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GMAT Math Review
Math properties to memorize before GMAT
127
Mathematics
Professional
07/11/2011
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Term
If __ then x is divisible by 3
 Definition
The sum x’s digits is divisible by 3
Term
If __ then x is divisible by 4
 Definition
The x’s last two digits divisible by 4
Term
If __ then x is divisible by 5
 Definition
The last digit of x is 0 or 5
Term
If __ then x is divisible by 6
 Definition
x is divisible by both 2 and 3
Term
If __ then x is divisible by 8
 Definition
the last 3 digits of x are divisible by 2 three times
Term
If __ then x is divisible by 9
 Definition
The sum of x’s digits is divisible by 9
Term
The first 25 prime numbers are __
 Definition
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Term
If a is a factor of b, and b is a factor of c, then __ is a factor of c
 Definition
a
Term
Odd ± Odd = __
 Definition
Even
Term
Even ± Even = __
 Definition
Even
Term
Odd ± Even = __
 Definition
Odd
Term
Odd x Odd = __
 Definition
Odd
Term
Even x Even = __
 Definition
Even
Term
Even x Odd =__
 Definition
Even
Term
Using prime columns, find the GCF by taking the __ count in each column
 Definition
Smallest
Term
Using prime columns, find the LCM by taking the __ count in each column
 Definition
Largest
Term
Perfect squares must have a __ number of total factors
 Definition
Odd
Term
The prime factorization of a perfect square contains only __ powers of prime
 Definition
Even
Term
Dividend (x), Quotient (Q), Remainder (R), and Divisor(N) have __ relationship
 Definition
x/N=Q+R/N
Term
You can __ and subtract remainders directly as long as __
 Definition

add or multiply

correct for excess and negative remainders
Term
In an evenly spaced set, the mean and median of the set are equal to the average of the __ terms
 Definition
First and Last
Term
In an evenly spaced set, the sum of all the elements in the set is the __ of the set multiplied by the __
 Definition

Average of the set

 

Number of items in the set
Term
The number of consecutive multiples in a set is __
 Definition
(Last – First) ÷ Increment + 1
Term
The product of any set of n integers is divisible by _
 Definition
n!
Term
For any set of consecutive integers with __ number of items, the sum of all the integers is always a multiple of the items
 Definition
Odd
Term
For any set of consecutive integers with an __ number of items, the sum of all the items is never a multiple of all the items
 Definition
Even
Term
When multiplying exponents, combine the exponents by __
 Definition
Adding
Term
When dividing exponents, combine the exponents by __
 Definition
Subtracting
Term
When raising exponents to a power, combine the exponents by __
 Definition
Multiplying
Term
xa · xb = __
 Definition
xa+b
Term
ax · bx = __
 Definition
(ab)x
Term
xa/xb= __
 Definition
x(a-b)
Term
(a/b)x= __
 Definition
ax/bx
Term
(ax)y= __
 Definition
axy
Term
x-a = __
 Definition
(1/x)a
Term
(x+y)2= __
 Definition
x2+2xy+y2
Term
ax · by = __
 Definition
ax · by
Term
ax + ay = __
 Definition
ax + ay
Term
ax + ax = __
 Definition
2ax
Term
a · ax = __
 Definition
a1+x
Term
Even square roots have __ value(s).
 Definition
one
Term
If two equations are linear, the equations will be SUFFICIENT unless __
 Definition
The two equations are mathematically identical
Term
If two equations contain nonlinear terms, the equations will usually be __
 Definition
INSUFFICIENT
Term
When question asks for a combination of variables use __
 Definition
MADS
Term
M in MADS stands for __
 Definition
Multiply or divide the whole equation by a number
Term
A in MADS stands for __
 Definition
Add or subtract from both sides
Term
D in MADS stands for __
 Definition
Distribute factors on ONE side
Term
S in MADS stands for __
 Definition
Square or unsquare both sides
Term
If there are absolute values on both sides of the equation, you need to consider the possibility that __ and __
 Definition

Neither expression changed signs

One of the expressions changed signs
Term
Integer constraints with __ can lead to just one solution
 Definition
Inequalities
Term
xw + yw + zx +zy = __
 Definition
(x+y)(w+z)
Term
mn-mn-1 = __
 Definition
mn-1 (m-1)
Term
Even exponent equations have __ solutions
 Definition
Two solutions
Term
Odd exponent equations have __ solutions
 Definition
One
Term
x2-y2 = __
 Definition
(x+y) (x-y)
Term
(x+y) (x-y) = __
 Definition
x2-y2
Term
x2+2x+1 = __
 Definition
(x+1)2
Term
(x+1)2 =__
 Definition
x2+2x+1
Term
x2-2x+1 = __
 Definition
(x-1)2
Term
(x-1)2 =__
 Definition
x2-2x+1
Term
sum of number n to m = __
 Definition
(m-n+1)(m+n)/2
Term
The direct formula for Sn=kAn where S1 = kA
 Definition
xAn
Term
The direct formula for Sn=Sn-1+A where S1 = k+A is __
 Definition
An+k
Term
The only way to combine two inequalities is to __ them or __ them if both sides of both inequalities are __
 Definition

