Term
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Definition
In general …
• Medium questions require 2 steps to solve.
• Difficult questions require at least 3 steps.
• The GMAT begins with a medium question. |
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Term
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Definition
Start with Choice ‘E’ and work back to ‘A’ when
backsolving from the answer choices. |
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Term
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Definition
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. |
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Term
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Definition
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Term
How to Check Whether Number
is Multiple of 3 |
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Definition
| Sum of digits is multiple of 3. |
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Term
How to Check Whether Number
is Multiple of 4 |
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Definition
Last two digits are multiple of 4.
The number can be divided by 2 twice. |
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How to Check Whether Number
is Multiple of 6 |
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Definition
| Number is multiple of 3 and 2. |
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Term
How to Check Whether Number
is Multiple of 9 |
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Definition
| Sum of digits is multiple of 9. |
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Term
How to Check Whether Number
is Multiple of 12 |
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Definition
| Sum of digits is multiple of 3, last two digits multiple of 4. |
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Term
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Definition
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.
CORRECT: 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 |
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Term
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Definition
| (# of favorable outcomes)/(# of possible outcomes) |
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Term
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Definition
| Gross profit = Selling Price – Cost |
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Term
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Definition
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) |
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Term
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Definition
Two events are said to be dependent events if the outcome
of one event affects the outcome of the other event. |
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Term
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Definition
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. |
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Term
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Definition
The number of ways independent events can occur
together can be determined by multiplying together the
number of possible outcomes for each event. |
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Term
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Definition
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. |
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Term
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Definition
Complementary Events: The probability of an event
occurring plus the probability of the event not
occurring = 1.
P(E) = 1 – P(not E) |
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Term
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Definition
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
already occurred.
P(A and B) = P(A) × P(B|A) |
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Term
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Definition
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) |
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Term
| Probability of Multiple Events |
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Definition
Rules:
• A and 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” |
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Term
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Definition
To find the number of distinct permutations of a set of
items with indistinguishable (“repeat”) items, divide the
factorial of the items in the set by the product of the factorials
of the number of indistinguishable elements.
Example: How many ways can the letters in TRUST
be arranged?
CORRECT:
Probability of Multiple Events
Rules:
• 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”
5!
2!
= 60
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Term
| Combinations: Order doesn’t matter |
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Definition
nCr = n!/r!(n-r)!
n = number of items
r = number of items chosen |
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Term
| Permutations: Order matters |
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Definition
Number of permutations of r objects from a set of
n objects:
nPr = n!/r!(n-r)!
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Term
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Definition
The number of ways to arrange n distinct objects along a
fixed circle is: (n – 1)! |
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Term
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Definition
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. |
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Term
| Multiple Event Probability |
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Definition
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. |
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Term
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Definition
Look at the probability of NOT OCCURRING.
P(Event Not Occurring) = 1 – P(Event Occurring) |
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Term
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Definition
y = mx + b
m = slope = (difference in y coordinates)/(difference in x coordinates) |
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Term
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Definition
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Term
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Definition
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) |
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Term
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Definition
| Odd numbers have only odd factors. |
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Term
| Purchase Price vs. Market Value |
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Definition
Remember: purchase price is not the same as market value.
Purchase Price = price purchased for by wholesaler
Market Value = price sold for by retailer (after markup) |
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Term
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Definition
To find roots of quadratic equation:
ax2+ bx + c = 0
x = [−b ± √b2 − 4ac ]/2a |
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Term
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Definition
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Term
Prime Factorization:
Greatest Common Factor (GCF) |
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Definition
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. Greatest Common Factor (GCF) 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 |
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Term
Prime Factorization:
Lowest Common Multiple (LCM) |
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Definition
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 |
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Term
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Definition
1. Pick a number n.
2. Start with the least prime number, 2. See if 2 is a factor
of your number. If it is, your number is not prime.
3. If 2 is not a factor, check to see if the next prime, 3, is a factor. If it
is, your number is not prime.
4. Keep trying the next prime number until you reach one that is a
factor (in which case n is not prime), or you reach a prime
number that is equal to or greater than the square root of n.
5. If you have not found a number less than or equal to the square
root of n, you can be sure that your number is prime. |
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Term
| Rate × Time = Distance (rt = d) |
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Definition
For a fixed distance, the average speed is inversely related
to the amount of time required to make the trip.
CORRECT: Since Mieko’s average speed was 3/4 of
Chan’s, her time was 4/3 as long.
rt = d
CORRECT:(3/4) r (4/3) t = d |
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Term
| Factoring Exponents Example |
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Definition
5k - 5k−1
5k - (1/5)5k
(1− 1/5)5k
(4/5)5k |
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Term
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Definition
When positive fractions between 0 and 1 are squared,
they get smaller.
(1/4)2 = (1/16) |
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Term
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Definition
Square root of 2 = 1.4
Square root of 3 = 1.7 |
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Term
| Inscribed Angle, Minor Arc |
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Definition
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