GMAT Math Latest Updated Graded A+
2 Sets, 3 Choices: Still a Double-Set Matrix - ANSWER-As long as each set of distinct
options is *complete* and has *no overlaps* you can extend the chart.
Y N Maybe Total
Female
Male
2 Types of "Or" Probability Problems - ANSWER-1) If an OR problem features events
that CANNOT occur together, then you can find the OR probability by adding the
probabilities of the 2 events. P (A or B) = P(A) + P(B)
2) If an OR problem features events that CAN occur together, then you use formula:
P(A or B) = P(A) + P(B) - P(A and B)
2nd Rule of Probability: Complementary events - ANSWER-Complementary Events:
The probability of an event occurring plus the probability of the event not occurring = 1.
P(E) = 1 - P(not E)
3-Set Problems: Venn Diagrams - ANSWER-3 overlapping sets are usually teams or
clubs, and each person is either on or not on any given team/club.
Only use Venn diagram problems with THREE SETS.
Work from the inside out - fill in the innermost section, then the middle section, the
outer.
30-60-90 Triangle - ANSWER-30-60-90
x (shorter leg), x(sqrt 3) (longer leg), 2x (hypotenuse)
3rd Rule of Probability: Conditional Probability - ANSWER-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)
4-Step Process of Factoring Terms When Adding/Subtracting Exponents - ANSWER-1)
Simplify/factor any additive or subtractive terms
2) Break down every non-prime base into prime factors
3) Distribute the exponents to every prime factor
4) Combine the exponents for each prime factor and simplify
45-45-90 Triangle - ANSWER-45-45-90
x (shorter legs), x(sqrt 2) (hypotenuse)
4th Rule of Probability: Probability of A OR B - ANSWER-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)
A Common Digits Problem - ANSWER-A Common Digits Problem
BA => 47 or 83
+AB +74 +38
CDC 121 121
A and B = 4 and 7 OR 3 and 8
Adding Fractions - ANSWER-1) Multiply numerator + denominator by integers that lead
to a greatest common denominator
Ex: 3/5 + 4/7 --> multiply both sides by 7/7 -->
add with denominator of 35
2) Cross-multiply
Ex: a/b + x/y --> (ay + bx)/by
Age Chart - ANSWER-Then Now Future
Person 1
Person 2
Always Try to Factor! - ANSWER-ex: x^3 − 2x^2 + x = −5(x − 1)^2
x(x^2 − 2x + 1) = −5(x − 1)^2
x(x − 1)2 + 5(x − 1)^2 = 0
(x + 5)(x − 1)^2 = 0
x = −5, 1
Approximations of Common Square Roots - ANSWER-Square root of 2 = 1.4
Square root of 3 = 1.7
Square root of 5 = 2.25
Area Equilateral Triangle - ANSWER-base = length S height = S(sqrt 3)/2
A = (S^2[sqrt 3])/4
Think A = S - 2 - 3 - 4
Area of a Circle and Sectors - ANSWER-A = π(r^2)
Sector: determine fraction of entire area that sector occupies by finding central angle,
then find that fraction of the circle's area.
Ex: Area = 9π, central angle = 60, sector area = 60/360 x 9π = 3/2(π)
Area of a Rhombus - ANSWER-A = bh OR
A = [(d1)(d2)]/2
Area of Trapezoid - ANSWER-A = (sum of bases)(height)/2
A = {[(b1 + b2)/2](height)}/2
, Arithmetic Sequence - ANSWER-The difference between successive terms is always
the same.
Sn = kn + x
k = constant difference between successive terms
n = number of terms
x = some other constant (based on starting # or s0)
Arithmetic with Remainders - ANSWER-1) You can add/subtract remainders directly, as
long as you correct excess or negative remainders
2) You can multiply remainders, as long as you correct excess remainders
Ex: x/6 has an R of 2, and y/6 has an R of 5. What is the R of 2x + y / 6?
2(R2) + R5 = R9 - 6 = R3
Average of Consecutive Numbers - ANSWER-The average of a set of evenly spaced
consecutive numbers is the average of the smallest and largest numbers in the set.
Average Set = (Smallest + Largest)/2
Average of evenly spaced sets - ANSWER--In an evenly spaced set with an odd # of
terms, the average is the middle #
-In an evenly spaced set with an even # of terms, the average is the average of the 2
middle #s
-Can just add 1st and last terms and divide by n
Average Rate - ANSWER-*If object moves same distance twice but at different rates,
the avg rate will NEVER be the average of the 2 rates for the 2 legs of the journey. The
avg rate will be closer to the rate spent longer on.
*To find avg rate, find TOTAL combined time for trips and TOTAL combined distance
(can pick #)
Average Rate - ANSWER-Average A per B = (Total A)/(Total B)
Average Speed = (Total Distance)/(Total Time)
Average Rate Chart - ANSWER-Rate x Time = Distance
Going r1 t1 d (pick #)
Returning r2 t2 d (pick #)
Total ? 2d
Average x n = Sum Table - ANSWER-Average x number = Sum
Old
New
Total
2 Sets, 3 Choices: Still a Double-Set Matrix - ANSWER-As long as each set of distinct
options is *complete* and has *no overlaps* you can extend the chart.
