GRE Quantitative Reasoning Prep 228 Questions with Verified Answers
Even + even = - CORRECT ANSWER even
Even - even = - CORRECT ANSWER even
Even
... [Show More] + odd = - CORRECT ANSWER odd
Even - odd = - CORRECT ANSWER odd
Odd + odd = - CORRECT ANSWER even
Odd - odd = - CORRECT ANSWER even
Odd × odd = - CORRECT ANSWER odd
Even × odd = - CORRECT ANSWER even
Even × even = - CORRECT ANSWER even
Least common multiple - CORRECT ANSWER 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) - CORRECT ANSWER 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 - CORRECT ANSWER an integer greater than 1 that has only two positive divisors: 1 and itself
first ten prime numbers - CORRECT ANSWER 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
prime factorization - CORRECT ANSWER 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 - CORRECT ANSWER An integer greater than 1 that is not a prime number
The first ten composite numbers - CORRECT ANSWER 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
add two fractions with the same denominator - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 = - CORRECT ANSWER positive
negative number raised to odd power = - CORRECT ANSWER negative
√a√b - CORRECT ANSWER √ab
(√a)^2 - CORRECT ANSWER a
√a^2 - CORRECT ANSWER a
√a/√b - CORRECT ANSWER √ab
interval - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER X item Y item Total
Ratio
Multiply by
Real
proportion - CORRECT ANSWER 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 - CORRECT ANSWER part / whole (100) = %
percent change - CORRECT ANSWER 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 - CORRECT ANSWER difference / original (100) = % increase
cumulative percent change - CORRECT ANSWER Must calculate each successive percent change by using the result of the previous change as the new original
Order of operations - CORRECT ANSWER BEDMAS (brackets, exponents, division / multiplication, addition / subtraction)
x^1 = - CORRECT ANSWER x
x^0 = - CORRECT ANSWER 1
x^-1 = - CORRECT ANSWER 1/x
x^m x^n = - CORRECT ANSWER xm+n
x^m/x^n = - CORRECT ANSWER x^m-n (also = 1 / x^m-n)
(x^m)^n = - CORRECT ANSWER x^mn
(xy)^n = - CORRECT ANSWER x^n y^n
(x/y)^n = - CORRECT ANSWER x^n/y^n
x^-n = - CORRECT ANSWER 1/x^n
(x^a)(y^a) = - CORRECT ANSWER xy^a
identity - CORRECT ANSWER A statement of equality between two algebraic expressions that is true for all possible values of the variables involved
(a + b)^2 = - CORRECT ANSWER a^2 + 2ab + b^2
(a - b)^3 - CORRECT ANSWER a^3 - 3a^2b + 3ab^2 - b^3
a^2 - b^2 = - CORRECT ANSWER (a + b) (a - b)
x^30 - x^29 = - CORRECT ANSWER x(x^29) - x^29
linear equation - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER Multiply the First, Outer, Inner, and Last terms of a pair of binomials
Inequality - CORRECT ANSWER < > ≤ ≥
Adding a positive or negative constant to both sides of inequality - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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) - CORRECT ANSWER 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) - CORRECT ANSWER rise/run, y2-y1/x2-x1
equation of a line - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER (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 - CORRECT ANSWER 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 - CORRECT ANSWER example: 2 (x) + 1 (y) / 2 + 1 = a (where 2 and 1 represent the ratio of each entity)
Opposite/vertical angles - CORRECT ANSWER 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 - CORRECT ANSWER 180 degrees
sum of the measures of the interior angles of an n-sided polygon - CORRECT ANSWER (n - 2)(180 degrees)
equilateral triangle - CORRECT ANSWER A triangle with three congruent sides is called an equilateral triangle. The measures of the three interior angles of such a triangle are also equal, and each measure is 60 degrees.
isosceles triangle - CORRECT ANSWER A triangle with at least two congruent sides is called an isosceles triangle. If a triangle has two congruent sides, then the angles opposite the two sides are congruent. The converse is also true.
right triangle - CORRECT ANSWER A triangle with an interior right angle is called a right triangle. The side opposite the right angle is called the hypotenuse; the other two sides are called legs.
