GRE Quan ta ve/GRE Quan ta ve “Cheat-Sheet + 100
Problem Set (2025)
even + even = even
even - even = even
even + odd = odd
even - odd = odd
odd + odd = even
odd - odd = even
odd × odd = odd
even × odd = even
even × even = even
least common mul ple the least posi ve integer that is a mul ple of both a and b. For
example, the least common mul ple of 30 and 75 is 150. This is because the posi ve mul ples
of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc., and the posi ve mul ples of 75 are
75, 150, 225, 300, 375, 450, etc. Thus, the common posi ve mul ples of 30 and 75 are 150, 300,
450, etc., and the least of these is 150.
,greatest common divisor (or greatest common factor) the greatest posi ve integer that is a
divisor of both a and b. For example, the greatest common divisor of 30 and 75 is 15. This is
because the posi ve divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the posi ve divisors of 75
are 1, 3, 5, 15, 25, and 75. Thus, the common posi ve divisors of 30 and 75 are 1, 3, 5, and 15,
and the greatest of these is 15.
prime number an integer greater than 1 that has only two posi ve divisors: 1 and itself
first ten prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
prime factoriza on Every integer greater than 1 either is a prime number or can be uniquely
expressed as a product of factors that are prime numbers, or prime divisors
composite number An integer greater than 1 that is not a prime number
The first ten composite numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
add two frac ons with the same denominator add the numerators and keep the same
denominator. For example, - + = -8 + = -
add two frac ons with different denominators To add two frac ons with different
denominators, first find a common denominator, which is a common mul ple of the two
denominators. Then convert both frac ons to equivalent frac ons with the same denominator.
Finally, add the numerators and keep the common denominator. So: 1/3 + -2/5 = 5/15 + -6/15 =
-1/15
To mul ply two frac ons mul ply the two numerators and mul ply the two denominators.
So: (10/7) (-1/3) = (10)(-1) / (7)(3) = -10/21
, To divide one frac on by another first invert the second frac on—that is, find its
reciprocal—then mul ply the first frac on by the inverted frac on. So (3/10)/(7/13) =
(3/10)(13/7) = 39/70
nega ve number raised to even power = posi ve
nega ve number raised to odd power = nega ve
√a√b √ab
(√a)^2 a
√a^2 a
√a/√b √ab
interval The set of all real numbers that are between, say, 5 and 8 is called an interval,
and the double inequality is o:en used to represent that interval: 5 < x < 8
ra o The ra o of one quan ty to another is a way to express their rela ve sizes, o:en in the
form of a frac on, where the first quan ty is the numerator and the second quan ty is the
denominator. Thus, if s and t are posi ve quan es, then the ra o of s to t can be wri<en as the
frac on .st The nota on "s to t" or "s : t" is also used to express this ra o. For example, if there
are 2 apples and 3 oranges in a basket, we can say that the ra o of the number of apples to the
number of oranges is 2/3 or that it is 2 to 3 or that it is 2:3.
Ra o Box X item Y item Total
Ra o
, Mul ply by
Real
propor on A propor on is an equa on rela ng two ra os; for example, 9 / `2 = . To
solve a problem involving ra os, you can o:en write a propor on and solve it by cross
mul plica on
percentage part / whole (100) = %
percent change If a quan ty increases from 600 to 750, then the percent increase is found
by dividing the amount of increase, 150, by the base, 600, which is the ini al number given
percent change formula difference / original (100) = % increase
cumula ve percent change Must calculate each successive percent change by using the result
of the previous change as the new original
Order of opera ons BEDMAS (brackets, exponents, division / mul plica on, addi on /
subtrac on)
x^1 = x
x^0 = 1
x^-1 = 1/x
x^m x^n = xm+n
Problem Set (2025)
even + even = even
even - even = even
even + odd = odd
even - odd = odd
odd + odd = even
odd - odd = even
odd × odd = odd
even × odd = even
even × even = even
least common mul ple the least posi ve integer that is a mul ple of both a and b. For
example, the least common mul ple of 30 and 75 is 150. This is because the posi ve mul ples
of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc., and the posi ve mul ples of 75 are
75, 150, 225, 300, 375, 450, etc. Thus, the common posi ve mul ples of 30 and 75 are 150, 300,
450, etc., and the least of these is 150.
,greatest common divisor (or greatest common factor) the greatest posi ve integer that is a
divisor of both a and b. For example, the greatest common divisor of 30 and 75 is 15. This is
because the posi ve divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the posi ve divisors of 75
are 1, 3, 5, 15, 25, and 75. Thus, the common posi ve divisors of 30 and 75 are 1, 3, 5, and 15,
and the greatest of these is 15.
prime number an integer greater than 1 that has only two posi ve divisors: 1 and itself
first ten prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
prime factoriza on Every integer greater than 1 either is a prime number or can be uniquely
expressed as a product of factors that are prime numbers, or prime divisors
composite number An integer greater than 1 that is not a prime number
The first ten composite numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
add two frac ons with the same denominator add the numerators and keep the same
denominator. For example, - + = -8 + = -
add two frac ons with different denominators To add two frac ons with different
denominators, first find a common denominator, which is a common mul ple of the two
denominators. Then convert both frac ons to equivalent frac ons with the same denominator.
Finally, add the numerators and keep the common denominator. So: 1/3 + -2/5 = 5/15 + -6/15 =
-1/15
To mul ply two frac ons mul ply the two numerators and mul ply the two denominators.
So: (10/7) (-1/3) = (10)(-1) / (7)(3) = -10/21
, To divide one frac on by another first invert the second frac on—that is, find its
reciprocal—then mul ply the first frac on by the inverted frac on. So (3/10)/(7/13) =
(3/10)(13/7) = 39/70
nega ve number raised to even power = posi ve
nega ve number raised to odd power = nega ve
√a√b √ab
(√a)^2 a
√a^2 a
√a/√b √ab
interval The set of all real numbers that are between, say, 5 and 8 is called an interval,
and the double inequality is o:en used to represent that interval: 5 < x < 8
ra o The ra o of one quan ty to another is a way to express their rela ve sizes, o:en in the
form of a frac on, where the first quan ty is the numerator and the second quan ty is the
denominator. Thus, if s and t are posi ve quan es, then the ra o of s to t can be wri<en as the
frac on .st The nota on "s to t" or "s : t" is also used to express this ra o. For example, if there
are 2 apples and 3 oranges in a basket, we can say that the ra o of the number of apples to the
number of oranges is 2/3 or that it is 2 to 3 or that it is 2:3.
Ra o Box X item Y item Total
Ra o
, Mul ply by
Real
propor on A propor on is an equa on rela ng two ra os; for example, 9 / `2 = . To
solve a problem involving ra os, you can o:en write a propor on and solve it by cross
mul plica on
percentage part / whole (100) = %
percent change If a quan ty increases from 600 to 750, then the percent increase is found
by dividing the amount of increase, 150, by the base, 600, which is the ini al number given
percent change formula difference / original (100) = % increase
cumula ve percent change Must calculate each successive percent change by using the result
of the previous change as the new original
Order of opera ons BEDMAS (brackets, exponents, division / mul plica on, addi on /
subtrac on)
x^1 = x
x^0 = 1
x^-1 = 1/x
x^m x^n = xm+n
