GRE Quantitative Reasoning Prep, GRE: Math d d d d d d
Combo, GRE Math Test With Mark Scheme d d d d d d
even + even = -d d d d d
d d d d d d d d d d d d d d even
even - even = -d d d d d
d d d d d d d d d d d d d d even
even + odd = - d d d d d
d d d d d d d d d d d d d d odd
even - odd = - d d d d d
d d d d d d d d d d d d d d odd
odd + odd = -
d d d d d
d d d d d d d d d d d d d d even
odd - odd = -
d d d d d
d d d d d d d d d d d d d d even
odd × odd = -
d d d d d
d d d d d d d d d d d d d d odd
even × odd = - d d d d d
d d d d d d d d d d d d d d even
even × even = -d d d d d
1|Page
,d d d d d d d d d d d d d d even
least common multiple -
d d d d
the least positive integer that is a multiple of both a and b. For example, the least
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
common multiple of 30 and 75 is 150. This is because the positive multiples of 30 are 30, 60, 90,
d d d d d d d d d d d d d d d d d d d d
120, 150, 180, 210, 240, 270, 300, etc., and the positive multiples of 75 are 75, 150, 225, 300, 375,
d d d d d d d d d d d d d d d d d d d d
450, etc. Thus, the common positive multiples of 30 and 75 are 150, 300, 450, etc., and the least of
d d d d d d d d d d d d d d d d d d d d
these is 150. d d
greatest common divisor (or greatest common factor) -
d d d d d d d d
the greatest positive integer that is a divisor of both a and b. For example, the greatest
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
common divisor of 30 and 75 is 15. This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10,
d d d d d d d d d d d d d d d d d d d d d d d
15, and 30, and the positive divisors of 75 are 1, 3, 5, 15, 25, and 75. Thus, the common positive
d d d d d d d d d d d d d d d d d d d d d
divisors of 30 and 75 are 1, 3, 5, and 15, and the greatest of these is 15.
d d d d d d d d d d d d d d d d d
prime number - d d d
d d d d d d d d d d d d d d an integer greater than 1 that has only two positive divisors: 1 and itself
d d d d d d d d d d d d d
first ten prime numbers -
d d d d d
d d d d d d d d d d d d d d 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
d d d d d d d d d d
prime factorization - d d d
Every integer greater than 1 either is a prime number or can be uniquely expressed as a
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
product of factors that are prime numbers, or prime divisors
d d d d d d d d d
composite number - d d d
d d d d d d d d d d d d d d An integer greater than 1 that is not a prime number
d d d d d d d d d d
The first ten composite numbers -
d d d d d d
d d d d d d d d d d d d d d 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
d d d d d d d d d d
add two fractions with the same denominator -
d d d d d d d d
add the numerators and keep the same denominator. For example, - + = -8 +
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
= -
d d d d d d
2|Page
,add two fractions with different denominators -
d d d d d d d
To add two fractions with different denominators, first find a common denominator, which
d d d d d d d d d d d d d d d d d d d d d d d d d d
is a common multiple of the two denominators. Then convert both fractions to equivalent fractions
d d d d d d d d d d d d d d d
with the same denominator. Finally, add the numerators and keep the common denominator. So:
d d d d d d d d d d d d d d d
1/3 + -2/5 = 5/15 + -6/15 = -1/15
d d d d d d d d
To multiply two fractions -
d d d d d
multiply the two numerators and multiply the two denominators. So: (10/7) (-1/3) = (10)(-
d d d d d d d d d d d d d d d d d d d d d d d d d d d
1) / (7)(3) = -10/21
d d d d
To divide one fraction by another -
d d d d d d d
first invert the second fraction—that is, find its reciprocal—then multiply the first fraction
d d d d d d d d d d d d d d d d d d d d d d d d d d d
by the inverted fraction. So (3/10)/(7/13) = (3/10)(13/7) = 39/70
d d d d d d d d d
negative number raised to even power = - d d d d d d d d
d d d d d d d d d d d d d d positive
