GMAT Study Guide - Number Theory Review and Basic Formulas
Prime Numbers to 100
2, 3, 5, 7, 11, 13, 17, 19
23, 29, 31, 37, 41, 43, 47
53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Only positive numbers can be prime
Odds and Evens
even ± even = even
even ± odd = odd
odd ± odd = even
even * even = even
even * odd = even
odd * odd = odd
Zero is even.
Positive and Negative Numbers
positive * positive = positive
positive * negative = negative
negative * negative = positive
positive / positive = positive
positive / negative = negative
negative / negative = positive
Zero is neither positive nor negative, however when GMAT refers to a "non-negative" number that number might be zero.
Divisibility Shortcuts
2: The last digit is even.
3: The sum of the digits is divisible by 3.
4: The last two digits form a number divisible by 4.
5: The last digit is 0 or 5.
6: The number is divisible by both 2 and 3.
9: The sum of the digits is divisible by 9.
10: The last digit is 0.
12: The number is divisible by both 3 and 4.
Fractions
irrational number: cannot be expressed as a fraction
numerator: The number on top of a fraction.
denominator: The number on the bottom of a fraction.
To add/subtract fractions with the same denominator: Add/subtract the numerator and place over the common denominator.
To add/sub fractions with different denominators: Find the least common denominator and convert the fractions.
To multiply fractions: Multiply the numerators and denominators.
To divide fractions: Invert the divisor fraction (find its reciprocal) then multiply.
Exponents
$x^0 = 1$
$x^1 = x$
$0^n = 0$
$0^{-n} = undefined$
$1^x = 1$
$x^{-n} = 1/x^n$
$x^n * y^n = (xy)^n$
$(xy)^n = x^n * y^n$
$x^n/y^n = (x/y)^n$
$(x/y)^n = x^n/y^n$
$x^n/y^n = (x/y)^n$
$(x^m)^n = x^{mn}$
$x^n * x^m = x^{n+m}$
$x^{n+m} = x^n * x^m$
$x^n/x^m = x^{n-m}$
$x^{n-m} = x^n/x^m$
$x^{1/n} = √^nx$
$x^{m/n} = √^nx^m$
$x^2 = 25$; solve for x; $x = ±5$
$x^3 = 125$; solve for x; $x = 5$
$x^3 = -125$; solve for x; $x = -5$
$√x * √y = √{xy}$
$√{xy} = √x * √y$
$√x / √y = √{x/y}$
$√{x/y} = √x / √y$
$a√r + b√r = (a+b)√r$
$(a+b)√r = a√r + b√r$
$a√r - b√r = (a-b)√r$
$(a-b)√r = a√r - b√r$
$(√x)^n = √x^n$
$√x^n = (√x)^n$
$x^{1/n} = √^nx$
$√^nx = x^{1/n}$
$x^{n/m} = √^mx^n$
$√^mx^n = x^{n/m}$
$√a + √b ≠ √{a+b}$
$√4 = 2$
$√9 = 3$
$√16 = 4$
$√25 = 5$
$√36 = 6$
$√49 = 7$
$√64 = 8$
$√81 = 9$
$√100 = 10$
$√121 = 11$
$√144 = 12$
$√164 = 13$
$√196 = 14$
$√225 = 15$
$√256 = 16$
$√289 = 17$
$√324 = 18$
$√361 = 19$
$√400 = 20$
$√625 = 25$
$√900 = 30$
$√^3 8 = 2$
$√^3 27 = 3$
$√^3 64 = 4$
$√^3 125 = 5$
$√^3 216 = 6$
$√^3 344 = 7$
$√^3 512 = 8$
$√^3 729 = 9$
$√^3 1000 = 10$
$√^3 8000 = 20$
$2^2 = 4$
$3^2 = 9$
$4^2 = 16$
$5^2 = 25$
$6^2 = 36$
$7^2 = 49$
$8^2 = 64$
$9^2 = 81$
$10^2 = 100$
$11^2 = 121$
$12^2 = 144$
$13^2 = 164$
$14^2 = 196$
$15^2 = 225$
$16^2 = 256$
$17^2 = 289$
$18^2 = 324$
$19^2 = 361$
$20^2 = 400$
$25^2 = 625$
$30^2 = 900$
$2^3 = 8$
$3^3 = 27$
$4^3 = 64$
$5^3 = 125$
$6^3 = 216$
$7^3 = 344$
$8^3 = 512$
$9^3 = 729$
$10^3 = 1000$
$20^3 = 8000$
compound interest = principal * (1 + (interest/C))time*C where C is the number of times compounded annually
Pythagorean Triplets:
3,4,5
5,12,13
8,15,17
Order of Operations:
PEDMAS - Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction
Approximations for Common Imperfect Roots
$√2≈1.41$
$√3≈1.73$
$√5≈2.24$
$√6≈2.45$
$√7≈2.65$
$√8≈2.83$
$√10≈3.16$
Related Pages
Overview of the Graduate Management Admissions Test
GMAT Exam Structure and Format
Ace the GMAT Analytical Writing Assessment
GMAT Math Review: Factors and Prime Factorization