# Shared Flashcard Set

## Details

GMAT Quant
GMAT Quant
61
Mathematics
Not Applicable
11/19/2019

Term
 When considering zero product property if one expression or variable is known to be zero, what about the other variable/expression. D.S. TIP!
Definition
 If one is 0, the other may or may not be 0. it could be other values. e.g. x=0  x(y-3)=0.   Here since x=0, y-3=0 or y-3/=0 so we cant with certainty equate y-3.
Term
 What can be said about 2 INTEGERS when the product is 1.
Definition
 D.S. TIP If we know 2 integers product = 1 then each integer is either -1 or +1
Term
 What are negative integers
Definition
 Numbers without fraction or decimal to left of 0 on the number line are negative integers, farther away from 0 smaller they are.
Term
 What are positive integers
Definition
 Whole numbers to the right of 0 on the number line are positive integers. Farther from 0, larger they are.
Term
 What are whole numbers
Definition
 All positive integers and 0 are whole numbers
Term
 Is 0 positive or negative.
Definition
 Zero is neither positive nor negative
Term
 What is the square root of 0
Definition
 Zero
Term
 What is k if k = -k
Definition
 0. 0 is the only number where k=-k
Term
 What is a multiple of every number
Definition
 0
Term
 What is x^0 for all x
Definition
 1. Any number raised to 0 is 1
Term
 Which number is a factor of all numbers
Definition
 1
Term
 What is the first prime number
Definition
 2. 0 is even and 1 is odd and not prime
Term
 What type of integer does the expression 2N represent
Definition
 Even integers.
Term
 What type of integer does the expression 2n+1 or 2n-1 represent for all integers n
Definition
 Odd integers
Term
 What combination of odd or even integers in addition or subtraction gives an odd integer?
Definition
 Odd+Even or Odd-Even. All other combinations are even
Term
 What combination of odd or even integers when multiplied results in an odd integer
Definition
 Odd*odd. All other integers combination give a even integer
Term
 Given XY + Y^2 is odd. What can we say about x and y.
Definition
 X must be even and Y must be odd. Y(X+Y) = odd. so Y and (x+Y) must be odd. For x+y to be odd, x has to be odd, since y is odd.
Term
 What could be said about x,y and z if xyz=even
Definition
 IF just one variable is even, xyz = even.Can have any combination of odds (yz, xz, zy). Just one even makes it even. Similarly if all odd, it would be odd.
Term
 If x is an integer. Is x odd or even if Even/Even = X
Definition
 X could be even or odd.
Term
 If x is an integer. Is x odd or even if Even/Odd = X
Definition
 X must be Even. This is corollary of Even*Odd=Even => Even = Even/Odd
Term
 What is the remainder when even numbers are divided be 2
Definition
 0
Term
 What is the remainder when odd numbers are divided by 2
Definition
 1
Term
 What is a factor. Define using x & Y
Definition
 Considering whole numbers, If X/Y = Integer. then Y is a factor of X.
Term
 What are the largest and smallest factors of any whole number?
Definition
 The smallest is 1 and largest is the number itself. range of values for the factor is 1<=y<=x, given x/y = whole number. Note this is the same as saying X is the factor of "something" if "something"/x = integer
Term
 How to check if "something" is a multiple of x
Definition
 "something"/X should be = integer/whole number
Term
 what number has only the number itself and 1 as factors
Definition
 prime numbers
Term
 If y is a positive integer. How many more prime factors does Y^5 and y^11 have compared to Y.
Definition
 None. A positive integer raised to another positive integer has the same number of unique prime factors as the base number
Term
 What can be said about GCF and LCM in a set of positive integers
Definition
 The LCM will be greater or equal to the largest number in the set.GCF will be greater than or equal to the smallest number in the set
Term
 What can be said about consecutive integers and the divisibility by 3
Definition
 3 consecutive integers, at least one will be divisible by 3. This can be extrapolated to 2,5 et.c
Term
 What is the factorial divisbility rule
Definition
 The product of any set of n consecutive integers is divisible by n!
Term
 Numbers that are perfect squares and perfect cubes under 1000
Definition
 1, 64 , 729 ,
Term
 How can we determine if a fraction m/n is going to be terminating decimal or not
Definition
 If denominator has only factors of 2 or only factors of 5 or only both 2&5. However, be careful of what the numerator is.
Term
 What is the power of prime factors of perfect cubes
Definition
 All exponents must be multiples of 3
Term
 What are the common prime factors of x and x+1 ?
Definition
 None. 2 consecutive integers don't share any prime factors.
Term
 What is the GCF of 2 consecutive integers?
Definition
 1
Term
 What is the units digit of x given 7,15 and 24 are factors of x ?
Definition
 0. Any number that has prime factors of at least one 2 and at least one 5 must end with at least one zero.
Term
 How do we get rid of a single term radical in the denominator
Definition
 Rationalize. x/(a)^(1/2) * (a/a)^(1/2)
Term
 For where x>1 & n>0 & both are integers.What is the relationship between xn and x if n is even
Definition
 xn > x
Term
 For x>1 and n>1 and both integers. What is the relationship between xn and x if n is odd?
Definition
 xn > x
Term
 For x<-1 and n>0, both integers. What is the relationship between xn and x if n is even?
Definition
 xn>x
Term
 For x<-1 and n>1, both integers. What is the relationship between xn and x if n is odd?
Definition
 x>xn
Term
 For 00  n is integer. What is the relationship between xn and x if n is even?
Definition
 x>xn
Term
 For -10  n is integer. What is the relationship between xn and x if n is even?
Definition
 xn>x
Term
 For 01  n is integer. What is the relationship between xn and x if n is odd?
Definition
 x>xn
Term
 For -11  n is integer. What is the relationship between xn and x if n is odd?
Definition
 xn>x
Term
 For x>1 and n where 0
Definition
 x>xn
Term
 For x where 0
Definition
 xn>x
Term
 If 0
Definition
Term
 What is the formula for consecutive even or odd integers?
Definition
 x, (x+2), (x+4), (x+6) and so on.
Term
 0 and 1 rules when talking about multiples
Definition
 0 is multiple of all numbers and is the only number equal to all its multiplesall numbers are a multiple of 1
Term
 Pattern of units digit 2^n
Definition
 starting n=1 2-4-8-6
Term
 Pattern of units digit 3^n
Definition
 starting n=1 3-9-7-1
Term
 Pattern of units digit 4^n
Definition
 starting n=1 4-6 (4 is odd power,6 is even)
Term
 Pattern of units digit 6^n
Definition
 starting n=1 all end in 6
Term
 Pattern of units digit 5^n
Definition
 Starting n=1 all powers end in 5
Term
 Pattern of units digit 7^n
Definition
 Starting n=1 7-9-3-1
Term
 Patterns of unit digit 8^n
Definition
 Starting n=1 8-4-2-6
Term
 Patterns of unit digit 9^n
Definition
 Starting n=1 9-1 (odd powers end 1, even powers end in 9)
Term
 Number of factors of perfect squares are
Definition
 Odd
Term
 Number of factors of positive integer other than a perfect square are
Definition
 Even
Term
 If a is a factor of b is b larger than a?
Definition
 Could be. a factor of a number is lesser than OR equal to that number. therefore a is equal or less than b
Supporting users have an ad free experience!