Properties of Numbers Flashcards
Divisibility by a Given Number
Number of Integers Divisible by a Given Number
Statistics Formula
[ ( Highest # Div By Given Number - Lowest # Div By Given Number ) / Given Number ] + 1.
Divisibility of Decimals
Divisibility of a Number with Decimal Values
Treat the number as an Integer and Add all the Digits
Factorial Prime Factor Frequency
How are the PRIME FACTORS in a prime factorized FACTORIAL related.
8! = 8 tms 7 tms 6tms 5 tms 4 tms 3 tms 2 tms 1.
8! = 2 (7) * 3 (2) * 5(1) * 7(1)
There are more 2’s than 3’s
Divisibility by 3
In a PRODUCT OF THREE CONSECUTIVE INTEGERS, how many are Divisible by 3?
At least one.
Divisibility by 4
In (n-1)(n)(n+1) where n is ODD, what is “n-1” or “n+1” DIVISIBLE by?
(n-1)(n+1) is a PRODUCT OF TWO CONSECUTIVE EVEN Integers, and either (n-1) or (n+1) is DIVISIBLE by 4.
Divisibility by 2 and 4
In the PRODUCT (n-1) (n+1) where both FACTORS are EVEN, what is each factor DIVISIBLE by?
One of the FACTORS is DIVISIBLE by 2, while the other is DIVISIBLE by 4.
Fraction Termination/Repitition
When will a FRACTION either TERMINATE or REPEAT?
When it is in its MOST REDUCED form, with an INTEGER NUMERATOR and NON-ZERO INTEGER DENOMINATOR.
What NUMBER is equal to its OPPOSITE?
Zero.
Even Number Expression
What EXPRESSION represents an EVEN number?
2n.
Odd Number Expression
What EXPRESSION represents an ODD number?
2n + 1.
Square Of Prime
How many FACTORS does the SQUARE of a PRIME NUMBER have?
3
p^0; p^1; p^2.
Cube of Prime
How many FACTORS does the CUBE of a PRIME NUMBER have?
4
p^0; p^1; p^2; p^3;
Factorial Inequalities
When you have an INEQUALITY with FACTORIALS, what are the BOUNDS of the INEQUALITY?
The value of the FACTORIALS.
Pick Numbers
What sign in a QUANT question INDICATES that we should PICK NUMBERS?
When there are no RESTRICTIONS on the VARIABLES in the QUESTION PROMPT.
LCM of an Integer and a Variable
Given that the LCM of 8 and n is 40, what can we deduce about n?
1. The LCM gives us the UNIQUE PF’s of 8 and n.
2. We must not ASSUME the TOTAL PF’s of 8 and n.
3. 40 = 2^3 * 5, therefore n = 5 at minimum.
4. As stated in “2”, n could also have 2, 2^2, and 2^3 as PF’s.
Series of Numbers Given Remainder Equation
If x/3 = Q + 2/3, what are the possible VALUES of x?
1. Smallest possible value is R = 2.
2. Adding the DIVISOR, we get the next value in the set of possible x.
Divisibility and Prime Factors
How do we know if some number X is divisible by some number Y?
1. X and Y share the same UNIQUE PRIME FACTORS.
2. The TOTAL number PRIME FACTORS in X is greater than or equal to the TOTAL number of PRIME FACTORS in Y.
Divisibility and Factors
If a NUMBER X, is not DIVISIBLE by a PF y, what can we deduce about the FACTORS of X?
y cannot be a FACTOR of X.
Numbers Share The Same Factors
If 24 and x share the same FACTORS, then this tells us what about x?
24 and x are equal.
Powers of ODD Numbers
What is the CARDINALITY of powers of ODD numbers?
ODD.
Powers of EVEN Numbers
What is the CARDINALITY of powers of EVEN numbers?
EVEN.
