GMAT: Quant
(a^b)*(c^b)
(a*c)^b
Arc Length
(n/360)*circumference
Special Right Triangles
- Sides with proportions such as 3:4:5 and 5:12:13 - 30-60-90 and 45-45-90 because lengths of those sides are x:x(radical 3):2x and x:x:x(radical 2)
(a^b)^c
a^(b*c)
a^b * a^c
a^(b+c)
a^b/a^c
a^(b-c)
Area of a Parallelogram
base * height
Length of Triangle
one side is less than the sum of the lengths of the other two sides, and is greater than the positive difference of the lengths of the other two sides
Vertical Angles
pair of opposite angles formed by two intersecting line segments
Integer
positive whole numbers, zero, and negative whole numbers
Bisection
splits the angle into two smaller, equal angles
Special Triangle: Angles 45 - 45 - 90
x - x - x(sqrt)2
Special Triangle: Angles 30-60-90
x - x(sqrt)3 - 2x
Even (plus/minus) Even
Even
Even * Even
Even
Even ^ (any pos int)
Even
Odd (plus/minus) Odd
Even
Factors (Divisors)
Number are the positive integers that divide into that number without a remainder
Odd (plus/minus) Even
Odd
Odd * Even
Odd
Odd * Odd
Odd
Odd ^ (any pos int)
Odd
Regular Polygon
Sides are equal length and interior angles of equal measure
Least Common Denominator (LCD)
Smallest positive number that is a multiple of all the terms
Volume of Rectangle
V = LWH
Volume of Cylinder
V = pi(r)^2* h
Transversal Line
When two parallel lines intersect with a third line, all acute angles formed are equal, all obtuse angles are equal, and any acute angle is supplementary to any obtuse angle
Special Triangle: Lengths
3:4:5 and 5:12:13
Area of Triangle
A = (1/2)bh
Standard Deviation Formula
1. Find the mean 2. Subtract average of set from each term 3. Square each result 4. Take average of the square 5. Calculate positive square root
Area of a Trapezoid
1/2*(sum of the bases)*height
Data Sufficiency Answer Choices
12TEN A: 1 only B: 2 only T: together E: either N: neither
Central Angle
Angle formed by two radii
Value Questions
Asks for a numeric value; sufficient information would allow you to calculate exactly one value for the unknown quantity
Circumference
C=pi(d) or 2(pi)r
Speed
Distance / time
Similar Triangles
Corresponding angles have the same measure;
Diagonal in Rectangle
Diagonal^2 = Length^2+Width^2+Height^2
Divisible by 7
Difference between its units digit multiplied by 2, and the rest of the number is a multiple of 7
Overlapping Sets Formula
Group 1 + Group 2 - Both + Neither = Total
Supplementary Angle
Measures of both add up to 180 degrees
N-Variables, N-Equations Rule
If you have at least as many distinct, linear equations as you have variables, you will be able to solve for the unique numerical values of all variables
Lateral Surface Area of Cylinder
LSA = 2(pi)r * H
Divisible by 8
Last three digits compose a three-digit number that is itself divisible by 8
Divisible by 4
Last two digits compose a two digit number that itself is divisible by 4
Diagonal of Polygon
Line segment connecting to nonadjacent lines
Chord
Line segment joining two points on the circle
Complementary Angle
Make up a right angle
Standard Deviation
Measures dispersion of a set of numbers around the mean;
Inscribed Angle
Opens up from the edge of the circle instead of its center
Altitude
Perpendicular distance from a vertex to the opposite side of the vertex; can fall inside, outside, or one of the sides of a triangle
Vertex of Polygon
Point where two adjacent sides meet
Compound Interest
Principal * (1+r)^t
Simple Interest
Principal * (1+rt)
Multiple
Product of given integer and another integer; an integer that is divisible by another integer without a remainder is a multiple of the integer
Rate A per B
Quantity of A / Quantity of B
Total Surface Area of Cylinder
SA = 2(pi)r^2+2(pi)rh
Surface Area of Rectangle
SA = 2LW + 2LH + 2WH
Yes/No Questions
Sufficient information would allow to determine the answer to the question definitely yes or definitely no
Divisible by 9
Sum of digits is divisible by 9
Divisible by 3
Sum of its digits is divisible by 3
Exterior Angle
Supplementary to interior angle; equal to sum of the measures of the two nonadjacent interior angles
Concentric
Two circles of different size with same center
