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36 Cards in this Set

  • Front
  • Back
Steps to Solve
In general…
• Medium questions require 2 steps to solve.
• Difficult questions require at least 3 steps.
• The GMAT begins with a medium question.
Assuming
• All numbers on the GMAT belong to the set of real numbers.

• Unless you’re explicitly told that a specific type of number is involved, do not make any further assumptions.

• For example, do NOT assume that variables represent positive integers.
How to check whether number
is multiple of 3
• Sum of digits is multiple of 3
Backsolving Strategy
• Start with Choice (E) and work back to (A) when backsolving from the answer choices.
Multiple
• Multiples of 3:
3, 6, 9…
How to check whether number
is multiple of 4
• Last two digits are multiple of 4.

• The number can be divided by 2 twice.
How to check whether number
is multiple of 6
• Number is multiple of 3 and 2.
How to check whether number
is multiple of 12
• Sum of digits is multiple of 3, last two digits multiple of 4.
Simple Probability
(# of favorable outcomes)/
(# of possible outcomes)
How to check whether number
is multiple of 9
• Sum of digits is multiple of 9.
Common Factor
• Break down both numbers to their prime factors to see what factors they have in common.
Multiply shared prime factors to find all common factors.

EX.
What factors greater than 1 do 135 and 225 have in common?
135 = 3 x 3 x 3 x 5
225 = 3 x 3 x 5 x 5
• Both share 3 x 3 x 5 in common—find all combinations of these numbers: 3 x 3 = 9;
3 x 5 = 15; 3 x 3 x 5 = 45
Gross Profit
• Gross profit = Selling Price – Cost
Combined Events
For events E and F:
• not E = P(not E) = 1 – P(E)
• E or F = P(E or F) = P(E) + P(F) – P(E and F)
• E and F = P(E and F) =
P(E)P(F)
Permutations
• Counting the number of ways that a set of objects can be ordered:
n!
Multiplication Principle
• If a first object may be chosen in m ways and a second object may be chosen in n ways, then there are mn ways of choosing both objects.
Combinations
• If order of selection is not relevant and only k objects are able to be selected from a larger set of n objects:

n
k = n!/k! (n-k)!
n
k = n/n - k
Multiplication Principle
• The number of ways independent events can occur together can be determined by multiplying together the number of possible outcomes for each event
1st Rule of Probability
• Basic rule: The probability of event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes.
2nd Rule of Probability
• Complementary Events: The probability of an event occurring plus the probability of the event not occurring = 1.
• P(E) = 1 – P(not E)
3rd Rule of Probability
• Conditional Probability:
The probability of event A AND event B occurring is the probability of event A times the probability of event B, given that A has all ready occurred.
4th Rule of Probability
• The probability of event A OR event B occurring is the probability of event A occurring plus the probability of event B occurring minus the probability of both events occurring.
• P(A or B) = P(A) + P(B) – P(A and B)
Dependent Events
• Two events are said to be dependent events if the outcome of one event affects the outcome of the other event.
Probability of Multiple Events
• A and B < A or B
• A or B > Individual probabilities of A, B

• P(A and B) = P(A) x P(B)  “fewer options”
• P(A or B) = P(A) + P(B)  “more options”
Indistinguishable Events
• To find the number of distinct permutations of a set of items with indistinguishable items, divide the factorial of the items in the set by the product of the factorials of the number of indistinguishable elements.

• How many ways can the letters in TRUST be arranged?

• Complementary Events: The probability of an event occurring plus the probability of the event not occurring = 1.
• P(E) = 1 – P(not E)
• Conditional Probability: The probability of event A AND event B occurring is the probability of event A times the probability of event B, given that A has all ready occurred.
Ex: 5!/2! = 60
Circular Permutations
• The number of ways to arrange n distinct objects along a fixed circle is: (n – 1)!
Probability and Geometry
• If a point is chosen at random within a space with an area, volume, or length of Y and a space with a respective area, volume, or length of X lies within Y, the probability of choosing a random point within Y is the area, volume, or length of X divided by the area, volume, or length of Y.
Multiple Event Probability
To determine multiple-event probability where each individual event must occur in a certain way:
• Figure out the probability for each individual event.
• Multiply the individual probabilities together.
Trial Problems
• Look at the probability of NOT OCCURRING.
P(Event Not Occurring) =
1 – P(Event Occurring)
Combinations:
Order doesn’t matter
n!/r! (n – r)!
Permutations: Order matters
n!/(n – r)!
Number Added or Deleted
Use mean to find number that was added or deleted.
• Total = mean x (number of terms)
• Number deleted = (original total) – (new total)
• Number added = (new total) – (original total)
Odd Factors
• Odd numbers have only odd factors.
Purchase Price vs. Market Value
• Remember: purchase price is not the same as market value.
Quadratic Formula
• To find roots of quadratic equation,
Prime Factorization:
Highest Common Factor (HCF)
1. Start by writing each number as product of its prime factors.
2. Write so that each new prime factor begins in same place.
3. Highest Common Factor is found by multiplying all factors appearing on BOTH lists.
60 = 2 x 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
HCF = 2 x 2 x 3 = 12
Prime Factorization:
Lowest Common Multiple (LCM)
1. Start by writing each number as product of its prime factors.
2. Write so that each new prime factor begins in same place.
3. Lowest common multiple found by multiplying all factors in EITHER list.
60 = 2 x 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
LCM = 2 x 2 x 2 x 3 x 3 x 5 = 360