# GRE Divisibility Rules: Math Fundamentals Part 1

• by
• Feb 20, 2014
• GRE Blog, GRE Tutor

# A GRE Math Cheat Sheet

There certainly is a lot to know when preparing for the GRE.  However, it is imperative that you are studying highly tested facts versus ambiguous material that rarely shows up on the test.  It’s easy to think that you simply need to focus on high school math concepts such as geometry, algebra, proportions, fractions, percents, decimals, and the order of operations (PEMDAS ), but it simply isn’t true.  That list is not exhaustive and it is extremely difficult to revisit four years of high school math plus a few university courses in the limited time you have to prepare for the GRE.  So, we made things easier!  Despite the fact that everyone’s exam is distinct, there are commonly tested concepts that will help rack up valuable Test Day points.  These are must know facts that are commonly tested on the GRE.

Divisibility rules are a must know for the GRE.  Although you are permitted to use a calculator on the GRE, knowing these divisibility rules will help make you calculations faster.  They also will help you pick the correct numbers when manage word problems and for many that is a huge time saver.  You may be familiar with some of these already, but these are definitely worth reading.

Dividing by 2

• All even numbers are divisible by 2. E.g., all numbers ending in 0,2,4,6 or 8.

Dividing by 3

• Add up all the digits in the number.
• Find out what the sum is. If the sum is divisible by 3, so is the number

For example: 12123 (1+2+1+2+3=9) 9 is divisible by 3, therefore 12123 is too!

Dividing by 4

• Are the last two digits in your number divisible by 4?
• If so, the number is too!

For example: 358912 ends in 12 which is divisible by 4, thus so is 358912.

Dividing by 5

• Numbers ending in a 5 or a 0 are always divisible by 5.

Dividing by 6

• If the Number is divisible by 2 and 3 it is divisible by 6 also.

Dividing by 7

• Take the last digit in a number.
• Double and subtract the last digit in your number from the rest of the digits.
• Repeat the process for larger numbers.

Example: 357 (Double the 7 to get 14. Subtract 14 from 35 to get 21 which is divisible by 7 and we can now say that 357 is divisible by 7.

Dividing by 8

• This one’s not as easy, if the last 3 digits are divisible by 8, so is the entire number.

Example: 6008 – The last 3 digits are divisible by 8, therefore, so is 6008.

Dividing by 9

• Almost the same rule and dividing by 3. Add up all the digits in the number.
• Find out what the sum is. If the sum is divisible by 9, so is the number.

For example: 43785 (4+3+7+8+5=27) 27 is divisible by 9, therefore 43785 is too!

Dividing by 10

• If the number ends in a 0, it is divisible by 10

Another commonly tested concept is positive and negative number properties.  For some of us, it has been awhile since we worked with multiplying or dividing positive and negative numbers.  You must understand the various properties of numbers because many GRE quantitative questions will use these concepts within algebraic expressions.  Making flashcards helps a lot of potential GRE test takers remember these concepts.

• When multiplying or dividing two numbers with the same sign, the result is always positive.  When multiplying or dividing two numbers with different signs, the result is always negative.
• Subtracting a negative number is the same as adding a positive number.
• When a negative number is raised to an even exponent, the result is positive.  When a negative number is raised to an odd exponent, the result is negative.

Column A                                                                    Column B

x>0

y<0

x^2 + y^2                                                                     (x-y)^2

Foiling column B yields (x-y)(x-y) = x^2 -2xy + y^2

Since y is negative, -2ab must be positive and even.

Column B is bigger.

Understanding the properties of negative numbers will save a lot of time on the GRE.  You can rack up points faster without doing a lot of math.

Another commonly tested GRE concept is odd and even number properties.  These abstract concepts are a great way to be able to simply read a math problem and understand the overarching properties of the correct answer.  This save a lot of time and avoids making math mistakes.

• Even x even = even
• Odd x odd = odd
• Even x odd = even
• Even ^positive integer = even
• Odd ^ positive integer = odd
• Even + even = even
• Even – even = even
• Odd + odd = even
• Odd – odd = even
• Odd + even = odd
• Odd – even = odd

The product of a series of integers will always be even, as soon as at least one single number is even.  This is true because any even number is a factor of 2, and whenever multiplying by the number 2 the result is always even.  There aren’t comparable, consistent rules for dividing.  The result can be odd or even as we divide.  For multiplication, subtraction and addition the rules are consistent.  If you have a difficult time remembering the rules, then you can always pick numbers to recall the math properties.  For example:  2 ^ 2 = 4 and 2^ 3 = 8.  You will always yield an even number is the base is even.

Example:  If a, b, and c are consecutive odd integers, which of the following must be true?

A)      (a + 1)(c – b)

B)      A(b + c)

C)      Abc

D)     A + 2b + 7c

E)      2bc

The correct answer is (c).  Odd numbers multiplied by odd numbers will always yield odd numbers.