GRE Quantitative Reasoning Prep exam
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
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GRE Quantitative Reasoning Prep exam
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2024/2025
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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 multiple - 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) - 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 - an integer greater than 1 that has only two positive divisors: 1 and itself first ten prime numbers - 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 prime factorization - 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
negative number raised to even power = - positive negative number raised to odd power = - negative √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 often used to represent that interval: 5 < x < 8 ratio - 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 - X item Y item Total Ratio Multiply by Real proportion - A proportion is an equation relating two ratios; for example, 9 / `2 = 3 / 4. To solve a problem involving ratios, you can often write a proportion and solve it by cross multiplication percentage - part / whole (100) = % percent change - If a quantity 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 initial number given percent change formula - difference / original (100) = % increase
(x/y)^n = - x^n/y^n x^-n = - 1/x^n (x^a)(y^a) = - xy^a identity - A statement of equality between two algebraic expressions that is true for all possible values of the variables involved (a + b)^2 = - a^2 + 2ab + b^ (a - b)^3 - a^3 - 3a^2b + 3ab^2 - b^ a^2 - b^2 = - (a + b) (a - b) x^30 - x^29 = - x(x^29) - x^ linear equation - A linear equation is an equation involving one or more variables in which each term in the equation is either a constant term or a variable
multiplied by a coefficient. None of the variables are multiplied together or raised to a power greater than 1 quadratic equation - An equation that can be written in the form ax^2 + bx + c = 0, where a,b,and c are real numbers and a ≠ 0 quadratic formula - x = -b ± √(b² - 4ac)/2a Use this to determine the value of variables in quadratic equations. Quadratic equations have at most two real solutions FOIL - Multiply the First, Outer, Inner, and Last terms of a pair of binomials Inequality - < > ≤ ≥ Adding a positive or negative constant to both sides of inequality - When the same constant is added to or subtracted from both sides of an inequality, the direction of the inequality is preserved and the new inequality is equivalent to the original. When both sides of the inequality are multiplied or divided by the same nonzero constant, the direction of the inequality is preserved if the constant is positive but the direction is reversed if the constant is negative. In either case, the new inequality is equivalent to the original.
slope (m) - rise/run, y2-y1/x2-x equation of a line - y = mx + b b is the y-intercept, y is the point on the y axis, x is the point on the x axis. graph of an equation - Equations in two variables can be represented as graphs in the coordinate plane. In the xy-plane, the graph of an equation in the variables x and y is the set of all points whose ordered pairs (, xy satisfy the equation. Graphing linear inequalities - Graphs of linear equations can be used to illustrate solutions of systems of linear equations and inequalities. Solve each equation for y in terms of x, then graph each. The solution of the system of equations is the point at which the two graphs intersect. Graph of a quadratic equation - The graph of a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0 is a parabola parabola - The graph of a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0 is a parabola The x-intercepts of the parabola are the solutions of the equation ax^2 + bx + c = 0. If a is positive, the parabola
opens upward and the vertex is its lowest point. If a is negative, the parabola opens downward and the vertex is the highest point. Every parabola is symmetric with itself about the vertical line that passes through its vertex. In particular, the two x-intercepts are equidistant from this line of symmetry. graph of a circle - (x - a)^2 + (y - b)^2 = r^2 (centre is at point a, b and radius of r) graphing a function in the xy-plane - To graph a function in the xy-plane, you represent each input x and its corresponding output (f)x as a point (x, y) where y = f(x). In other words, you use the x-axis for the input and the y-axis for the output. weighted average - example: 2 (x) + 1 (y) / 2 + 1 = a (where 2 and 1 represent the ratio of each entity) Opposite/vertical angles - Created when two lines intersect at a point. Opposite angles have equal measures, and angles that have equal measures are called congruent angles. Hence, opposite angles are congruent. The sum of the measures of the four angles is 360. Sum of the measures of the interior angles of a triangle - 180 degrees
parallelogram - A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. In a parallelogram, opposite sides are congruent and opposite angles are congruent rectangle / square - A quadrilateral with four right angles is called a rectangle. Opposite sides of a rectangle are parallel and congruent, and the two diagonals are also congruent. A rectangle with four congruent sides is called a square. area of a quadrilateral - A = bh (or lw): the base times height or length times width Area of a trapezoid - half the product of the sum of the lengths of the two parallel sides b1 and b2 and the corresponding height h: a = 1/2 (b1 + b2)(h) radius - the length of a line segment between the center and circumference of a circle or sphere (r) diameter - the length of a straight line passing through the center of a circle and connecting two points on the circumference (d) circumference - The distance around a circle. C = 2(pi)r