negative number raised to odd power = - d d d d d d d d
d d d d d d d d d d d d d d negative
√a√b - d d
d d d d d d d d d d d d d d √ab
(√a)^2 - d d
d d d d d d d d d d d d d d a
√a^2 - d d
d d d d d d d d d d d d d d a
√a/√b - d d
d d d d d d d d d d d d d d √ab
3|Page
, interval - d d
The set of all real numbers that are between, say, 5 and 8 is called an interval, and the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
double inequality is often used to represent that interval: 5 < x < 8
d d d d d d d d d d d d d
ratio - d d
The ratio of one quantity to another is a way to express their relative sizes, often in the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
form of a fraction, where the first quantity is the numerator and the second quantity is the
d d d d d d d d d d d d d d d d d
denominator. Thus, if s and t are positive quantities, then the ratio of s to t can be written as the
d d d d d d d d d d d d d d d d d d d d d
fraction .st The notation "s to t" or "s : t" is also used to express this ratio. For example, if there are
d d d d d d d d d d d d d d d d d d d d d d d
2 apples and 3 oranges in a basket, we can say that the ratio of the number of apples to the
d d d d d d d d d d d d d d d d d d d d d
number of oranges is 2/3 or that it is 2 to 3 or that it is 2:3.
d d d d d d d d d d d d d d d d
Ratio Box - d d d
d d d d d d d d d d d d d d X item Y item Total
d d d d
Ratio d
Multiply by d d
Real
proportion - d d
A proportion is an equation relating two ratios; for example, 9 / `2 = . To solve a
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
problem involving ratios, you can often write a proportion and solve it by cross multiplication
d d d d d d d d d d d d d d
percentage - d d
d d d d d d d d d d d d d d part / whole (100) = % d d d d d
percent change - d d d
If a quantity increases from 600 to 750, then the percent increase is found by dividing the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
amount of increase, 150, by the base, 600, which is the initial number given
d d d d d d d d d d d d d
percent change formula - d d d d
d d d d d d d d d d d d d d difference / original (100) = % increase d d d d d d
cumulative percent change - d d d d
4|Page
Combo, GRE Math Test With Mark Scheme d d d d d d
even + even = -d d d d d
d d d d d d d d d d d d d d even
even - even = -d d d d d
d d d d d d d d d d d d d d even
even + odd = - d d d d d
d d d d d d d d d d d d d d odd
even - odd = - d d d d d
d d d d d d d d d d d d d d odd
odd + odd = -
d d d d d
d d d d d d d d d d d d d d even
odd - odd = -
d d d d d
d d d d d d d d d d d d d d even
odd × odd = -
d d d d d
d d d d d d d d d d d d d d odd
even × odd = - d d d d d
d d d d d d d d d d d d d d even
even × even = -d d d d d
1|Page
,d d d d d d d d d d d d d d even
least common multiple -
d d d d
the least positive integer that is a multiple of both a and b. For example, the least
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
common multiple of 30 and 75 is 150. This is because the positive multiples of 30 are 30, 60, 90,
d d d d d d d d d d d d d d d d d d d d
120, 150, 180, 210, 240, 270, 300, etc., and the positive multiples of 75 are 75, 150, 225, 300, 375,
d d d d d d d d d d d d d d d d d d d d
450, etc. Thus, the common positive multiples of 30 and 75 are 150, 300, 450, etc., and the least of
d d d d d d d d d d d d d d d d d d d d
these is 150. d d
greatest common divisor (or greatest common factor) -
d d d d d d d d
the greatest positive integer that is a divisor of both a and b. For example, the greatest
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
common divisor of 30 and 75 is 15. This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10,
d d d d d d d d d d d d d d d d d d d d d d d
15, and 30, and the positive divisors of 75 are 1, 3, 5, 15, 25, and 75. Thus, the common positive
d d d d d d d d d d d d d d d d d d d d d
divisors of 30 and 75 are 1, 3, 5, and 15, and the greatest of these is 15.
