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GMAT Exam Prep
Original Sections
- Analytical writing (analysis of an argument)- 30 min. Type essay on keyboard. Scored on a scare of 0-6.
- Integrated reasoning (multi-source reasoning, table analysis, graphics interpretation, two-part analysis)- 30 min. Get computer calculator. Multiple choice. 12 questions. Take break after.
- Quantitative (problem solving and data sufficiency)- 75 min. No calculator. Multiple choice. Scored on a scale of 0-60. 37 questions. Take break after.
- Verbal (reading comprehension, critical reasoning, sentence correction) - 75 min. Multiple choice. Scored on a scale of 0-60. 41 questions. No notes/scratch paper allowed, but they give a dry erase board and marker. Total GMAT score is between 200 and 800, based on verbal and quantitative sections. Determined by # questions answered, # answered correctly/incorrectly, and the level of difficulty and other characteristics of the questions. If you answer easy questions correctly, get a chance to answer harder ones, making a higher score possible. AWA and Integrated reasoning scores reported separately from the rest of the test and have no effect on verbal, quantitative, or total score. General Test-taking tips
- Use time wisely- 1 3/4 min per verbal Q, 2 min per quantitative Q. 2 1/ min per IR Q. Onscreen clock shows the amount of time left during the test. It will auto alert when there are only 5 min left in the section.
- Answer practice Qs ahead of time- familiarize self with all question types then do practice Qs, preferably timed.
- Read directions carefully- if forget them, click on the help icon. Try not to do this bc that time still counts. Just try to remember at the beginning.
- Read each question carefully/thoroughly.
- Don't spend too much time on any one question- more worthwhile to move on.
- Confirm answers only when ready to move on- can't go back and change once it is confirmed. Can't skip questions. For the IR section there could be multiple questions based on one prompt. When this happens, if they show on one screen, you can change your response to any of the questions on the screen before going to the next screen. However, you can't go back to that screen again once you've moved on.
- Plan your essay answer before you begin writing. Even though the first 10 questions help the algorithm to determine your ability for the following questions, focus on them all equally, as the score is computed based on your answers to all of them, and it is more important to complete the test than to respond correctly to every question. Basic Grammar Rules for Sentence Correction Portion
- Agreement: -non-verb agreement: singular subjects w singular verbs, plural w plural. I walk to the store not I walks to the store. -pronoun agreement: pronoun must agree w/ noun/pronoun it refers to in person, number, and gender. When you dream, you are usually asleep, not when one dreams, you are usually asleep.
- Diction: -among vs between: among refers to relationships involving >2 objects. Between is for relationships with only 2 objects. -as vs like: As can be a preposition meaning "in capacity of" or can be a conjunction of manner followed by a verb. Like is used as a preposition, and should be followed by a noun, object pronoun, or verb ending in -ing. -mass and count words: mass words are nouns quantified by an amount rather than a number. Count words are nouns quantified by a number. -pronouns: myself shouldn't substitute I or me.
- Grammatical Construction: -fragments: parts of a sentence disconnected from the main clause. -run-on sentences: two independent clauses that run together without proper punctuation. -constructions: wordy and redundant.
- Idiom: Nonstandard expressions should be avoided, although English idioms don't always follow conventional grammatical rules. Be sure to use the correct idiom when using the constructions and parts of speech.
