GMAT
1/7 (what's the decimal?)
0.1428
a^(-b) =
1 / (a^b)
combined work question formulas: more than 2 workers?
1 / T = 1 / A + 1 / B + 1 / C ....
Overlapping sets questions strategy?
(1) Table (2) Venn diagram if more than 2 sets (3) formula: Total = Group 1 + Group 2 - Both + Neither
6 children (ABCDEF) are to be seated on a row of 6 chairs. A and E cannot sit next to each other. How many different arrangements?
(1) calculate cases where A and B do sit together. AE can be arranged in 10 different ways (AE or EA in 5 different ways) the rest of the children can sit in 4! ways (2) total number of arrangements: 6! = 720 answer is (2) - (1)
5 distinguishable wires. 2 cable wires and 3 phone wires. How many combinations of 3 wires with at least 1 of the wires being cable?
(1) total combos: ⁵C₃ (2) number of combos of 3 wires with 3 phone wires: 1 (as this is combination and not permutation) answer is (1) - (2)
how do you solve an inequality in absolute signs? e.g. |4x - 2| < 10
(4x - 2) < 10 AND (4x - 2) > -10
how do you solve an equation in absolute signs? e.g. |4x - 2| = 10
(4x - 2) = 10 AND (4x - 2) = -10
Distance (how it relates to speed) =
(S)(T)
number of terms in a sequence of evenly spaced integers e.g. by space of 3
(largest - smallest)/(3+1)
Polygons with n sides sum of interior angles = ?
(n-2)(180°)
To calculate number of arrangements where some of the elements are indistinguishable e.g.(1) possible 7-digit codes out of a choice of 3A's, 2B's, 1C and 1D e.g.(2) probability of 2 heads in a series of 3 coin tosses
(total number of arrangements) / (Factorial of number of indistinguishable elements) e.g.(1) 3A's and 2B's are indistinguishable hence 7! / (3! x 2!) e.g.(2) a specific combination has the probability of 0.5 x 0.5 x 0.5 = 0.125 (or 1/8). Multiply this by number of ways of arranging HHT, which is 3! / (2! x 1!) = 3. Answer is 0.125 x 3 = 0.375
(x^z)(y^z)
(xy)^z
√(a+b) ≠
(√a) + (√b)
√(a−b) ≠
(√a) - (√b)
√(a/b) =
(√a) / (√b)
√ab = ?
(√a) x (√b)
what is the sum of differences between each term and the average?
0
strategy for questions involving same route traveled by 2 people... 1) when leaving at different times 2) in opposite direction 3) in same direction
1) recalculate distance from the point at which both people are moving 2) sum of speeds = Distance (from time when both people are moving)/ (Time); Time = (Distance)/(Sum of speeds) 3) Difference of speeds = (Distance/Time)
What is the Kaplan method for problem solving?
1. Analyze the question 2. State the task 3. Approach strategically 4. Confirm your answer
1/9 (what's the decimal?)
0.11111
Strategy if asked for different combinations/permutations of 2 distinct groups:
separate calculation of combination/permutation by group, then multiply the 2 results
if a, b, and c are different positive prime numbers how many distinct positive factors does the product abc have?
8 (1, abc, a, b, c, ab, bc, ac)
list the prime numbers to 50
2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 37, 41, 43, 47
⁶C₃ = ?
20
how many problem solving questions are there?
22
1 foot = ? inches
12
how many data sufficiency problems are there?
15
166 foot sidewalk, plant trees evenly spaced by 14 feet, each tree takes up 1 foot. what is the max number of trees?
166/(14+1) = 11 with a remainder of 1, which means there is 1 more foot left for another tree, hence 12 trees
1 yard = ? feet
3
name all known right triangles and their dimensions
3:4:5 (and proportional) 5:12:13 (and proportional) 7:24:25 8:15:17 9:40:41 isosceles right triangle: x:x:x√2 30-60 right triangle: x:x√3:2x
4! = 7! = 1! = 0! =
4! = 4 x 3 x 2 x 1 = 24 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 1! = 1 0! = 1
1 mile = ? feet
5,280
How to convert 25⁷ x 4⁸ into the format A x 10^b?
5¹⁴ x 2¹⁶ = 2² x 2¹⁴ x 5¹⁴
Parallelogram area and properties:
Base x Height opposite sides are equal opposite angles are equal diagonals bisect
FAST strategy for system of 2 equations, 2 variables
COMBINATION: add or subtract one equation from the other to cancel out one of the variables
speed =
D/T
multi part journeys involving speeds: what strategy should be used?
DTS table
Even x any number =
Even
Even ± Even =
Even
Even^(positive integer) =
Even
Odd ± Odd =
Even
Strategy if asked for number of outcomes using combination and then imposing a rule. e.g. choose 4 out of a set of 8 people BUT at least 1 of Jane and Austin needs to be in the 4 chosen
First calculate total outcomes using combination rule, then deduct the number of outcomes where the rule does not apply. ⁸C₄ - ⁶C₄ = 70 - 15 = 55
Area = ?