Pythagorean theorem - CORRECT ANSWER a^2 + b^2 = c^2
area of a triangle - CORRECT ANSWER A=½bh or bh/2
parallelogram - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER A = bh (or lw): the base times height or length times width
Area of a trapezoid - CORRECT ANSWER 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 - CORRECT ANSWER the length of a line segment between the center and circumference of a circle or sphere (r)
diameter - CORRECT ANSWER the length of a straight line passing through the center of a circle and connecting two points on the circumference (d)
circumference - CORRECT ANSWER The distance around a circle. C = 2(pi)r
arc - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER A central angle of a circle is an angle with its vertex at the center of the circle.
area of a circle - CORRECT ANSWER A=∏r²
sector - CORRECT ANSWER A sector of a circle is a region bounded by an arc of the circle and two radii
area of a sector - CORRECT ANSWER A = ∏r² (c/360), where c = the central angle)
rectangular solid - CORRECT ANSWER A rectangular solid has six rectangular surfaces called faces, as shown in the figure below. Adjacent faces are perpendicular to each other. Each line segment that is the intersection of two faces is called an edge, and each point at which the edges intersect is called a vertex. There are 12 edges and 8 vertices. The dimensions of a rectangular solid are the length l, the width w, and the height h.
volume of rectangular solid - CORRECT ANSWER V = lwh
surface area of rectangular solid - CORRECT ANSWER A = 2(lw + lh + wh) -- the sum of the areas of the six faces
length of diagonal in rectangular prism - CORRECT ANSWER A^2+B^2+C^2 = D^2 or L^2+W^2+H^2 = D^2 (A is not area, just a side length)
circular cylinder - CORRECT ANSWER A circular cylinder consists of two bases that are congruent circles and a lateral surface made of all line segments that join points on the two circles and that are parallel to the line segment joining the centers of the two circles. The latter line segment is called the axis of the cylinder. A right circular cylinder is a circular cylinder whose axis is perpendicular to its bases.
volume of a right circular cylinder - CORRECT ANSWER V = (pi)r^2h
surface area of a right circular cylinder - CORRECT ANSWER A = 2(Πr^2) + 2Πrh
frequency/count - CORRECT ANSWER 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 - CORRECT ANSWER 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) - CORRECT ANSWER To calculate the average of n numbers, take the sum of the n numbers and divide it by n.
weighted average/mean - CORRECT ANSWER 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 - CORRECT ANSWER 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 - CORRECT ANSWER The mode of a list of numbers is the number that occurs most frequently in the list
range - CORRECT ANSWER 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 - CORRECT ANSWER 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-Q1
standard deviation - CORRECT ANSWER 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
sample standard deviation - CORRECT ANSWER computed by dividing the sum of the squared differences by instead of n. The sample standard deviation is only slightly different from the standard deviation but is preferred for technical reasons for a sample of data that is taken from a larger population of data. Sometimes the standard deviation is called the population standard deviation to help distinguish it from the sample standard deviation
Set - CORRECT ANSWER The objects of a set are called members or elements. Some sets are finite, which means that their members can be completely counted. Finite sets can, in principle, have all of their members listed, using curly brackets, such as the set of even digits {}0,2,4,6,8.
list - CORRECT ANSWER A list is like a finite set, having members that can all be listed, but with two differences. In a list, the members are ordered; that is, rearranging the members of a list makes it a different list. Thus, the terms "first element," "second element," etc., make sense in a list. Also, elements can be repeated in a list and the repetitions matter. For example, the lists 1, 2, 3, 2 and 1, 2, 2, 3 are different lists, each with four elements, and they are both different from the list 1, 2, 3, which has three elements
multiplication principle - CORRECT ANSWER Suppose there are two choices to be made sequentially and that the second choice is independent of the first choice. Suppose also that there are k different possibilities for the first choice and m different possibilities for the second choice. The multiplication principle states that under those conditions, there are km different possibilities for the pair of choices.
permutation - CORRECT ANSWER 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 - CORRECT ANSWER n! / (n-k)!
combination - CORRECT ANSWER 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 - CORRECT ANSWER n! / k!(n-k)!, sometimes notated as nCk
probability - CORRECT ANSWER 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 - CORRECT ANSWER P(A and B) = P(A) x P(B)
probability of EITHER one or another event occurring - CORRECT ANSWER P(A) + P(B) - P(AB)
probability of neither of multiple events occurring - CORRECT ANSWER the product of 1 - P(A), 1 - P(B), etc.
group equation - CORRECT ANSWER 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 - CORRECT ANSWER E x F (if E and F are independent)
probability of event E OR F - CORRECT ANSWER E + F (if E and F are mutually exclusive)
probability of event E OR F but not both - CORRECT ANSWER E + F - P(E and F)
continuous probability distribution - CORRECT ANSWER 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
length of a diagonal in a parallelogram - CORRECT ANSWER p^2 + q^2 = 2((a^2) + (b^2)), where p and q are the diagonals and a and b are sides. You may need to construct a right triangle by connecting a top corner with the baseline and then finding its hypotenuse (which will serve as the length of the angled side).
average of two averages - CORRECT ANSWER find total amount for each average (a = total / number of items), then determine the new average, deriving your new total from the sum of these totals.
harmonic mean formula - CORRECT ANSWER n / ((1/a1)+(1/a2)+(1/an))
Formula for "n percent greater/less than x" - CORRECT ANSWER x ± (n/100)x
x² - y² - CORRECT ANSWER (x + y) (x - y)
x² + 2xy + y² - CORRECT ANSWER (x + y) (x + y) or (x + y)²
x² - 2xy + y² - CORRECT ANSWER (x - y) (x - y) or (x - y)²
(x + y) / xy - CORRECT ANSWER 1/x + 1/y if x, y ≠ 0
(x - y) / xy - CORRECT ANSWER 1/x - 1/y if x, y ≠ 0
xy + xz - CORRECT ANSWER x (y + z)
xy - xz - CORRECT ANSWER x (y - z)
If x > y, then - CORRECT ANSWER x + z > y + z
If x > y and w > z, then - CORRECT ANSWER x + w > y + z
If w > 0 and x > y, then - CORRECT ANSWER wx > wy
If w < 0 and x > y, then - CORRECT ANSWER wx < wy
If x > y > 0 and w > z > 0, then - CORRECT ANSWER xw > yz
If x < 0 and z = x + y, then - CORRECT ANSWER z > y
If xy > 0, then - CORRECT ANSWER x > 0 and y > 0 or x < 0 and y < 0
If xy < 0, then - CORRECT ANSWER x > 0 and y < 0 or x < 0 and y > 0
If a vehicle travels a certain distance at a mph and travels the same distance at b mph, the average rate is - CORRECT ANSWER 2ab / a + b (only works when the distance is the same at both speeds!)
Common right triangle length ratios - CORRECT ANSWER 1: 1 :√2
1: 2 :√3
3: 4 :5
5: 12 :13
8: 15 :17
7: 24 :25
9: 40 :41
measurement of angle x originating on the edge of a circle - CORRECT ANSWER 1/2 the arc it cuts (between the points of the two lines extending from it across the circle)
units digit of 3^x - CORRECT ANSWER Will always end in 3, 9, 7, 1, in that sequence
(a + b) (a -b) - CORRECT ANSWER a² - b²
- (a - b) - CORRECT ANSWER (b - a)
y x 10^x - CORRECT ANSWER move decimal point x digits to the left/right
a² x b² - CORRECT ANSWER (ab)²
central angle of sector - CORRECT ANSWER arc/2
solve the percentage of circumference covered by an arc in terms of the central angle - CORRECT ANSWER x/360 = % of circumference
Measure of any inscribed angle (within a circle) whose triangle base is a diameter - CORRECT ANSWER 90 degrees
Inscribed angle y in terms of arc - CORRECT ANSWER y = arc/2
Adding fractions with different denominators - CORRECT ANSWER cross multiply (bottom to top, top to bottom), taking those values as your new numerator, and then also multiply the denominators and use that as your new denominator
- (- y < - x) - CORRECT ANSWER y > x (note the reversal of the inequality
(a + b) (c + d) - CORRECT ANSWER ac + ad + bc + bd
x¹ - CORRECT ANSWER x
x⁰ - CORRECT ANSWER 1
(ab)ⁿ - CORRECT ANSWER aⁿbⁿ
a³/a² - CORRECT ANSWER a³−²
Multiplying Decimals - CORRECT ANSWER Work as if they were whole integers. Then, count the number of digits to the right of the decimal place in each factor, combine them, and place the point that many digits to the left of your new product