d d d d d d d d d d d d d d d d d
prime number - d d d
d d d d d d d d d d d d d d an integer greater than 1 that has only two positive divisors: 1 and itself
d d d d d d d d d d d d d
first ten prime numbers -
d d d d d
d d d d d d d d d d d d d d 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
d d d d d d d d d d
prime factorization - d d d
Every integer greater than 1 either is a prime number or can be uniquely expressed as a
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
product of factors that are prime numbers, or prime divisors
d d d d d d d d d
composite number - d d d
d d d d d d d d d d d d d d An integer greater than 1 that is not a prime number
d d d d d d d d d d
The first ten composite numbers -
d d d d d d
d d d d d d d d d d d d d d 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
d d d d d d d d d d
add two fractions with the same denominator -
d d d d d d d d
add the numerators and keep the same denominator. For example, - + = -8 +
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
= -
d d d d d d
2|Page
,add two fractions with different denominators -
d d d d d d d
To add two fractions with different denominators, first find a common denominator, which
d d d d d d d d d d d d d d d d d d d d d d d d d d
is a common multiple of the two denominators. Then convert both fractions to equivalent fractions
d d d d d d d d d d d d d d d
with the same denominator. Finally, add the numerators and keep the common denominator. So:
d d d d d d d d d d d d d d d
1/3 + -2/5 = 5/15 + -6/15 = -1/15
d d d d d d d d
To multiply two fractions -
d d d d d
multiply the two numerators and multiply the two denominators. So: (10/7) (-1/3) = (10)(-
d d d d d d d d d d d d d d d d d d d d d d d d d d d
1) / (7)(3) = -10/21
d d d d
To divide one fraction by another -
d d d d d d d
first invert the second fraction—that is, find its reciprocal—then multiply the first fraction
d d d d d d d d d d d d d d d d d d d d d d d d d d d
by the inverted fraction. So (3/10)/(7/13) = (3/10)(13/7) = 39/70
d d d d d d d d d
negative number raised to even power = - d d d d d d d d
d d d d d d d d d d d d d d positive
negative number raised to odd power = - d d d d d d d d
d d d d d d d d d d d d d d negative
√a√b - d d
d d d d d d d d d d d d d d √ab
(√a)^2 - d d
d d d d d d d d d d d d d d a
√a^2 - d d
d d d d d d d d d d d d d d a
√a/√b - d d
d d d d d d d d d d d d d d √ab
3|Page
, interval - d d
The set of all real numbers that are between, say, 5 and 8 is called an interval, and the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
double inequality is often used to represent that interval: 5 < x < 8
d d d d d d d d d d d d d
ratio - d d
The ratio of one quantity to another is a way to express their relative sizes, often in the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
form of a fraction, where the first quantity is the numerator and the second quantity is the
d d d d d d d d d d d d d d d d d
denominator. Thus, if s and t are positive quantities, then the ratio of s to t can be written as the
d d d d d d d d d d d d d d d d d d d d d
fraction .st The notation "s to t" or "s : t" is also used to express this ratio. For example, if there are
d d d d d d d d d d d d d d d d d d d d d d d
2 apples and 3 oranges in a basket, we can say that the ratio of the number of apples to the
d d d d d d d d d d d d d d d d d d d d d
number of oranges is 2/3 or that it is 2 to 3 or that it is 2:3.
d d d d d d d d d d d d d d d d
Ratio Box - d d d
d d d d d d d d d d d d d d X item Y item Total
d d d d
Ratio d
Multiply by d d
Real
proportion - d d
A proportion is an equation relating two ratios; for example, 9 / `2 = . To solve a
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
problem involving ratios, you can often write a proportion and solve it by cross multiplication
d d d d d d d d d d d d d d
percentage - d d
d d d d d d d d d d d d d d part / whole (100) = % d d d d d
percent change - d d d
If a quantity increases from 600 to 750, then the percent increase is found by dividing the
d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
amount of increase, 150, by the base, 600, which is the initial number given
d d d d d d d d d d d d d
percent change formula - d d d d
d d d d d d d d d d d d d d difference / original (100) = % increase d d d d d d
cumulative percent change - d d d d
4|Page
