GMAT Number Theory in Action

GMAT Quantitative Prep course

Created byGustavo Luyo

Last updated 6/2023

English

English [Auto],

What you'll learn

Understand the difference between Easy and Medium difficulty levels in Number Theory questions
Notice the fundamental templates for Number Theory questions including fractions and decimals
Notice the fundamental templates for Number Theory questions including integers
Be exposed to a wider range of question topics for GMAT Number Theory

Course content

3 sections • 18 lectures • 48m total length

Dealing with combined operations6:05
Apply ballpark estimation to a numeric compound expression with combined operations, quickly discarding unlikely choices and predicting the answer is greater than three.
How do you arrange powers of decimals?7:10
Analyze how negative decimals behave under even and odd exponents in GMAT number theory, using x = -0.256 and a sample -1/2 to compare x^3, x^4, and x^-5.
Can you tell a factor from a prime factor?1:32
Evaluate sufficiency: a factor of seven forces Q to be seven, prime, so statement 1 is sufficient; 42 factor can be prime or not, so statement 2 is not sufficient.
Learn to simplify sums/differences of powers2:15
Learn to simplify sums and differences of powers by factoring the smallest power, canceling exponents, and using plausible approximations to estimate results instead of exact values.
Handle Integer Parity carefully in Data Sufficiency2:34
handles integer parity in data sufficiency by treating x/2 as integer or fraction, showing statement 1 is not sufficient; statement 2, with an odd exponent, makes x even and sufficient.
When insufficient numeric data is available be smart: assume the easiest values1:51
Plug in the simplest values satisfying P/4 = Q with Q prime >3, such as Q = 7 and P = 28, then count divisors to identify evens.
Watch for negative numbers when working Data Sufficiency questions with integers1:48
Evaluate data sufficiency for GMAT number theory with integers, watch for negative values in AB relationships like AB = A or AB = 1, and combine statements to assess sufficiency.

Always factor the power with the lesser exponent in a sum/difference of powers1:13
In this GMAT number theory problem, factor the smallest power 2^(x-6) from the expression, use 2^6−1=63 to cancel, and equate exponents to get x=12.
Learn to use Parity rules for questions with integer operations1:42
Apply parity rules: a product is odd only when both factors are odd; a sum is odd when terms have opposite parity. Therefore x*y is even; statement is not sufficient.
Use negative exponent properties cleverly for unraveling variables1:09
Apply negative exponent properties to rewrite the expression as inverses of numbers, simplify to powers of three, and equate exponents to solve for m equals two.
The power of the quotient approach when handling factor/multiple questions2:02
Apply the quotient approach to factor and multiple questions, determining when x is a multiple of y by treating x/y as an integer and evaluating two statements for sufficiency.
Use variables to represent digits of a number with different place values6:48
Represent a three-digit number as A B C to study place values and rounding; apply rules for N, 10N, 100N, and combine statements to deduce the tens digit B.
Remember the by-default multiple of a number of integers is always the LCM2:45
Calculate the minimum n as the least common multiple of 2445 and 700, 12,600, and note that 72 divides n while it exceeds 12,000 for multiples and 27 does not.
Rationalize to untangle an expression with combined roots and radicals1:12
Rationalize to untangle an expression with combined roots and radicals by using the conjugate, cancel radical terms, and simplify to a clean result of 4.
Mind the formula for the number of factors of even if you don't know the factors1:37
Use the divisor-counting formula for X = 2^1 3^2 5^1 to get 12 factors; removing one leaves 11 factors greater than one.
The best template to tackle divisibility questions in Data Sufficiency7:08
Apply a clean reformulation by identifying the minimum x from each statement and using the least common multiple to combine them, revealing that x must be a multiple of 200.

Requirements

Full English Proficiency

Description

There is one topic prevailing among the GMAT Quantitative questions with an almost 25% frequency of occurrence in the whole section: Number Theory. It's time for you to realize that a solid foundation for GMAT Prepping must be based on the reassurance that Number Theory is a learning must, and that your chances of reaching a good score can only improve if you decide to get serious about Number Theory.

My previous course provided an introduction to Number Theory. Now it's time to move from Theory to Practice. In this course I will prove how the concepts discussed in my previous course:

+constitute the core of your Arithmetic knowledge needed for acing the GMAT Quant section.

+appear repeatedly in the most basic Number-Theory-related GMAT questions.

+require careful crafting and logic ellaboration at the time of tackling Quant questions of a higher level of difficulty.

Learning to solve GMAT Quant questions based on Number Theory requires undergoing two stages of Modeling and Mimicking. Modeling here refers to the fact you need good sample materials, theory and solutions to learn from. This has been my objective when assembling a collection of video solutions for the most typical questions you will find in the Quant section regarding Number Theory. Mimicking implies your own work, which involves watching the solutions carefully over and over in order to reach two targets:

- understanding how the theory presented and developed in my previous course on Number Theory can be used to tackle the simplest questions.

- memorizing the optimal sequence of logical steps used to approach the solution for each typical question presented.

Working the videos in this way will guarantee a maximum satisfaction at the time of tackling new questions yourself because:

- you will recognize the patterned questions

- you will recall the solutions in your mind and attempt to tackles the questions likewise.

Who this course is for:

Candidates to B-school

GMAT Number Theory in Action

What you'll learn

Explore related topics

Course content

Applying the fundamentals of Number Theory to tackle Quant questions7 lectures • 23min

Medium-difficulty questions require a perfect sequence of properties application9 lectures • 26min

Practice questions2 lectures • 1min

Requirements

Description

Who this course is for: