GRE Math With absolute solution latest

GRE Math With absolute solution latest The sum of the angles in a quadrilateral is - 360° Any n-sided polygon can be divided into how many triangles? (by drawing diagonals from one vertical) - n-2 The sum of the measures of the n angles in a polygon with n sides - (n-2) x 180 In any polygon, all external angles equal up to - 360° If you measure all exterior angles in a polygon, they all equal - 360° In any Regular Polygon, the measure of each interior angle - (n-2)x180/n In a Regular Polygon, the measure of each exterior angle - 360/n The consecutive angles in a parallelogram equal - 180° A quadrilateral where two diagonals bisect each other - Parallelogram In a rectangle, all angles are - Right In a Rectangle, each angles measures - 90° Each diagonal divides a square into 2 - 45 45 90 Right triangles (x, x, x*square root of 2) What kind of trapezoid has equal parallel sides? - Isosceles Trapezoid The Perimeter of a rectangle - P=2(l+w) The Perimeter of a Square - P=4s (s=side) Area of a Parallelogram: - A=(base)(height) Area of a Rectangle: - A=(side)² or A=½(diagonal)² Area of a Trapezoid: - A=½(base₁+base₂)(height) For any given perimeter, the rectangle with the largest AREA is a - Square (versus a rectangle) For any given Area, the rectangle with the smallest perimeter is a - Square (versus a rectangle) (x-y)(x+y) - x²-y² (x-y)² - x²-2xy+y² (x+y)² - x²+2xy+y² An Angle that's 180° - Straight Angle The sum of all angles around a point - 360° If one of the angles formed by an intersection is right, they're all right - True If a pair of parallel lines is cut by a transversal that's not perpendicular, the sum of any acute angle and any obtuse angle is - 180 Distance - (rate)(time) d=rt Rate - d/t (distance)/(time) Time - (distance)/(rate) d/r Average - Sum/n Sum of numbers in an average - n/Average The total deviation below the average is equal to - The total deviation above the average (80, 90, 90, 90, 100) Assume that the average of a set of numbers is A. If a number x is added to the set and a new average is calculated, then the new average will be less than, equal to, or greater than A, depending on whether x is less than, equal to , or greater than A, respectfully. - 1+2+3/3=2 1+2+3+4/4=10/4=2.5 If "n" is even, the average of the numbers is the average of what? - The middle two terms (10, 20, 30, 40, 50, 60) 30+40/2=35 To calculate the weighted average: Multiply each number in the set by the number of times it appears, add all the products, and divide by the total number of numbers in the set. - ... In a set of n numbers that are arranged in increasing order, it is the middle number, if n is odd or the average of the middle two if it is even. - Median It is the number in the set that occurs most often - Mode Ratios: If a set of objects is divided into 2 groups in the ratio of a:b, then the first group contains - a/a+b and the second group contains b/a+b of the objects. 4:6 becomes 4/4+6=4/10=2/5 6/4+6=6/10=3/5 If two numbers are in the ratio of a:b (2:4), then for some number x (3), the first number is ax (2x3) and the second number is bx (4x3). If the ratio is in the lowest terms, and if the quantities must be integers, then x(3) is also an integer. - 2(3)+4(3)=6(3) If a set of objects is divided into 3 groups in the radio a:b:c, then the first group contains a/a+b+c, second group contains b/a+b+c, etc. - 2:3:4 An equation that states that two ratios are equivalent i.e. 4/6=10/15=2/3 - Proportion How do you solve proportions? - Cross multiplication a/b=c/d ad=cb 4/6=10/15 4(15)=6(10) 60=60 A fraction that compares two quantities measures in different units - Rate. "Miles per hour" "Dollars per week" "cents per ounce" "students per classroom" ½% of 100 is - ½ a% of b - b% of a The percent increase of a quantity - (Actual increase/original amount)100% If a lamp increases from $80 to $100, what is the percent increase? - 25%. (actual increase/original amount)100% 20/80x100%=1/4x100%=25% The percent decrease of a quantity - (actual decrease/Original amount)100% If a lamp decreases to $80, from $100, what is the decrease in price? - (actual decrease/Original amount)100% 20/100x100% is 20% If ab, the percent increase in going from a to b is always greater than the - percent decrease in going from b to a To increase a number by k% - multiply by 1+k% i.e. 100 x (1+50%)=100x1.5=150 To decrease a number by k% - multiply by 1-k% i.e. 100 x (1-50%)=100x.5=50 An increase of k% followed by a decrease of k% is equal to a decrease of k% followed by an increase of the k% and is always less than the original value. - The original value is never re-gained. 100+50==75 versus 100-50=50+25=75