GRE MATH With Absolute Solution 2023

GRE MATH With Absolute Solution 2023 general strategy 1 - Be careful if your answer comes too easily, especially if the question is toward the end of the section. Especially beware of Choice A answer. It is often a 'lure'. General strategy 2 - It's a good ideas to learn directions and familiarize yourself with the types of questions early before taking the exam. Never waste time reading directions on the test. General strategy 3 - Do not leave any answer blank. There is no penalty for guessing. general strategy 4 - Write as much as you want on scrap paper or test booklet, they are not graded General strategy 5 - Use a coding system to indicate which questions you need to return to Odd integer x odd integer = - Odd integer only Odd integer +/- odd integer = - Even integer only Even integer x even integer = - Even integer only Even integer +/- even integer - Even integer only (Odd integer) ^ odd power - Odd integer only (Even integer) ^ even power - Even integer only (Even integer) ^ odd power - Even integer only Multiplication of exponents (with same base) - Add the exponents ( a^2 * a^5 = a^7) Multiplication of exponents (with different base) - Multiply the exponents ( a^4 * b^4 = (ab)^16) If an exponent is negative.. - Move it to the denominator (a^3)^5 = - a^15 When you are asked to find x percent of number, n... - x/100 * n = % When asked to find the value of x given two equations with unknowns, x & y..... - Add the two equations together to cancel y. This may have to be done by multiplying one or the other equation by some number. Rules of parallel lines - When a pair of parallel lines is cut with another line known as an intersecting transversal, it creates pairs of angles with special properties. Corresponding angles are equal. The lines make an F shape. Alternate angles are equal. The lines make a Z shape which can also be back to front. Angles in a triangle add up to - 180 degrees If given two sides of a triangle and asked to find the possible value of the third side and it is NOT a right triangle... - The sum of any two sides must be grater than the third side If angle B is across from line segment b and angle A is across from line segment a in a triangle... - If BA, then ba If ba, then BA Area of a triangle equals - 0.5(base)(height) Area of a circle - A=πr² Circumfrence of a circle - 2πr Inscribed angle of a circle = - 1/2 * arc Central angle of a circle (angle comes from center)= - the arc Any inscribed angle whose triangle base is a diameter is... - 90 degrees In a rectangle with equal sides, diagonals will be.... - equal Area of a rectangle - A=bh Volume of a rectangular solid - (length)(width)(height) Slope of a line - y2-y1/x2-x1 Inequalities (a mathematical sentence involving , , or = plus or ) - - If you can multiply both sides of the equation by the same quantity and get the second equation, then the statement is ALWAYS true - In the case where you are given two conditions and the second equation uses multipication, beware because the answer is often SOMETIMES What is the average speed in mph of a car traveling 40 miles in 4 hours? - 40/4 = 10 Go through shortcut example questions on page 51 of GRE book - Math strategy 1 - Cancel numbers or expression that appear on both sides of an equation; cancel numerators and denominators when they are the same. When canceling a variable on both sides of an equation however, beware. Determine what the answer is first if the variable were 0. For example: If R * a = a * 4/5, then R = cannot be determined. This is because if a=0, R can be any number. If a+ba-b, which must follow? - Cancel a: b-b Add b to both sides: 2b0 Simplify: b0 Math strategy 2 - Translate English words into mathematical expressions (see pg. 74-79 & translation table on page 74) Math strategy 3 - Know how to find unknown quantities from known quantities (The whole equals the sum of its parts) Math strategy 4 - Memorize the following factorizations and expressions: x^2 + y^2 = (x+y)(x-y) x^2 + 2xy + y^2 = (x+y)(x+y) = (x+y)^2 x^2 -2xy + y^2 = (x-y)(x-y) = (x-y)^2 (x+y)/(xy) = 1/x + 1/y, where x and y do not equal 0 (x-y)/(xy) = 1/x - 1/y, where x and y do not equal 0 xy + xz = x(y+z) xy-xz = x(y-z) Math Strategy 5 - Know how to manipulate averages. Almost all problems involving averages can be solved by remembering that: Average= (sum of the individual quantities or measurements)/(number of quantities or measurements) Math strategy 6 - Know how to manipulate inequalities (important inequality statements found on page 88) Math strategy 7 - When you do not want to do a lot of algebra, or when you are unable to prove what you think is the answer, try substituting answer choices. Math strategy 8 - If