Math Notes for Gmat
Combination v permutation
Combination order doesn’t matter
Permutation order matters
Permutation
-can be with replacement, which means same probability every time
N x n x n x n (r times)
-Without replacement: decrease in possibilities: n x (n-1) x(n-2) etc (n!/(n-r)!)
Combination
Without repetition (like lottery): you assume its permutation then you divide by r! (there are r! ways to arrange when order counts)
(n!/ r!(n-r)!)
the sum of the angles in any polygon is 180 x (number of angles -2) the variance is the average of the squared differences between mean and number (the standard deviation is the √variance) interest = principle x rate x time, x0=1 the diagonal in a rectangle = √(L2+l2) the sum and difference of two even numbers or two odd numbers is even consecutive even integers are expressed as 2n, 2n+2, 2n+4; odd is 2n+1, 2n+3… thousands, hundreds tens ones (units). Tenths hundredths thousandths, which means 0.321 = 3/10 + 2/100 + 1/1000 mode is the number that occurs most frequently range: greatest number – lowest scientific notation is written n x 10a median of an even number of numbers is the average of the two middle items, median of an odd number of numbers is the middle number number the more the data is spread away from the mean the greater the standard dev. 0!=1!=1
Pobability of E or F = Probability of E + Probability of F – Probability (E and F), when P(E and F)= 0, E and F are called mutually exclusive when A and B are independent the occurance of one has no effect on the other (calculate the occurance of one then calculate it knowing that the other event took place and check whether the probability is the same)
a2-b2= (a-b) (a+b) ax2+bx+c=0 then x = (-b+√(b2-4ac))/2a or x=(-b-√(b2-4ac))/2a xr/s = s√xr
when dealing with inequalities < or >, and multiplying or dividing with (-) you need to invert the symbol
1/8 = 12.5% 1/6= 16.6 % 1/9 = 11.1% 1/3=33.3%
Combination order doesn’t matter
Permutation order matters
Permutation
-can be with replacement, which means same probability every time
N x n x n x n (r times)
-Without replacement: decrease in possibilities: n x (n-1) x(n-2) etc (n!/(n-r)!)
Combination
Without repetition (like lottery): you assume its permutation then you divide by r! (there are r! ways to arrange when order counts)
(n!/ r!(n-r)!)
the sum of the angles in any polygon is 180 x (number of angles -2) the variance is the average of the squared differences between mean and number (the standard deviation is the √variance) interest = principle x rate x time, x0=1 the diagonal in a rectangle = √(L2+l2) the sum and difference of two even numbers or two odd numbers is even consecutive even integers are expressed as 2n, 2n+2, 2n+4; odd is 2n+1, 2n+3… thousands, hundreds tens ones (units). Tenths hundredths thousandths, which means 0.321 = 3/10 + 2/100 + 1/1000 mode is the number that occurs most frequently range: greatest number – lowest scientific notation is written n x 10a median of an even number of numbers is the average of the two middle items, median of an odd number of numbers is the middle number number the more the data is spread away from the mean the greater the standard dev. 0!=1!=1
Pobability of E or F = Probability of E + Probability of F – Probability (E and F), when P(E and F)= 0, E and F are called mutually exclusive when A and B are independent the occurance of one has no effect on the other (calculate the occurance of one then calculate it knowing that the other event took place and check whether the probability is the same)
a2-b2= (a-b) (a+b) ax2+bx+c=0 then x = (-b+√(b2-4ac))/2a or x=(-b-√(b2-4ac))/2a xr/s = s√xr
when dealing with inequalities < or >, and multiplying or dividing with (-) you need to invert the symbol
1/8 = 12.5% 1/6= 16.6 % 1/9 = 11.1% 1/3=33.3%