Distance formula - CORRECT ANSWER speed x time = distance
Work formula - CORRECT ANSWER rate x time = work/output
mixture formula - CORRECT ANSWER concentration x amount of solution = amount of ingredient
cost - CORRECT ANSWER rate x number of items = value
Area of square calculated in relation to its diagonal - CORRECT ANSWER a = 1/2d²
Area of a parallelogram - CORRECT ANSWER a = bh (do not mistake with the formula for the height of a triangle. note also that "height" must be a straight line drawn from the base, not one of the diagonal sides)
Area of an equilateral triangle - CORRECT ANSWER a = 1/4s²√3
Area of a trapezoid - CORRECT ANSWER a = 1/2h(B + b), where B and b represent the "bases" (i.e. typically the straight lines at the bottom and the top of the figure, between which the height is drawn and measured)
Perimeter of a semicircle - CORRECT ANSWER P = d(1/2π + 1)
Volume of a cube - CORRECT ANSWER V = e³ (where e is any edge of the cube)
Surface area of a cube - CORRECT ANSWER S = 6e² (where e is any edge of the cube)
Surface area of a cylinder (bases incl.) - CORRECT ANSWER S = 2πrh(h + r)
Surface area of a cylinder (without bases) - CORRECT ANSWER S = 2πrh
Volume of a sphere - CORRECT ANSWER V = 4/3πr²
Surface area of a sphere - CORRECT ANSWER S = 4πr²
Volume of a hemisphere - CORRECT ANSWER V = 2/3πr²
Surface area of a hemisphere - CORRECT ANSWER S = 2πr² (without base); S = 3πr² (with base)
Area of an equilateral triangle - CORRECT ANSWER √3s² / 4
Area of a hexagon - CORRECT ANSWER a = (3√3 / 2)t (where t is the side length)
diagonal of a square - CORRECT ANSWER d = s√2 (where s equals the length of a side)
area of a triangle - CORRECT ANSWER ab sin C / 2, where a and b are any two sides and C is the angle between them
Relationship between diagonal of a hexagon and side - CORRECT ANSWER The longest diagonal is 2s (where s is the length of a side)
perimeter of a hexagon - CORRECT ANSWER p = 6r (where r is a given radius)
formula for distance between two points on a coordinate graph - CORRECT ANSWER d = √(x₂ - x₁)² + (y₂ - y₁)² (NB that the sqrt sign extends across the entire formula
Coordinates for the midpoint of the line segment joining 2 points - CORRECT ANSWER (x₁ + x₂ / 2, y₁ + y₂ / 2) (an average of the coordinates of the endpoints)
Subtracting from both sides of an inequality - CORRECT ANSWER reverse the central sign
Adding to both sides of an inequality - CORRECT ANSWER central sign remains the same
multiplying or dividing by a negative number in an inequality - CORRECT ANSWER reverse the central sign
multiplying or dividing by a positive number in an inequality - CORRECT ANSWER central sign remains the same
Types and characteristics of triangles - CORRECT ANSWER Scalene: no two sides or angles equal
Isosceles: two equal sides and angles
Equilateral: All three sides and all angles equal
Each angle must be 60 degrees
Right: one angle is a right angle (90)
Congruent triangles - CORRECT ANSWER 1. each side of the first triangle equals the corresponding sides of the second triangle
2. Two sides of the first triangle equal the corresponding angles of the second triangle, and their included angles are equal. The included angle is formed by the two sides of the triangle
3. Two angles of the first triangle equal the corresponding angles of the second triangle, and any pair of corresponding sides are equal
Median of a triangle - CORRECT ANSWER A line drawn from a vertex (point) to the midpoint of its opposite side. The medians of a triangle cross at a point that divides each median into two parts: one part of one third the length of the median and the other part of two thirds the length
Angle bisectors of a triangle - CORRECT ANSWER Lines that divide each angle of a triangle into two equal parts; they cross in the middle of a circle inscribed in the center of the triangle
Sum of any two sides of a triangle - CORRECT ANSWER Greater than the length of the third side
