Questions involve
-
Arithmetic operations
- Powers
- Operations on radical expressions
- Estimation
- Percent
- Absolute value
- Properties of numbers (e.g. divisibility,
prime numbers, odd and even integers)
- Factoring
Basic Arithmetic
The whole numbers,
or counting numbers, are 0,1,2,3,4,5,6… The integers are …-4, -3, -
2, -1,0,1,2,3,4… Recall the number line in deciding whether one negative number is larger than
another. Positive integers increase as they move away from 0; negative integers decrease as
they move away from 0. For example, 4 is greater than 3, but -4 is less than –3.
Consecutive
integers are in increasing order without any integers missing between them. For
example, 0,1,2,3,4… are consecutive integers; -2,0,2,4…are consecutive even integers; -3,
-
1,1,3… are consecutive odd integers.
Zero is
both a whole number and an even integer, but it is neither positive nor negative. The
sum of 0 and any number is that number; the product of 0 and any number is 0.
There are 10 digits in
our number system: 0,1,2,3,4,5,6,7,8,9. An integer greater than 9 is
made up of several digits. For example, in the number 5234, 4 is the ones digit, 3 is the tens
digit, 2 is the hundreds digit, 5 is the thousands digit.
When multiplying positive and negative numbers,
a positive times a positive is a positive; a
negative times a negative is a positive; a positive times a negative is a negative:
|
neg
+ neg = neg
|
(neg)
x (neg) = pos
|
|
pos
+ pos = pos
|
(pos)
x (pos) = pos
|
|
neg
+ pos = !
|
(neg)
x (pos) = neg
|
An even
number is any number that can be divided evenly by 2 with no remainder left over.
An odd number cannot be divided evenly by 2. Any integer is even if its ones digit is even; an
integer is odd if its ones digit is odd. Don’t confuse even/odd with positive/negative. On the
GRE, remember the following:
|
even
+ even = even
|
(even)
x (even) = even
|
|
odd
+ odd = even
|
(odd)
x (odd) = odd
|
|
even
+ odd = odd
|
(even)
x (odd) = even
|
An integer is divisible by
2 if its ones digit is divisible by 2.
An integer is divisible
by 3 if the sum of its digits is divisible by 3.
An integer is divisible
by 5 if its ones digit is either 0 or 5.
An integer is divisible
by 10 if its ones digit is 0.
A prime number
is a number that can be divided evenly by only itself and 1. 0 and 1 are not
prime numbers; 2 is the only even prime number. Some examples of prime numbers are 2, 3, 5,
7, 11, 13, 17…
A number x
is a factor of a number y if y is divisible by x. For example, 2, 3, 4,
and 6 are all
factors of 12 since they all divide evenly into 12.
A multiple of
a number x is x multiplied by any integer except 0.
For example, 10, 20, 30, 40, etc. are all multiples of 10.
The following is
a list of symbols and their meanings you need to know on the GRE:
= equal to
not equal to
> greater than
< less than
greater than or equal to
less than or equal to
The following is
a list of terms and their definitions you need to know on the GRE:
sum the result of addition
difference the result of subtraction
product the result of multiplication
quotient the result of division
numerator the "top" number in a fraction
denominator the "bottom" number in a fraction
The six basic
operations you will need to perform on the GRE are as follows. Let a and b be
any numbers.
1. addition: a + b
2. subtraction: a – b
3. multiplication: ab = = ab = (a)(b)
4. division: a/b = ab
5. raising a number to an exponent: a2
6. finding square roots and cube roots:
In order to find
an answer when more than one operation is involved, you must know the
correct order of operations. Remember the following mnemonic: Please Excuse My Dear
Aunt Sally. PEMDAS stands for Parentheses, Exponents,
Multiplication, Division, Addition,
and Subtraction. This is the order in which the operations must be performed. For example,
10(2) + (11-1) 5 – 4 = 18.
NOTE: MULTIPLICATION
AND DIVISION GOES LEFT TO RIGHT, i.e., 1025 =25
NOT 1; ADDITION AND SUBTRACTION ALSO GOES LEFT TO RIGHT, i.e., 10 – 2 +
5 =13 NOT 3.
The associative
laws of addition and multiplication allow you to regroup numbers in any order
when adding or multiplying. If a, b, and c are any numbers,
a + (b + c) = (a
+ b) + c and a (b c) = (a b) c
For example, 2
+ (4 + 6) = 4 + (2 + 6) = (6 + 4) + 2 = 2 + 4 + 6 and 2(46) = (42)6 = 6(24)
= 6 4 2.
The distributive
laws are very important on the GRE. Apply them every chance you get. If a,
b, and c are any numbers, then
|
a(b
+ c) = ab + ac
|
and
|
(b
+ c)a = ba + ca = ab + ac
|
|
a(b – c) = ab - ac
|
and
|
(b – c)a = ba – ca = ab –ac
|
When you use the
distributive law to go from ab + ac to a(b + c), you are actually factoring
the expression ab + ac by finding the common term to ab and ac which is "a".
1. readin'
