GMAT Math
15^2
225
5^2
25
Divisibility Rules - 25
25 - Numbers ending with 00, 25, 50, or 75 represent numbers divisible by 25.
ODD*ODD
ODD*
Greatest Common Factor (Divisior) - GCF (GCD)
The greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
gcd(a, b)*lcm(a, b)
a*b
If the first term is a1 and the common difference of successive members is d, then the nth term of the sequence is given by:
an=a1+d(n-1)
If n is even, the sum of consecutive integers is never divisible
by n
If n is odd, the sum of consecutive integers is always divisible
by n
Even and Odd Numbers: Multiplication
even * even = even; even * odd = even; odd * odd = odd.
Finding the Sum of the Factors of an Integer
(a^(p+1) - 1)*(b^(q+1) - 1)*(c^(r+1) - 1) / (a-1)(b-1)(c-1)
Finding the Number of Factors of an Integer
(p+1)(q+1)(r+1)....(z+1)
1/12
.0833
1/10
.1
1/9
.111
1/8
.125
1/7
.14
1/6
.166
1/5
.2
1/4
.25
1/3
.333
1/2
.5
1^2
1
2^0
1
√2
1.414
√3
1.732
Area of Trapezoid
1/2 (long base+short base) * height
Area of a Triangle
1/2 base * height
Divisibility Rules - 10
10 - If the number ends in 0, it is divisible by 10.
10^2
100
Divisibility Rules - 11
11 - If you sum every second digit and then subtract all other digits and the answer is: 0, or is divisible by 11, then the number is divisible by 11. Example: to see whether 9,488,699 is divisible by 11, sum every second digit: 4+8+9=21, then subtract the sum of other digits: 21-(9+8+6+9)=-11, -11 is divisible by 11, hence 9,488,699 is divisible by 11.
Divisibility Rules - 12
12 - If the number is divisible by both 3 and 4, it is also divisible by 12.
11^2
121
35^2
1225
2^7
128
12^2
144
2^4
16
4^2
16
13^2
169
14^2
196
2^1
2
Circumference
2 * π * radius
Divisibility Rules - 2
2 - If the last digit is even, the number is divisible by 2.
The first twenty-six prime numbers are
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, 101 Note: only positive numbers can be primes
prime #
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 43,47
√5
2.236
16^2
256
2^8
256
17^2
289
Divisibility Rules - 3
3 - If the sum of the digits is divisible by 3, the number is also.
Right Triangle Frequent Combos
3 4 5 and 6 8 10 and 5 12 13
2^5
32
18^2
324
6^2
36
19^2
361
2^2
4
Divisibility Rules - 4
4 - If the last two digits form a number divisible by 4, the number is also
Volume of sphere
4/3 * π *r^3
20^2
400
21^2
461
7^2
49
Divisibility Rules - 5
5 - If the last digit is a 5 or a 0, the number is divisible by 5.
2^9
512
75^2
5625
Divisibility Rules - 6
6 - If the number is divisible by both 3 and 2, it is also divisible by 6.
25^2
625
2^6
64
8^2
64
all prime numbers above 3 are of the form
6n - 1 or 6n + 1
Divisibility Rules - 7
7 - Take the last digit, double it, and subtract it from the rest of the number, if the answer is divisible by 7 (including 0), then the number is divisible by 7.
2^3
8
Divisibility Rules - 8
8 - If the last three digits of a number are divisible by 8, then so is the whole number
9^2
81
3^2
9
Divisibility Rules - 9
9 - If the sum of the digits is divisible by 9, so is the number
ODD+EVEN
ODD +
Rate Problem
How far we have to go/ how fast we are getting there
Lowest Common Multiple - LCM
The lowest common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple both of a and of b. Since it is a multiple, it can be divided by a and b without a remainder. If either a or b is 0, so that there is no such positive integer, then lcm(a, b) is defined to be zero. To find the LCM, you will need to do prime-factorization. Then multiply all the factors (pick the highest power of the common factors).
Every common divisor of a and b is a divisor of
gcd(a, b).
Volume of Cylinder
height * π *r^2
In any evenly spaced set the arithmetic mean (average) is equal to the median and can be calculated by the formula
mean = median = (a1+aN) / 2
The product of n consecutive integers is always divisible by
n!
The number of trailing zeros in the decimal representation of n!, the factorial of a nonnegative integer n, can be determined with this formula:
n/5 + n/5^2 + n/5^3 + ... + n/5^k
Finding the number of powers of a prime number P, in the N!.
n/p + n/p^2 + n/p^3... till p^x < n
POSITIVE AND NEGATIVE NUMBERS: Multiplication
positive * positive = positive positive * negative = negative negative * negative = positive
POSITIVE AND NEGATIVE NUMBERS: Division
positive / positive = positive positive / negative = negative negative / negative = positive
The sum of the elements in any evenly spaced set is given by:
sum = (a1+aN)/2 * N or (2a1 + d(n-1)) / 2 * n
Sum of n consecutive integers equals
the mean multiplied by the number of terms,
Area of a circle
π * r^2
Length of diagonal for square
√2 * side
Height in Equil Triangle
√3/2 * side
Perfect Square
A perfect square, is an integer that can be written as the square of some other integer. For example 16=4^2, is an perfect square. There are some tips about the perfect square: • The number of distinct factors of a perfect square is ALWAYS ODD. • The sum of distinct factors of a perfect square is ALWAYS ODD. • A perfect square ALWAYS has an ODD number of Odd-factors, and EVEN number of Even-factors. • Perfect square always has even number of powers of prime factors.
If a number equals the sum of its proper divisors, it is said to be a perfect number.
Example: The proper divisors of 6 are 1, 2, and 3: 1+2+3=6, hence 6 is a perfect number.
EVEN+EVEN
EVEN
ODD+ODD
EVEN
ODD*EVEN
EVEN *
EVEN*EVEN
EVEN2
If P is a prime number and P is a factor of AB then
P is a factor of A or P is a factor of B.
If is a positive integer greater than 1, then there is always a prime number
P whth N<P<2N
Even and Odd Numbers: Addition / Subtraction
even +/- even = even; even +/- odd = odd; odd +/- odd = even.