Angle inscribed in a semicircle - CORRECT ANSWER Must be a right angle
converting diameter to radius - CORRECT ANSWER d = 2r; so d² = 4r²
Combination formula - CORRECT ANSWER C = (n)(n - 1)(n - 2)...(n - r+1) / (r)(r - 1)(r - 2)...(1)
Permutation formula - CORRECT ANSWER P = (n)(n - 1)(n - 2)...(n - r+1)
| | - CORRECT ANSWER Absolute value sign -- that is, the numerical value regardless of plus or minus sign. All absolute values are positive
The union of sets A and B - CORRECT ANSWER A ∪ B (do not repeat items/digits shared between the two sets when unifying them)
The intersection of sets A and B - CORRECT ANSWER A ∩ B (this is the list of members shared between the two sets)
Subset - CORRECT ANSWER a set, all of whose members comprise part of a larger set. so (1, 2, 4) is a subset of (1, 2, 3, 4, 7, 9, 19)
number of subsets in a set with n items - CORRECT ANSWER Set with n items has 2ⁿ subsets
Set of ordered pairs - CORRECT ANSWER A relation, denoted by (x, y). The order of the elements in the pair matters
Domain of a relation - CORRECT ANSWER the set of the first components of the ordered pairs
Range of a relation - CORRECT ANSWER Set of the second components of the ordered pairs
Function (set theory) - CORRECT ANSWER a relation in which each element of the domain occurs only once as a first component
Solution sets - CORRECT ANSWER the set of solutions to an equation or inequality
Closed set - CORRECT ANSWER a set in which, under an operation, any two members of the set constitute an element of the set (i.e., if multiplying two members of the set gives you another element of the same set). Sets are closed and open not absolutely, but in relation to these specific equations
Diagonal of a square - CORRECT ANSWER d = s√2
ounces in a pound - CORRECT ANSWER 16
pints in a quart - CORRECT ANSWER 2
feet in a yard - CORRECT ANSWER 3
feet in a mile - CORRECT ANSWER 5280
Area of an equilateral triangle with side s - CORRECT ANSWER A = s²√3 / 4
Quantity A = 𝑥
Quantity B = 𝑦
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER a. Quantity A is greater.
(𝑥 - 2𝑦)(𝑥 + 2𝑦) = 4
Quantity A = 𝑥² - 4𝑦²
Quantity B = 8
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER b. Quantity B is greater.
Quantity A = The amount of sugar required for the same recipe to make 30 cookies
Quantity B = 2 cups
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER b. Quantity B is greater.
A power station is located on the boundary of a square region that measures 10 miles on each side. Three substitutions are located inside the square region.
Quantity A = The sum of the distances from the power station to each of the substations
Quantity B = 30 miles
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER d. The relationship cannot be determined from the information given.
6 < 𝑥 < 7
𝑦 = 8
Quantity A = 𝑥⁄𝑦
Quantity B = 0.85
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER d. The relationship cannot be determined from the information given.
𝑂 is the center of the circle and the perimeter of ∆𝐴𝑂𝐵 is 6.
Quantity A = The circumference of the circle
Quantity B = 12
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER a. Quantity A is greater.
Quantity A = The standard deviation of a set of 5 different integers, each of which is between 0 and 10
Quantity B = The standard deviation of a set of 5 different integers, each of which is between 10 and 20
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER d. The relationship cannot be determined from the information given.
𝑥 > 1
Quantity A = (𝑥²)
Quantity B = (𝑥³)³
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER c. The two quantities are not equal.
𝑥 ≠ 0
Quantity A = │𝑥│+│-2│
Quantity B = │𝑥 - 2│
a. Quantity A is greater.
b. Quantity B is greater.
c. The two quantities are not equal.
d. The relationship cannot be determined from the information given. - CORRECT ANSWER d. The relationship cannot be determined from the information given.
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