Quantitative Flashcards
Volume of a cylinder
V=pi (r^2) h
Area of a circle
pi(r^2)
What happens to the mean, median and standard deviation if x is added to each score?
Mean and median are increased by x but standard deviation stays the same
Sum of the interior angles of any polygon
180(n-2) where n is the number of sides
Prime numbers up to 20
2,3,5,7,11,13,17,19
Integer
Includes 0
Improper fraction
Numerator is larger than the denominator
Mixed number
Mix of a whole number and a fraction
Reciprocal
Upside down version of the fraction
17/51
1/3
Least common denominator
Lowest common multiple of the denominators of two fractions
1/6
0.166666
5/6
0.83333
1/7
0.14
1/8
0.125
3/8
0.375
5/8
0.625
7/8
0.875
1/9
0.11111
17/85
1/5
1/11
0.91
Linear equation
An equation in which the variables aren’t modified by exponents or roots
How to determine if an equation is solvable?
Both equations are linear and distinct
How to solve a quadratic equation?
Find two numbers which add to give the coefficient on the x term and multiply to give the constant
Factors for difference of squares: x^2 - y^2
(X+y)(x-y)
Quadratic equation
[ -b +/- root(b^2 -4ac) ] /2a
Square root of 225
15
When to change the direction of an equality sign
When dividing or multiplying by a negative number
How to work with 3 part inequalities?
Each part has the operation done to it (addition, subtraction, multiplication and division)
Integer
Integer is a number that can be written without fractional or decimal component.
Bisect
To divide in two equal parts
Area of a triangle
1/2 b * h
When measuring for area of a triangle base and height must be perpendicular
–
No side of a triangle can be greater than or equal to the sum of the other two
–
No side of a triangle can be less than or equal to the difference of the other two sides
–
Pythagorean triplets (3 sets)
3: 4:5
5: 12:13
7: 24:25
Lengths of a 45:45:90 triangle (diagonal of a square)
X:x:[x root 2]
Lengths of a 30:60:90 triangle (splitting an equilateral triangle)
X: [x root 3] : 2x
Area of a trapezoid
(B1+b2)/2 * h where b1 and b2 are the lengths of the parallel lines
Circumference of a circle
2pi(r) or 2pi(d)
To find arcs and sectors
Multiply the normal area and circumference formulas by angle/360
Chord
A chord is a line connecting two points on a circle but it is not necessarily the diameter of the circle
Surface area of a rectangular solid
2(lw) + 2(lh) + 2(wh)
Surface area of a cylinder
2pi(r)(h) + 2pi(r^2)
Equation for slope
Y2-y1/(x2-x1)
Bisect
Cut in half
Sum of the interior angles of a polygon
180(n-2)
Adding or subtracting from a ratio
Write the ratio as a fraction and subtract or add only from the group that is changing.
Work equation to use when given the time to complete a task
(A*B)/(A+B)
Prime number
Any number that is divisible only by 1 and itself. Does not include 1.
How many even prime numbers are there?
Only one: 2
How to check if a number is prime?
Check if it is divisible by all the numbers less than its closest square root
How to tell if a number is divisible by 3
Add all of the digits and see if that number is divisible by 3
How to tell if a number is divisible by 4
Check if last two digits are divisible by 4
How to tell if a number is divisible by 6?
Divisible by 2 and 3
How to tell if a number is divisible by 9
Check if the sum of digits is divisible by 9
How to calculate how many factors a number has
Find the prime factorization. Find the powers and add one to each. Multiply the resulting numbers.
Square of an integer is defined by having an even number of all its prime factors
How to find the least common multiple
Find the prime factorization of both numbers, and then find every unique prime number and raise that to the highest power in either of the two numbers.
Is zero an even number?
Yes.
In a series of consecutive numbers, the average and the median are the same
Consecutive numbers
Numbers that are evenly spaced
Sum of consecutive numbers
Find the midpoint and multiply by the number of terms
Consecutive odds
Odd numbers right after each other
Opposite to a remainder?
