Properties of Numbers

Question 1

Divisibility by a Given Number

Number of Integers Divisible by a Given Number

Statistics Formula

Answer 1

[ ( Highest # Div By Given Number - Lowest # Div By Given Number ) / Given Number ] + 1.

Question 2

Divisibility of Decimals

Divisibility of a Number with Decimal Values

Answer 2

Treat the number as an Integer and Add all the Digits

Question 3

Factorial Prime Factor Frequency

How are the PRIME FACTORS in a prime factorized FACTORIAL related.

Answer 3

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

Question 4

Divisibility by 3

In a PRODUCT OF THREE CONSECUTIVE INTEGERS, how many are Divisible by 3?

Answer 4

At least one.

Question 5

Divisibility by 4

In (n-1)(n)(n+1) where n is ODD, what is “n-1” or “n+1” DIVISIBLE by?

Answer 5

(n-1)(n+1) is a PRODUCT OF TWO CONSECUTIVE EVEN Integers, and either (n-1) or (n+1) is DIVISIBLE by 4.

Question 6

Divisibility by 2 and 4

In the PRODUCT (n-1) (n+1) where both FACTORS are EVEN, what is each factor DIVISIBLE by?

Answer 6

One of the FACTORS is DIVISIBLE by 2, while the other is DIVISIBLE by 4.

Question 7

Fraction Termination/Repitition

When will a FRACTION either TERMINATE or REPEAT?

Answer 7

When it is in its MOST REDUCED form, with an INTEGER NUMERATOR and NON-ZERO INTEGER DENOMINATOR.

Question 8

What NUMBER is equal to its OPPOSITE?

Answer 8

Zero.

Question 9

Even Number Expression

What EXPRESSION represents an EVEN number?

Answer 9

2n.

Question 10

Odd Number Expression

What EXPRESSION represents an ODD number?

Answer 10

2n + 1.

Question 11

Square Of Prime

How many FACTORS does the SQUARE of a PRIME NUMBER have?

Answer 11

3
p^0; p^1; p^2.

Question 12

Cube of Prime

How many FACTORS does the CUBE of a PRIME NUMBER have?

Answer 12

4
p^0; p^1; p^2; p^3;

Question 13

Factorial Inequalities

When you have an INEQUALITY with FACTORIALS, what are the BOUNDS of the INEQUALITY?

Answer 13

The value of the FACTORIALS.

Question 14

Pick Numbers

What sign in a QUANT question INDICATES that we should PICK NUMBERS?

Answer 14

When there are no RESTRICTIONS on the VARIABLES in the QUESTION PROMPT.

Question 15

LCM of an Integer and a Variable

Given that the LCM of 8 and n is 40, what can we deduce about n?

Answer 15

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.

Question 16

Series of Numbers Given Remainder Equation

If x/3 = Q + 2/3, what are the possible VALUES of x?

Answer 16

1. Smallest possible value is R = 2.
2. Adding the DIVISOR, we get the next value in the set of possible x.

Question 17

Divisibility and Prime Factors

How do we know if some number X is divisible by some number Y?

Answer 17

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.

Question 18

Divisibility and Factors

If a NUMBER X, is not DIVISIBLE by a PF y, what can we deduce about the FACTORS of X?

Answer 18

y cannot be a FACTOR of X.

Question 19

Numbers Share The Same Factors

If 24 and x share the same FACTORS, then this tells us what about x?

Answer 19

24 and x are equal.

Question 20

Powers of ODD Numbers

What is the CARDINALITY of powers of ODD numbers?

Answer 20

ODD.

Question 21

Powers of EVEN Numbers

What is the CARDINALITY of powers of EVEN numbers?

Answer 21

EVEN.