GMAT Focus Quant
Multiplying Remainders
(2/5)*(3/5)*(2/5) = 12/5 --> R = 2/5
Convert the Following Fractions to Decimals 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10
0.5 0.333 0.25 0.20 0.167 0.143 0.125 0.111 0.10
0!
1
Determine number of prime factors in a factorial
1. Factor divisor into prime #s 2. Determine limiting prime factor 3. Divide numerator by factor to the 1st, 2nd, 3rd, etc. power until quotient = 0 4. Add quotients ex. 21!/3^n 21/3 = 7 21/9 = 2 n=9
Greatest Common Factor
1. Prime Factorize 2. Identify Repeated Factors 3. Select those with smallest exponent and multiply
Lowest Common Multiple
1. Prime Factorize 2. Select prime factors with largest exponent 3. Multiply non-repeating prime factors
Determine total factors in a number
1. Prime Factorize 36 -> 2²3² 2. Add 1 to the value of each exponent (2 + 1) 3. Multiply the exponents (2 + 1)*(2 + 1) = 9
Comparing Fractions
1. Reference Point (i.e. greater than or less than 1/2) 2. Bowtie method (7/9 vs. 6/8 --> 56 vs. 54 --> 7/9 is larger)
Prime Numbers 0 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
Numbers ending with these digits are not perfect squares
2, 3, 7, 8
Base 2 Exponent Ones Digit Pattern
2, 4, 8, 6, 2...
2^4 + 2^4 =
2^5
Base 3 Exponent Ones Digit Pattern
3, 9, 7, 1, 3, 9, 7, 1, ...
3^9 + 3^9 + 3^9 =
3^10
Approximate Cube Roots 3√2 = 3√3 = 3√4 = 3√5 = 3√6 = 3√7 = 3√8 = 3√9 =
3√2 = 1.3 3√3 = 1.4 3√4 =1.6 3√5 = 1.7 3√6 = 1.8 3√7 = 1.9 3√8 = 2 3√9 = 2.1
Base 4 Exponent Ones Digit Pattern
4, 6, 4, 6, 4, 6...
4^5 + 4^5 + 4^5 + 4^5=
4^6
Base 6 Exponent Ones Digit Pattern
6, 6, 6, 6, ...
Base 7 Exponent Ones Digit Pattern
7, 9, 3, 1, 7, 9, 3, 1...
Base 8 Exponent Ones Digit Pattern
8, 4, 2, 6...
Base 9 Exponent Ones Digit Pattern
9, 1, 9, 1, ...
Adding/Subtracting Remainders
Add remainders and find outstanding amount *If negative, add divisor to correct i.e. remainder of 13/5 - 17/5 R of 13/5 = 3/5 R of 17/5 = 2/5 3/5-2/5 = -1/5 add 5/5 --> R = 4/5
Integer
All Natural Numbers (both positive and negative) and zero.
When solving a system of equations with a Square Root...
Check that the solution does not create a negative value in the square root
Discriminant = positive Discriminant = negative Discriminant = 0
Discriminant = positive --> 2 roots Discriminant = negative --> 0 roots Discriminant = 0 --> 1 root
Convert Non-Repeating, Non-Terminating Decimals to Fraction
Impossible
Number of leading zeros for a number where the denominator has k digits and IS NOT a perfect power of 10
Leading Zeros = k-1
Number of leading zeros for a number where the denominator has k digits and IS a perfect power of 10
Leading Zeros = k-2
Determine units digit of large numbers squared
Look at the last digit
Convert Terminating Decimal to Fraction
Multiply by 10/10
Convert Fraction to Percent
Multiply by 100 (i.e. 1/4 * 100 = 25%)
Whole Number
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Proper Fraction
Numerator < Denominator
Improper Fraction
Numerator > Denominator
Opposite
Opposite of x is -x
Reciprocal
Reciprocal of x is 1/x Zero does not have a reciprocal
Unique Prime Factors of x raised to a power
Same as x
0 to the 0 power
Undefined
x/0
Undefined
Wage
Wage = (total compensation)/(total hours worked)
|a + b| ≤ |a| + |b| if |a + b| = |a| + |b|
a and b have the same sign
|a - b| ≥ |a| - |b| if |a - b| = |a| - |b|
a and b have the same sign and a > b
Mixed Number
a whole number and a proper fraction
Discriminant
b²-4ac
Prime factorization of a perfect square
contains only even exponents
Prime factorization of a perfect cube
contains only exponents that are a multiple of 3
Determine # of trailing zeros
determine number of 5x2 pairs when you prime factorize
A number is divisible by 12 if...
divisible by 3 and 4
A number is divisible by 7 if...
do the long division
Is zero even or odd?
even
Adding and Subtracting Even and Odd Numbers
even + even = even 4 + 2 = 6 even + odd = odd 4 + 3 = 7 odd + odd = even 5 + 3 = 8
Multiplying and Dividing Even and Odd Numbers
even x even = even 4 x 2 = 8 even x odd = even 4 x 3 = 12 odd x odd = odd 5 x 3 = 15
If you multiply/divide an inequality by a negative number...
flip inequality
A number is divisible by 6 if...
if even, and the sum of the digits are divisible by 3
A number is divisible by 5 if...
if the ones digit is 0 or 5
Product of any n number of consecutive digits is divisible by
n!
product of consecutive integers
n(n-1) = n² - n n(n+1) = n² + n (n-1)n(n+1) = n^3 - n (n-2)(n-1)n(n+1)(n+2) = n^5 - 5n^3 + 4n
Decimal equivalent of a fraction will terminate if and only if...
prime factorization of denominator contains only 2s and 5s
A number is divisible by 4 if...
the last 2 digits are divisible by 4
A number is divisible by 8 if...
the last 3 digits are divisible by 8
A number is divisible by 9 if...
the sum of all digits is divisible by 9
A number is divisible by 3 if...
the sum of all of its digits is divisible by 3
A number is divisible by 11 if...
the sum of the odd-numbered place digits minus the sum of the even-numbered place digits is divisible by 11
Quadratic Formula
x = -b ± √(b² - 4ac)/2a
When solving a system of equations, if you divide by x...
x is a possible solution
LCM(x,y)*GCF(x,y)
x*y
x/y =
x/y = Q + r/y
(x^a)*(x^b) =
x^(a+b)
(x^a)^b =
x^ab
(x + y)²
x² + 2xy + y²
(x - y)²
x² - 2xy + y²
(x - y)(x + y)
x² - y²
Square and Square Root of numbers 0 < x < 1
x² < x < √x
x² > 64
x² > 64 |x| > 8 -x > 8 or x > 8 x < -8 or x > 8
If z is divisible by x and y...
z is also divisible by the LCM of x and y
√(x+y)² =
|x+y|
√x² =
|x|
Approximate Square Root Values √2 = √3 = √5 = √6 = √7 = √8 =
√2 = 1.4 √3 = 1.7 √5 = 2.2 √6 = 2.4 √7 = 2.6 √8 = 2.8