Y N Maybe Total
Female
Male
2 Types of "Or" Probability Problems - ANSWER-1) If an OR problem features events
that CANNOT occur together, then you can find the OR probability by adding the
probabilities of the 2 events. P (A or B) = P(A) + P(B)
2) If an OR problem features events that CAN occur together, then you use formula:
P(A or B) = P(A) + P(B) - P(A and B)
2nd Rule of Probability: Complementary events - ANSWER-Complementary Events:
The probability of an event occurring plus the probability of the event not occurring = 1.
P(E) = 1 - P(not E)
3-Set Problems: Venn Diagrams - ANSWER-3 overlapping sets are usually teams or
clubs, and each person is either on or not on any given team/club.
Only use Venn diagram problems with THREE SETS.
Work from the inside out - fill in the innermost section, then the middle section, the
outer.
30-60-90 Triangle - ANSWER-30-60-90
x (shorter leg), x(sqrt 3) (longer leg), 2x (hypotenuse)
3rd Rule of Probability: Conditional Probability - ANSWER-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)
4-Step Process of Factoring Terms When Adding/Subtracting Exponents - ANSWER-1)
Simplify/factor any additive or subtractive terms
2) Break down every non-prime base into prime factors
3) Distribute the exponents to every prime factor
4) Combine the exponents for each prime factor and simplify
45-45-90 Triangle - ANSWER-45-45-90
x (shorter legs), x(sqrt 2) (hypotenuse)
4th Rule of Probability: Probability of A OR B - ANSWER-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)
A Common Digits Problem - ANSWER-A Common Digits Problem
BA => 47 or 83
+AB +74 +38
CDC 121 121
A and B = 4 and 7 OR 3 and 8
Adding Fractions - ANSWER-1) Multiply numerator + denominator by integers that lead
to a greatest common denominator
Ex: 3/5 + 4/7 --> multiply both sides by 7/7 -->
add with denominator of 35
2) Cross-multiply
Ex: a/b + x/y --> (ay + bx)/by
Age Chart - ANSWER-Then Now Future
Person 1
Person 2
Always Try to Factor! - ANSWER-ex: x^3 − 2x^2 + x = −5(x − 1)^2
x(x^2 − 2x + 1) = −5(x − 1)^2
x(x − 1)2 + 5(x − 1)^2 = 0
(x + 5)(x − 1)^2 = 0
x = −5, 1
Approximations of Common Square Roots - ANSWER-Square root of 2 = 1.4
Square root of 3 = 1.7
Square root of 5 = 2.25
Area Equilateral Triangle - ANSWER-base = length S height = S(sqrt 3)/2
A = (S^2[sqrt 3])/4
Think A = S - 2 - 3 - 4
Area of a Circle and Sectors - ANSWER-A = π(r^2)
Sector: determine fraction of entire area that sector occupies by finding central angle,
then find that fraction of the circle's area.
Ex: Area = 9π, central angle = 60, sector area = 60/360 x 9π = 3/2(π)
Area of a Rhombus - ANSWER-A = bh OR
A = [(d1)(d2)]/2
Area of Trapezoid - ANSWER-A = (sum of bases)(height)/2
A = {[(b1 + b2)/2](height)}/2
, Arithmetic Sequence - ANSWER-The difference between successive terms is always
the same.
Sn = kn + x
k = constant difference between successive terms
n = number of terms
x = some other constant (based on starting # or s0)
Arithmetic with Remainders - ANSWER-1) You can add/subtract remainders directly, as
long as you correct excess or negative remainders
2) You can multiply remainders, as long as you correct excess remainders
Ex: x/6 has an R of 2, and y/6 has an R of 5. What is the R of 2x + y / 6?
2(R2) + R5 = R9 - 6 = R3
Average of Consecutive Numbers - ANSWER-The average of a set of evenly spaced
consecutive numbers is the average of the smallest and largest numbers in the set.
Average Set = (Smallest + Largest)/2
Average of evenly spaced sets - ANSWER--In an evenly spaced set with an odd # of
terms, the average is the middle #
-In an evenly spaced set with an even # of terms, the average is the average of the 2
middle #s
-Can just add 1st and last terms and divide by n
Average Rate - ANSWER-*If object moves same distance twice but at different rates,
the avg rate will NEVER be the average of the 2 rates for the 2 legs of the journey. The
avg rate will be closer to the rate spent longer on.
*To find avg rate, find TOTAL combined time for trips and TOTAL combined distance
(can pick #)
Average Rate - ANSWER-Average A per B = (Total A)/(Total B)
Average Speed = (Total Distance)/(Total Time)
Average Rate Chart - ANSWER-Rate x Time = Distance
Going r1 t1 d (pick #)
Returning r2 t2 d (pick #)
Total ? 2d
Average x n = Sum Table - ANSWER-Average x number = Sum
Old
New
Total
