Fun with numbers…
So I’m neck deep in my GRE studies. I’ve already gone through two GRE books and an ebook. I’m close to finishing my third book (this test is NOT easy). I’m learning some interesting properties of numbers such as the following:
Integers:
- Integers are whole numbers (whether positive or negative)
- Fractions are not integers
- Zero is an integer!
- Positive integers get larger as they move farther from zero
- Negative integers get smaller as they move farther from zero
Consecutive numbers:
- Listed in order of increasing value without any numbers missing between them
- Fractions and decimals cannot be consecutive numbers; only integers can!
- You can even have consecutive even integers: 2, 4, 6, 8…
Properties of Zero:
- 0 is even
- 0 plus any other number is equal to that number
- 0 multiplied by any other number is equal to 0.
Positives and Negatives:
- pos x pos = pos
- neg x neg = pos (“two wrongs make a right” is my memorization tool)
- pos x neg = neg
Even or odd?
- Any number that can be cleanly divided by 2 is even (i.e. no remainder)
- Any number that cannot be cleanly divided by 2 is odd (i.e. has a remainder)
- Zero is even
- Fractions are neither even nor odd
- Any integer is even if its units digit is even, and odd if its units digit is odd
- Multiplying and adding odd and even integers
- even x even = even
- odd x odd = odd
- even x odd = even
- even + even = even
- odd + odd = even
- even + odd = odd
Absolute Value:
- Absolute value is how far away a number is from zero
- Absolute value is always a positive integer whether or not the number in question is positive or not
Prime Numbers:
- A number is prime when it is only divisible by itself and the number 1
- Here’s all the prime numbers less than 30: 2,3,5,7,11,13,17,19,23,29
- Zero is not a prime number
- 1 is not a prime number
- 2 is the only even prime number
- Prime numbers are always positive integers. There’s no such thing as a negative prime number
Rules of Divisibility:
- An integer is divisible by 2 if its units digit is divisible by 2. For example, 598,447,896 is divisible by 2 because the units digit (6) is divisible by 2.
- An integer is divisible by 3 if the sum of its digits is divisible by 3. For example, 2,145 is divisible by 3 because (2+1+4+5 = 12) is divisible by 3.
- An integer is divisible by 4 if its last 2 digits form a number that’s divisible by 4. For example, 712 is divisible by 4 because 12 is divisible by 4.
- An integer is divisible by 5 if its units digit is either 0 or 5
- An integer is divisible by 6 if it’s divisible by both 2 and 3
- An integer is divisible by 9 if the sum of its digits is divisible by 9
- An integer is divisible by 10 if its units digit is 0
Remainders:
- When one integer cannot be divided evenly by another, the remainder is what is left over after the division
- When one integer divides evenly by another the remainder is zero (no remainder)
Factors:
- A number is a factor of another number if the second number can be divided by the first with no remainder
- Factors of 12: 1,2,3,4,6,12
- Best to write factors in pairs to make sure you get them all:
- 1 and 12
- 2 and 6
- 3 and 4
Multiples:
- A multiple of a number is that number multiplied by an integer
- Multiples of 10: -20 (10 x -2), -10 (10 x -1), 10 (10 x 1), 20 (10 x 2), etc…
There’s obviously far more to the GRE than these simple concepts but some are quite handy and will make short work of doing calculations for the GRE. Yea, you can’t use a calculator at all. Fire up those neurons!