arc - Given any two points on the outside edge of a circle, an arc is the part of the circumference containing the two points and all the points between them. Two points on a circle are always the endpoints of two arcs. It is customary to identify an arc by three points to avoid ambiguity. measure of an arc - The measure of an arc is the measure of its central angle, which is the angle formed by two radii that connect the center of the circle to the two endpoints of the arc. An entire circle is considered to be an arc with measure 360 degrees length of an arc - An arc is a piece of the circumference. If n is the degree measure of the arc's central angle, then the formula is: Length of an Arc = 1 (n/360) (2πr) central angle - A central angle of a circle is an angle with its vertex at the center of the circle. area of a circle - A=∏r² sector - A sector of a circle is a region bounded by an arc of the circle and two radii area of a sector - A = ∏r² (c/360), where c = the central angle)
volume of a right circular cylinder - V = (pi)r^2h surface area of a right circular cylinder - A = 2(Πr^2) + 2Πrh frequency/count - The frequency, or count, of a particular category or numerical value is the number of times that the category or value appears in the data. A frequency distribution is a table or graph that presents the categories or numerical values along with their associated frequencies. relative frequency - The relative frequency of a category or a numerical value is the associated frequency divided by the total number of data. Relative frequencies may be expressed in terms of percents, fractions, or decimals. A relative frequency distribution is a table or graph that presents the relative frequencies of the categories or numerical values average (arithmetic mean) - To calculate the average of n numbers, take the sum of the n numbers and divide it by n. weighted average/mean - When several values are repeated in a list, it is helpful to think of the mean of the numbers as a weighted mean of only those values in the list that are different. The number of times a value appears in the list, or the frequency, is called the weight of that value.
median - To calculate the median of n numbers, first order the numbers from least to greatest. If n is odd, then the median is the middle number in the ordered list of numbers. If n is even, then there are two middle numbers, and the median is the average of these two numbers mode - The mode of a list of numbers is the number that occurs most frequently in the list range - The range of the numbers in a group of data is the difference between the greatest number G in the data and the least number L in the data; that is, G-L interquartile range - The difference between the scores (or estimated scores) at the 75th percentile and the 25th percentile. Used more than the range because it eliminates extreme scores. Formula: IQR = Q3-Q standard deviation - The standard deviation of a group of n numerical data is computed by (1) calculating the mean of the n values, (2) finding the difference between the mean and each of the n values, (3) squaring each of the differences, (4) finding the average of the n squared differences, and (5) taking the nonnegative square root of the average squared difference
for the second choice. The multiplication principle states that under those conditions, there are km different possibilities for the pair of choices. permutation - The number of ways in which a set of values can be ordered. Formula: n(n-1)(n-2)(n-3) etc. Symbolized by n! number of permutations of n objects taken k at a time - n! / (n-k)! combination - In contrast with permutation, this is the number of ways in which a set of values can be ordered but without counting different orders for the same values. Formula: number of ways to select with order / number of ways to order = number of combinations of n objects taken k at a time - n! / k!(n-k)!, sometimes notated as nCk probability - probability of event occurring is defined by the ratio P(E) = number of outcomes that satisfy event E / the number of possible outcomes probability of two or more events BOTH occurring - P(A and B) = P(A) x P(B) probability of EITHER one or another event occurring - P(A) + P(B) - P(AB)
probability of neither of multiple events occurring - the product of 1 - P(A), 1 - P(B), etc. group equation - T = G1 + G2 - B + N (T is total, groups G, B is members of both group, N is members of neither) probability of event E AND F - E x F (if E and F are independent) probability of event E OR F - E + F (if E and F are mutually exclusive) probability of event E OR F but not both - E + F - P(E and F) continuous probability distribution - relative frequency distributions are often approximated using a smooth curve—a distribution curve or density curve—for the tops of the bars in the histogram. The region below such a curve represents a distribution, called a continuous probability distribution. There are many different continuous probability distributions, but the most important one is the normal distribution, which has a bell-shaped curve