GRE Quant Topics

Properties of 0

neither positive or negative, even, multiple of every integer, cannot divide by 0, 0! = 1, x^0 where x doesn’t equal 0 is 1

Adding subtracting inequality systems

a + b > 11

a > 12 + b

Then you can set up: a+b > 11 and a-b > 12.

Add these up to get 2a > 23 and a > 11.5

We can do this since the inequalities are facing the same direction

Permutations

“choice method”

order matters

formula: n! / (n-r)!

always greater than combinations

Combinations

order doesn’t matter

formula = n! / r!(n-r)!

How to calculate arrangements in a circle

(n-1)!

Probability + Combinatorics

ex) What is the probability of flipping exactly 3 heads in 5 coin flips?

answer) (1/2)^5 times 5!/(3!2!)

ie) find the probability of each outcome you want and multiply it by number of ways you can arrange the total with repeats

Mutually Exclusive (A and B events)

P(A and B) = 0. P (A or B) = the sum of their probabilities

Independent (A and B events)

the outcome of each event doesn’t depend on the other and can happen simultaneously - ex) flipping two coins, flipping a die and a coin

P(A or B) = P(A) + P(B) - P(A and B)

If not told whether independent or mutually exclusive…

need to consider extremes…

• if they are mutually exclusive

• if one is completely subsumed in another

Inclusion - Exclusion Principle

Total = A + B - AB + neither

Total = A + B+ C - exactly two - 2(A, B, and C)

If x > 1

sqrt(x) < x < x²

If 0 < x < 1

x² < x < sqrt(x)

If b is 300% of a…

then b = 3a

If b is 300% MORE than a…

b = 4a

Relative speed

if going in opposite directions: add their respective speeds

if going in the same direction: subtract their respective speeds