Quotient
Equation to find quotient, remainder or divisor
X=qy + r
How to find common remainders
Find lowest common remainder for the two equations and then add the lowest common multiple of the two divisors
If x,y,z are consecutive integers…
Both the sum and product will be divisible by 3
Range
Difference between the largest and smallest numbers in a set
Standard deviation
Square root of Average of the differences between value and mean
What happens if you had a value to every number in a set?
Average is increased but standard deviation is the same.
What happens if you multiply every number in a set?
Standard deviation increases or decreases by that same number.
Equation for combined sets
Total = group 1 + group 2 - both + neither
Permutation equation
N!/(n-k)!
When one of the spots of a permutation is fixed…
Use the visual method
0! Equals
1
Circular permutation problem
Find the number of unique rows and divide by the number of duplicates. Becomes (n-1)!
If you have to find the dofference of the squares of two large numbers
You the difference of squares to simplify
Circle inside an equilateral triangle…
Radius will bisect the angles.
Find all factors of a number
Find the prime factorization. List all the exponents. Add one to each of the exponents. Multiply the resulting numbers.
Which numbers should you pick for data sufficiency when looking at exponents with no efficients?
-1, 0, 1. Pick numbers within those ‘zones’
Disjoint set
Two sets that have no elements in common (mutually exclusive)
Polygon
Closed plane figure formed by three or more line segments
Altitude
Segment drawn from a vertex perpendicular to the side opposite that vertex
Inscribed in a circle…
Each vertex of a polygon lies on a circle
Circumscribed…
Each side of a polygon is tangent to a circle
To find the distance between two points in the coordinate plane…
Use the Pythagorean theorem
Equation to calculate rate at which two people or machines work together
Add the two rates together
E +/- E
E
E +/- O
O
O +/- O
E
E * E
E
E * O
E
O * O
O
X^y + X^y
2x^y
X^-y
1/x^y
(X^y)(x^z)
X^(y+z)
(X^y)^z
X^(y*z)
X^(1/2)
Rt(x)
R2
1.4
R3
1.7
R(xy)
R(x)*r(y)
11*11
121
13*13
169
14*14
196
15*15
225
Adding radicals
Must have the same base (e.g r2 and r2)
Squares of non primes
16, 36, 64, 81
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144
Numbers under 100 with several prime factors
30, 42, 60, 78, 84
Number under 100 that is the square of an integer and a cube of an integer
64
Numbers above 1 that are squares of an integer and squares of squares
16, 81
Smallest numbers with at least 3 prime factors
30 and 42
How to determine what the divisor is or what the remainder is
Find the fractional element and simplify to the smallest possible value. The remainder must be a multiple of this number. The divisor is the denominator associated with the correct remainder.
Dividend
Number being divided by a divisor to produce a quotient and a remainder
To be a perfect square…
A number must have an even number of each of its prime factors (see 155 gmat book)
Formula to find the sum of the first n integers
N(n+1)/2
In any reflection through the line y=x the x coordinate and y coordinate
Become interchanged
125 of 1000
1/8
Z^2<4
-2<2
M>2N
Does not imply M>N…
A number has only one prime factor…
It is either prime or a prime number raised to an integer power
Is r and integer if r^2 is an integer?
Don’t know
How many numbers between 1 and 20 inclusive? How many numbers between 50 and 70 inclusive
20 and 21.
3 consecutive numbers will have the following properties
Sum is divisible by 3 and product is divisible by 3
Z^2<4
-2<2
M>2N
Does not imply M>N…
A number has only one prime factor…
It is either prime or a prime number raised to an integer power
Is r and integer if r^2 is an integer?
Don’t know
How many numbers between 1 and 20 inclusive? How many numbers between 50 and 70 inclusive
20 and 21.
3 consecutive numbers will have the following properties
Sum is divisible by 3 and product is divisible by 3
