GRE Quantitative Reasoning Practice test Latest Update

GRE Quantitative Reasoning Practice Test Latest Update 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 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 fractions with the same denominator - add the numerators and keep the same denominator. For example, - 8 / 11 + 5 / 11 = -8 + 5 / 11 = -3 / 11 add two fractions with different denominators - 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 - 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 - 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 = - 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 cumulative percent change - Must calculate each successive percent change by using the result of the previous change as the new original Order of operations - BEDMAS (brackets, exponents, division / multiplication, addition / subtraction) x^1 = - x x^0 = - 1 x^-1 = - 1/x x^m x^n = - xm+n x^m/x^n = - x^m-n (also = 1 / x^m-n) (x^m)^n = - x^mn (xy)^n = - x^n y^n (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^2 (a - b)^3 - a^3 - 3a^2b + 3ab^2 - b^3 a^2 - b^2 = - (a + b) (a - b) x^30 - x^29 = - x(x^29) - x^29 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. function - An algebraic expression in one variable can be used to define a function of that variable. Usually denoted by letters such as f, g, and h. For example, the algebraic expression 3x+5 can be used to define a function f by: f(x) = 3x+5 Simple interest - Simple interest is based only on the initial deposit, which serves as the amount on which interest is computed, called the principal, for the entire time period. If the amount P is invested at a simple annual interest rate of r percent, then the value V of the investment at the end of t years is given by the formula v = p (1 + rt / 100) (v and p in dollars) compound interest - In the case of compound interest, interest is added to the principal at regular time intervals, such as annually, quarterly, and monthly. Each time interest is added to the principal, the interest is said to be compounded. After each compounding, interest is earned on the new principal, which is the sum of the preceding principal and the interest just added. If the amount P is invested at an annual interest rate of r percent, compounded annually, then the value V of the investment at the end of t years is given by the formula v = p (1 + r/100)^t compound interest (compounded more than once annually) - If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formula v = p (1 + r/100n)^nt slope (m) - rise/run, y2-y1/x2-x1 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