Add

Multiply

Positive
Term
Implication of xy>0 is __
 Definition
x and y are same sign
Term
Implication of xy<0 is __
 Definition
x and y are different signs
Term
Implication of x2-x<0 is __
 Definition
0
Term
__ think about inequalities as ranges on a number line
 Definition
DO
Term
__ treat inequalities like equations when adding or subtracting, or when multiplying and dividing by a positive number on both sides of the inequality
 Definition
DO
Term
__ line up multiple inequalities to form a compound inequality when doing so may help solve the problem
 Definition
DO
Term
__ add inequalities together when doing so may help to solve the problem
 Definition
DO
Term
Use __ to solve inequality range problems, problems containing both inequalities and equations, and many optimization problems
 Definition
extreme values
Term
Set terms with even exponents equal to __ when trying to solve optimization problems
 Definition
zero
Term
Draw a number line to think through inequality problems involving __ or __ exponents
 Definition
absolute values
even
Term
Flip the inequality sign if you __ or__ both sides of an inequality by a negative number
 Definition
Multiply or divide
Term
__ multiply or divide an inequality by a variable without knowing the sign of the variable
 Definition
DO NOT
Term
Take the most __ inequality when dealing with multiple inequalities involving the same variable
 Definition
restrictive
Term
Perform order of operations on every __ when manipulating a compound inequality
 Definition
expression
Term
Optimizing a __ function, the boundaries are at the minimum and maximum values given
 Definition
linear
Term
If x 1/y when x and y are the … sign
 Definition
same
Term
If both sides of an inequality are negative then the sign … when you square it
 Definition
flips
Term
If both sides of an inequality are positive then the sign … when you square it
 Definition
stays the same
Term
If one side of an inequality is positive and the other is negative then you … square it
 Definition
cannot
Term
If the signs in an inequality are unclear then you … square it
 Definition
cannot
Term
In an age chart, the … are in rows and the … are in columns using variable to indicate how old the people are
 Definition
people / ages / now
Term
In a combination, the order of items ___ matter
 Definition
does not
Term
In a permutation, the order of items ___ matter
 Definition
does
Term
Where r items are chosen from a pool of n items, ___ is the number of combinations
 Definition
n!/((n-r)!·r!)
Term
Where r items are chosen from a pool of n items, ___ is the number of permutations
 Definition
n!/(n-r)!
Term
The formula for anagrams is to divide ___ by ___
 Definition
factorial of the number of letter
Term
4! = ___
 Definition
24
Term
5! = ___
 Definition
120
Term
6! = ___
 Definition
720
Term
A fraction becomes a non-terminating decimal if it only has ____ in the denominator
 Definition
2’s and 5’s as prime factors
Term
Sum of interior angles of a polygon with n sides is ___
 Definition
(n-2) * 180
Term
Area of a trapezoid is ___
 Definition
½ * Base1 * Base2 * Height
Term
Area of a rhombus is ____
 Definition
½ * Diagonal1 * Diagonal2
Term
Angles in a triangle correspond to their ___ sides
 Definition
opposite
Term
The sum of any two sides of a triangle must be ___ than the third side
 Definition
greater
Term
In a right triangle, a2 + b2 = __
 Definition
c2
Term
In a right triangle with sides 3 and 4, the third side is ___
 Definition
5
Term
In a right triangle with sides of 5 and 12, the hypotenuse is __
 Definition
13
Term
In a right triangle with sides 8 and 15, the third side is ___
 Definition
17
Term
In a right triangle with sides 7 and 24, the third side is ___
 Definition
25
Term
In an isosceles right triangle, the hypotenuse is ___ times the length of the legs
 Definition
21/2
Term
In a 30-60-90 triangle, the ratio of the short side to the long side is ___
 Definition
1: 31/2
Term
In a 30-60-90 triangle, the ratio of the short side to the hypotenuse is ___
 Definition
1:2
Term
In a 30-60-90 triangle, the ratio of the long side to the hypotenuse is ___
 Definition
31/2:2
Term
Diagonal of a square is __ times the length of a side
 Definition
21/2
Term
Diagonal of a cube is __ times the length of a side
 Definition
31/2
Term
Two similar triangles with side lengths of ratio a:b will have areas in a ratio of ___
 Definition
a2:b2
Term
Area of an equilateral triangle with a side of s is ___
 Definition
¼ s231/2
Term
An inscribed angle is __ the angle of the central angle whose arc it intercepts
 Definition
half
Term
If one side of an inscribed triangle is the ____ of the circle, then the triangle must be a right triangle
 Definition
diameter
Term
Exterior angle of a triangle is equal to ___ the non-adjacent interior angles
 Definition
the sum of
Term
Perpendicular lines have slopes that are ___ of each other
 Definition
the negative reciprocal
Term
The midpoint between two points (x1,y1) and (x2,y2) is
 Definition
(½ (x1+x2), ½ (y1+y2))
Term
Of all quadrilaterals with a given perimeter, a square has the ___ area
 Definition
largest
Term
Of all quadrilaterals with a given area, a square has the ___ perimeter
 Definition
smallest
Term
Maximize the area of a triangle or parallelogram by placing the two sides ___ to each other
 Definition
perpendicular
Term
Sum of the exterior angles of any polygon is ___
 Definition
360
Term
If x
 Definition

negative

positive
Term
When adding an extreme values to a number __ the sign of the extreme value
 Definition
keep
Term
When subtracting an extreme value from a number, __ the sign of the extreme value
 Definition
flip
Term
When multiplying an extreme values by a positive number, __ the sign of the extreme value
 Definition
keep
Term
When multiplying extreme values by a negative number, __ the sign of the extreme value
 Definition
flip
Term
When dividing a number by an extreme value, __ the sign of the extreme value
 Definition
flip
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