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GRE Quantitative (Arithmetic) exam Cheat sheet





All integers belong to the rational numbers. A rational number is a number which can be written as a/b, b 0, where both a and b are integers, for example: number 7 is an integer as well as a rational number, it is an integer as it can be written without a decimal component and a rational number as it can be written as 7/1, whereas 1/4 =0.25 is a rational number but not an integer, or repeating as in 1/6 = 0.8333. All rational numbers belong to the real numbers


Every terminating or repeating decimal represents a rational number, not all decimals are terminating or repeating; for instance, the decimal that is equivalent to √3 is 1.7320508075-----and it can be shown that this decimal does not terminate or repeat. Since this decimal does not terminate or repeat, they are not rational numbers. Such numbers are called irrational numbers


A number's absolute value is the distance between a number x and 0. It is represented as |X|. The absolute value of a number X, denoted by |X|, is defined to be X, if X is positive or zero and -X if X is negative. Example |-5| = 5 For any number a, and positive number b, (a) |a|=b gives a=b or a=-b (b) |a| < b gives -b < a < b (c) |a| >b gives a < -b or a > b


A ratio can be written in 3 different ways and can be read as the ratio of x to y or x: y or x/y If a set of objects is divided into 2 groups in the ratio of x: y, then the first group is a/(a+b) and the second group contains b/(a+b)


Proportion is an equation where two ratios are equivalent for eg: if one pack of flour mix gives us 20 cakes, then 2 pack will give us 40 cakes, 40 /2 = 20/ 1, A proportion can be read as if a is to b as c is to d, and can be written as a/b =c/d where b, d 0. If one number in proportion is unknown, we can find that number by solving the proportion.


Percent = Part / Whole. The term percent means per hundred; Percent’s are ratios that are represented as parts of a whole. The easiest way to convert a fraction to a percentage is to divide the numerator by denominator then multiple the result by 100, and then add % sign. And to convert a percentage to a fraction, we must first convert it to a decimal (divide by 100) and then use the steps of converting decimal to fractions for example :(a)15 is 75% of x, find number x? Convert the math into English, per above problem 75/100 of a number is 15, (75/100) x=15, gives x =

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.

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