you must check each answer choice for the answer, start with the last choice and work backward. The test maker often puts the correct answer as the last choice in these types of questions. Math strategy 9 - Know how to solve the problems using the formula: R (rate) x T (elapsed time) = D (distance) Math strategy 10 - Know how to use units of time, distance, area, or volume to find or check your answer (by knowing what units in your answer must be, you will often have an easier time finding or checking your answer) How many feet in a yard? - 3 Math strategy 11 - Use new definitions and functions carefully. Some GRE questions use new symbols, functions, or definitions that were created in the question and make them look difficult. However, most of these questions can be solved through simple substitution or application of a simple definition. Math strategy 12 - Know how to find unknown expressions by adding, subtracting, multiplying, or dividing equations or expressions, instead of solving for x and then y directly. Math strategy 13 - Draw or extend lines in a diagram to make the problem easier; Label unknown quantities with a variable If a circle is inscribed within a square, the side of the square will equal... - two times the radius of the circle The sum of the angles in a quadrilateral is - 360° Math strategy 14 - Watch out for questions that seem very easy and use choice A as a "lure choice", but that can be actually pretty tricky. Statements about triangles to remember: - 1.) The base angles of an isosceles triangle are equal. 2.) If the base angles of a triangle are equal, the triangle is isosceles (the corresponding sides of the angle are equal). 3.) The measure of an exterior angle is equal to the sum of the measures of the remote interior angles. 4.) In a triangle, the greater angle lies opposite the greater side, and vice versa. 5.) In similar triangles ( ABC & DEF), angle A equals angle D, angle B equals angle E, angle C equals angle F and a/d = b/e = c/f. 6.) The sum of the interior angles of a triangle equal 180 degrees. 7.) The area of a triangle equals 1/2bh. 8.) In a right triangle, c^2 = a^2 + b^2 and acute angles add to 90 degrees. 9.) Memorize common standard triangles (pg.116) 10.) The sum of the lengths of two sides of a triangle is greater than the length of the third side (a +b c, a+cb, and c+ba) Math strategy 15 - When calculating answers, never multiply and/or do long division if you can reduce first Memorize the directions for Quantitative Comparison questions as follows: - - If quantity A is always greater than quantity B, select choice A - If quantity A is always less than quantity B, select choice B - If quantity A is always equal to quantity B, select choice C - If a definite comparison or relationship cannot be made between quantities A and B, then select choice D 2.) If they tell you want a variable is between both quantities, use that variable in both quantity formulas. 3.) You can add or subtract the same quantity from both columns to obtain a comparison or multiply and divide both columns by a same positive number, never divide or multiply columns by a negative number or zero. Math Strategy A - Cancel numbers or expressions common to both columns by addition or subtraction Math Strategy B - Cancel numbers or expressions (positive quantities only) common to both columns by multiplication or division Math Strategy C - When a comparison of the two columns is difficult, use numbers in place of variables. If you feel like a definite comparison cannot be made, try to find a number that makes the columns equal and another number that makes them unequal to ensure that D is the right answer. Math Strategy D - To make a comparison easier, especially if fractions, multiply, divide, add to, or subtract, from both columns by a quantity (but never multiply or divide by a negative number or zero) - To simply a problem you can often get rid of minus signs just by adding the same quantity to both columns. - Often you can multiply or divide each quantity by the same number to simplify the problem and avoid tedious calculations - In comparing square roots, instead of calculating or substituting numbers, you can usually just square the square roots to get rid of the square root signs. Math Strategy C - Use the Choice C method when straightforward computations must be made. This strategy should only be used if you must guess the answer and you do not have enough time to finish the answer. When the answer to a problem requires only a straightforward computation and uses very specific numbers, choice C is almost always correct. How do you change a fraction to a percent? - Find the decimal form of the fraction, multiply by 100 and add a percent sign.