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# GRE Quantitative (Arithmetic) exam Cheat sheet

### Integers

### Factors

### Some real problems...

__15 is 77% of some number x, find number x?__

First thing is to form a equation for above problem, according to above problem 60/100 of number is 15, which means

(75/100)x=15, which means x = 20.

- Integers : ..-3,-2,-1,0,1,2,...

- A whole number either positive, negative or zero. Example: (-1.-2.-3 .0,1,2,3,4â€¦â€¦.)
- If an integer is divisible by 2, it is called an even integer; otherwise it is an odd integer. Note that when a positive odd integer is divided by 2, the remainder is always 1. The set of even integers is ..., 6, 4, 2,0,2,4,6, ... and the set of odd, integers is ..., -5, -3, -1,1,3,5, ...
- The sum of two odd integers is an even integer.
- The sum of an even integer and an odd integer is an odd integer.
- The product of two odd integers is an odd integer.
- The product of an even integer and an odd integer is an even integer
- The product of two even integers is an even integer.
- 0 is neither neither positive or negative. 0 is even number.
- real numbers are integers and have decimal values between them..
- a
^{0}=1, 1/a^{n}=a^{-n} - The absolute value of a number N, denoted by N , is defined to be N if N is positive or zero and -N if N is negative. Example |-5| =5
- Integer divisible by 2 is called even integer (including 0 and 2). Examples are -8,-6,-4,-2,0,2,4,6,8

- Factors of a number are it's divisors. For instance, the factors of 21 are 3 and 7, because 3*7 = 21.
**The greatest common divisor (or greatest common factor)**of two nonzero integers x and y is the greatest positive integer that is a divisor of both x and y. For example GCF of 30 and 45 is 15, GCF of 60 and 90 is 30.**Least Common Multiple: (LCM)**of two non â€"zero integers x and y is the smallest +ve integer that is a divisor of both x and y, for example LCM of 50 and 60 is 300, LCM of 30 and 40 is 120.- A prime number is an integer greater than 1 that has only two positive divisors: 1 and itself, examples are 2,3,5,7,11,13,17 (remember 2 is a prime number). 1 is not a prime number, 2 is the smallest prime and the only even prime. Primes numbers below 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 ,61,67,71,73,79,83,97

First thing is to form a equation for above problem, according to above problem 60/100 of number is 15, which means

(75/100)x=15, which means x = 20.

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