GMAT Math

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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.


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