Length X Width
Even ± Odd =
Odd
Probability of A is p and probability of B is q. what is the probability of one of A or B occurring?
P(A and not B) + P(B and not A) = p(1-q) + q(1-p) = p + q - 2pq
Probability of event A or event B (assuming A and B are independent)
P(A) + P(B) - P(A and B) P(A) + P(B) - P(A) x P(B)
Probability of events A and B
P(A) x P(B)
trapezoid area?
[(1/2)(sum of bases)](height)
(√a)² =
a
if a triangle is incribed in a circle so that on of its sides is a diameter of the circle, then the triangle is:
a right triangle
√a
a^(1/2)
a^b x a^c =
a^(b+c)
a^b / a^c =
a^(b-c)
if given a ratio for item x to item y as a:b and then a separate ratio for item y to item z as c:d then what is ratio of item x to item z?
ac:bd
divisibility test by 6...
both divisible by 2 and by 3
if the order doesn't matter, it is a _____. if the order does matter, it is a ____.
combination, permutation
0 is an ___ integer.
even
2 is the only ___ prime number
even
addition rules for odd and even numbers
even + even = even even + odd = odd odd + odd = even
multiplication rules for odd and even numbers
even x even = even even x odd = even odd x odd = odd
what is the exterior angle theorem for triangles?
exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle
if given a rectangle's area and perimeter...
find area's factors and see which ones add up to perimeter ÷ 2
Strategy for a code which needs to contain a combination of certain specific numbers as well as indistinguishable numbers e.g. 6-digit code where 1 digit is a 3, 2 digits are 4, 1 digit is 5 AND the each other digit is 7 or 8
for combination of specific numbers, think of (1) ways in which the given numbers can be ordered (e.g. for 7 and 8, this would be 7:8, 7:7, 8:8, 8:7) and then the ways in which they can be put into the required spaces (e.g. ⁶C₂ or 15). Multiply the 2. For the other numbers, use the factorial divided by factorials of duplicates e.g. 4 remaining numbers to place where 2 numbers are duplicates means 4! / 2!. Multiple 2 results.
how do you solve x + 6 < |x| ?
if x is positive: x+6< x (not possible) if x is ): 6<0 (not possible) if x is negative: x+6<-x (x<-3)
perfect square?
is an integer which is the square of an integer
what and how many are the prime factors of a prime number?
itself. there is only 1 prime factor as 1 is not a prime number.
number of terms in a sequence of consecutive integers =
largest - smallest + 1
if a number N has to be a multiple of one of the answers and we know N is a multiple of x and y, then what should you look for?
look for the least common multiple of x and y. LCM is a multiple of the answer
sum of sequence of consecutive or evenly spaced integers
multiply the avg of largest and smallest term by the number of terms
the remainder of n / 3 is 1. what does this imply?
n = 3x +1 or (n-1) is a multiple of 3
permutation formula:
n! / (n - k)! where n is the number of things to choose from, and we choose k of them (no repetition, order matters)
combination formula:
n! / [k! (n - k)!] (n + k - 1)!/ r!(n-1)! (without repetition)
when a negative number is raised to an odd exponent, the result is
negative
is zero positive or negative?
neither one nor the other
what is the mode of a set of data?
number appearing the most
divisibility test by 8...
number formed by the last 3 digits is divisible by 8, including 000
rule for divisibility by 4
number formed by the last two digits is divisible by 4 (including 00)
what does the permutation formula give?
number of ORDERED subgroups of k items that can be selected from a group of n different items
what does combination formula give?
number of UNORDERED subgroups of k items that can be selected from a group of n different items
odd^(positive integer) =
odd
which only combinations of 2 terms yield odd numbers?
odd x odd odd + even
when a negative number is raised to an even exponent, the result is...
positive
define a prime number
positive integer greater than 1 that is divisible only by 1 and itself
integer is ...
positive whole numbers, zero, and negative whole numbers
if a and b are integers greater than 1, their product cannot be ___.
prime
combined work question (same task performed by several people): what strategy should be used?
rate = (number of tasks) / (time to complete tasks) 2 workers: T = (AB)/(A+B)
slope of 2 point in a coordinate plane =
rise/run = (y₂ - y₁) / (x₂ - x₁)
divisibility test for 7
separate the units digits from the rest of the number, then multiply that unit digit by 2. subtract from what's left of the original number. if the result is a multiple of 7 or 0, the original number is a multiple of 7.
raising a positive fraction less than 1 to a positive exponent greater than 1 results in a ____ value. the higher the exponent, the ___ the result.
smaller value, smaller
what is the root of an equation?
solution
standard deviation =
square root of average squared difference with mean
divisibility test by 9...
sum of the digits is divisible by 9
a line with exactly 1 point in common with a circle is ______ and is ____ with reference to the radius
tangent to the circle and is perpendicular to the radius
in a mixed fraction, what is the same as the numerator?
the remainder
average speed =
total distance / total time
x^a x x^b
x^(a+b)
(x^a)^b
x^ab
(x+y)(x-y)
x² - y²
can you derive an overall average from weighted averages?
yes