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GMAT Exam Prep Questions with Complete Verified Answers
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GMAT Exam Prep Questions withComplete Verified Answers
Properties of Integers - ✔✔An integer is any number in a set {-1, 0, 1}. If x and y are integers and x
>0, x is a factor of y as long as y=xn for some integer n. In other words, y would be divisible by/a
multiple of x. A quotient is the number that can be evenly divided into another, the remainder is what is
left over if it is not even. y is divisible by x only if the remainder is 0. When a small integer is divided by a
large integer, the quotient is 0 and the remainder is the small integer. (5/7= 7(0) + 5).
Integers divisible by two are called even. Those not divisible by two are called odd. If at least one factor
in a product of integers is even, the product itself is even. Otherwise, it is odd. If two numbers are both
even or odd, their sum and difference will be even. Otherwise, it is odd.
A prime number is a positive integer with only two different positive divisors, 1 and itself. 2, 3, 5, 7, 11. 1
is not a prime number because it only has 1 divisor. Every number > 1 is either prime or a can be shown
as a product of prime numbers.
Consecutive integers are all in a row. n, n+1, n+2, etc. Consecutive even integers= 2, 4, 6, 8. 2n,
2n+2, 2n+4, etc. Consecutive odd integers= 1, 3, 5, 7. 2n+1, 2n+3, etc.
If n is any number then 1 x n = n. If n is not 0 then n x 1/n=1.
0 is neither positive nor negative. Cant divide by 0.
Fractions - ✔✔Denominator can never be 0. Two fractions are equivalent if they represent the
same number. Fractions can be reduced to their lowest terms by dividing the num and denom by their
greatest common divisor.
, Adding/subtracting fractions: Fractions with the same denom can be added or subtracted through the
numerators, leaving the denom the same. If the denom isn't the same, make it the same by expressing
them as equivalent fractions w the same denom. Multiply by the least common multiple to do this.
Multiplying/dividing fractions: For multiplying, multiply the numerators and the denominators. Done.
To divide, invert the divisor (do the reciprocal, 4= 1/4), and multiply as normal.
Mixed numbers: A whole number and a fraction. 7 and 2/3 is an example. To change this into a fraction,
multiply the whole number by the denom of the fraction and add this number into the num of the
fraction. 7 and 2/3 = [7(3) + 2]/3 = 23/3.
Decimals - ✔✔Scientific notation= 2.31 x 10^2 is 231 or 2.31 x 10^-2 is .0231.
Adding/subtracting decimals: line up the decimal points of both numbers (add 0s at the end if one
has fewer digits to the right of the decimal point).
Multiplying decimals: multiply them as though they were whole numbers and then add the decimal
point in so that the number of digits to the right of it is the sum of the numbers of digits to the right of
the decimal points being multiplied. 2.09 x 1.3 = 2.717.
Dividing decimals: to divide a number by a decimal, move the decimal point of the divisor to the right
until the divisor is a whole number, then move the decimal point of the dividend (num) the same
number of places to the right, and divide as you would by a whole number. The decimal point in the
quotient will be directly above where it is in the new dividend.
Real Numbers - ✔✔Real numbers all correspond to points on the number line, and all points on the
number line correspond to real numbers. The distance between a number and 0 on the number line is
called the absolute value of the number. 3 and -3 have the same absolute value |3|. Absolute values
are always positive in any nonzero number.
xy + xz is the same as x(y+z).
|x=y| is < or = |x| +|y|.
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