK6

Session # 1

• Word Problems and Inequalities

Session # 2,3,4

• Rate Work Problems
1. Speed, Distance, Time
• Speed
• Average Speed
• Converging Speed
• One Specialized Problem Type
1. Weighted Averages
• Recognizing Weighted Averages
• Weighted Averages Strategy
• Weighted Averages and Data Sufficiency

Session # 5

1. Venn Diagrams
• Two Set Problems, Maxima/ Minima in Two Set Problems
• Three Set Problems, Maxima/ Minima in Three Set Problems

Session # 6

• Recognizing Formulas
• Logic Problems and Proof by Contradiction
• Miscellaneous Topics

Detailed Word Problems Quiz comprising the trickiest 700-800 level Questions

WEEK 7

MODULE IV: Statistics

Session # 1

The Average (Arithmetic Mean)

1. The Median
2. The Mode
• The Range

Session # 2 and 3

1. Standard Deviation
• Properties of Standard Deviation
• Comparing Sets
• Standard Deviations from the Mean
• Standard Deviation and Frequency Distributions

Session # 4

1. Typical Question Types
• Equally Spaced Sums
• Conceptual Stats Questions
• Frequency Tables
• Modifying a Set
• Max/Min Stats Problems

• Detailed Statistics Quiz comprising the trickiest 700-800 level Questions

…BREAK…

Week 8: REST

WEEK 9 and 10

MODULE V:COUNTING

(PERMUTAITON, COMBINAITON AND PROBABILITY)

Session # 1

1. The Pigeonhole Principle
2. Counting in Equally Spaced Sets
• Mathematical Counting: The Basic Principles
• Counting by Cases: the OR rule
• When Cases Overlap
• Counting When Making a Sequence of Choices: the AND rule
• When One Choice Affects Another
• The NOT Rule
• When Order is Not Important
• Formulas
• When is Order Important?
• Notation and Terminology

Session # 2

1. Counting: Techniques
• Counting by Enumeration
• Counting by Construction
• Counting by Cases
• Counting using the NOT rule
1. Typical Questions
• Selecting Fixed Numbers From Two Groups
• The Handshake Problem
• Counting Words

Session # 3

• Further Examples
• Specialized Counting Situations
• The Pizzeria Problem
• Variations on Seating Problems
• Circular Permutations
• Words With Repeated Letters
• Partitions
• Derangements
• Dividing a Group into Subgroups

Session # 4

• Probability
• The Definition of Probability
1. Marbles Problems and The Basic Probability Rules
• The Marbles Problem
• The AND Rule
• The OR Rule
• The NOT Rule
• Two Approaches to Probability
• Typical Examples of Marbles Problems
• Tricks For Some Other Common Situations
• Coin Flip Problems
• Coin Flip Problems If The Probability Is Not 0.5

Session # 5

1. Probability and Data Sufficiency

WEEK 10

SESSION # 1

1. Specialized Question Types
• Conditional Probability
• Stopping Problems
• Geometric Probability

Detailed Counting Quiz comprising the trickiest 700-800 level Questions

WEEK 11and 12

MODULE VI: Geometry

Session # 1

1. Thinking Geometrically
• Fundamental Principles
• Estimation
• Traps

• Squares Rectangles, Area and Perimeter , and Parallelograms

Session # 2

• Triangles
• Angles, Area, Sum of angles
• Triangle Inequality
• Pythagorean Theorem: PT with Whole Numbers, PT and Area
• Pythagorean Inequalities
• Angles and Special Triangles
• Similar Triangles

Session # 3

1. Circles and Rings
2. Angles
• Angles in a Straight Line
• The X and Z-pattern
• Angles within a Circle
• Tangent Lines
• Further Misc. Examples

Session # 4

1. 3-dimensional Geometry
• Distances in 3 Dimensions
• Volumes andSurface Areas
• Ratios of Areas and Volumes

WEEK12

Session # 1

• Geometry in Data Sufficiency
• Ratios When Inscribing
• Freedom in a Diagram

Session # 2, 3 and 4

• Coordinate Geometry
• Points
• Distances
• Midpoints
• Areas
• Slopes
• Equations of Lines
• Intersection Points
• Parallel and Perpendicular Lines
• Curves and other Non-Linear Equations
• x and y Intercepts
• Inequalities in Coordinate Geometry
• Visualization Problems
• Coordinate Geometry and Ordinary Geometry

Detailed Geometry Quiz comprising the trickiest 700-800 level Questions

Q)Is all Quant Material provided by M. Ali Tariq and his Team:

Yes. All the material is provided by us.

The Quant material consists of:

These are not Manhattan Prep’s guides disguised as ours.

These are our Copyrighted guides that cover the holistic conceptual walkthroughs and application on very tricky questions.

à 2000 plus 500-550 level unofficial question(to help you get in the flow)

à 2000 unofficial Quant questions (700-800 level questions)

à3500 plus official GMAT questions.

This compilation is from all the published Quant questions by GMAC.

1. Q) IS the over all GMAT Quant Mastery Plan that lasts 3 months good for me or the hourly plan?

Hourly plans are a great option for applicants who need help with discrete areas rather than overall GMAT Quant.

For example:

àPerhaps you feel your Coordinate Geometry and Number Theory are strong but are unsure of InEqualities or Absolute Values.

àPerhaps just one topic in Number Theory is giving you trouble, so you feel you only need assistance with it.

Whatever the task, we can assess your weaknesses in particular narrow area and serve your needs accordingly.