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