Integers divisible by two are called even. Those not divisible by two are called odd. If at least one factor in a product of integers is even, the product itself is even. Otherwise, it is odd. If two numbers are both even or odd, their sum and difference will be even. Otherwise, it is odd. A prime number is a positive integer with only two different positive divisors, 1 and itself. 2, 3, 5, 7, 11. 1 is not a prime number because it only has 1 divisor. Every number > 1 is either prime or a can be shown as a product of prime numbers. Consecutive integers are all in a row. n, n+1, n+2, etc. Consecutive even integers= 2, 4, 6, 8. 2n, 2n+2, 2n+4, etc. Consecutive odd integers= 1, 3, 5,
- 2n+1, 2n+3, etc. If n is any number then 1 x n = n. If n is not 0 then n x 1/n=1. 0 is neither positive nor negative. Cant divide by 0. Fractions Denominator can never be 0. Two fractions are equivalent if they represent the same number. Fractions can be reduced to their lowest terms by dividing the num and denom by their greatest common divisor. Adding/subtracting fractions: Fractions with the same denom can be added or subtracted through the numerators, leaving the denom the same. If the denom isn't the same, make it the same by expressing them as equivalent fractions w the same denom. Multiply by the least common multiple to do this. Multiplying/dividing fractions: For multiplying, multiply the numerators and the denominators. Done. To divide, invert the divisor (do the reciprocal, 4= 1/4), and multiply as normal. Mixed numbers: A whole number and a fraction. 7 and 2/3 is an example. To change this into a fraction, multiply the whole number by the denom of the fraction and add this number into the num of the fraction. 7 and 2/3 = [7(3)
Decimals Scientific notation= 2.31 x 10^2 is 231 or 2.31 x 10^-2 is .0231. Adding/subtracting decimals: line up the decimal points of both numbers (add 0s at the end if one has fewer digits to the right of the decimal point). Multiplying decimals: multiply them as though they were whole numbers and then add the decimal point in so that the number of digits to the right of it is the sum of the numbers of digits to the right of the decimal points being multiplied. 2.09 x 1.3 = 2.717. Dividing decimals: to divide a number by a decimal, move the decimal point of the divisor to the right until the divisor is a whole number, then move the decimal point of the dividend (num) the same number of places to the right, and divide as you would by a whole number. The decimal point in the quotient will be directly above where it is in the new dividend. Real Numbers Real numbers all correspond to points on the number line, and all points on the number line correspond to real numbers. The distance between a number and 0 on the number line is called the absolute value of the number. 3 and -3 have the same absolute value |3|. Absolute values are always positive in any nonzero number. xy + xz is the same as x(y+z). |x=y| is < or = |x| +|y|. Ratios and Proportions The ratio of a to b where b is not 0 = a/b. Can be written several ways, a/b, a to b, a:b. A proportion is a statement that two ratios are equal. 2/3=8/12. A proportion involving an unknown can be solved by cross multiplying and solving for x. Percents 37% = 37/100 = 0.37. Percent change: if a problem asks for a % incr or decr from one quantity to
sum of the number of elements in both sets minus the number of elements in the intersection. If they are mutually exclusive then it's just the sum of the number of elements in both sets. Counting Methods Can count objects and sets of objects without listing the elements to be counted with the multiplication principle: If an object is to be chosen from a set of m objects and a second object is to be chosen from a set of n objects, there are mn ways of choosing both objects simultaneously. n! is the product of all the integers from 1 to n. Also 0!=1!=1. Can use the factorial to count the number of ways that a set of objects can be ordered- n(n-1)(n-2)....=n! This is a permutation, a selection process in which objects are selected one by one in a certain order. If the order of selection is not relevant and k objects are to be selected from a larger set of n objects, where 0<=k<=n, the number of possible selections of k objects is called the number of combinations of n objects taken k at a time, and is denoted (n above k). This equls n!/[k! x (n-k)!]. Every subset chosen of (n above k) is equal to a subset (n above n-k) of elements not chosen. Discrete Probability Concerned with experiments that have a finite number of outcomes. An event is a particular set of outcomes. The probability that an event E occurs P(E) is a number between 0 and 1, inclusive. If E has no outcomes, it is impossible and P(E)=0. If E is the set of all possible outcomes of the experiment then E is certain to occur and P(E)=1. Otherwise E is possible but uncertain, and 0<P(E)<1. If F is a subset of E, P(F)<P(E). If the probability of each of the outcomes is equally likely, the probability of each one is 1/number outcomes, and the probability of an event E is P(E) = total number of outcomes in E/total number of possible outcomes. In an experiment with events E and F, the probability that E doesn't occur is 1- P(E). The probability that the union of E and F occurs is P(E or F)= P(E) + P(F) - P(intersection of E and F). Two events A and B are said to be independent if the occurence of either one
doesn't alter the probability that the other will occur. The probability of A assuming B occurs is (number of outcomes in A intersection w/ B)/number of outcomes in B. If A is independent of B, this will be the same as the normal probability of A occurring. Same thing w B. For independent events, the multiplication rule is that P(E and F)= P(E) x P(F). This will equal the intersection if there is one, and thus it follows from the addition rule that P(E or F) = P(E) + P(F) - [P(E) x P(F)]. Simplifying Algebraic Expressions Simplify by factoring (9x+3y = 3(3x+y)) or combining like terms. If there are common factors in the numerator and denominator of an expression, they can be divided out, provided that they are not equal to 0. To multiply algebraic expressions, each term of one expression is multiplied by each term of the other. Equations Solutions must make an equation true when they are entered into it. Two equations with the same solution(s) are equivalent. If there are two unknowns in equivalent equations, they have an infinite number of solutions. Solving Linear Equations with One Unknown Isolate the unknown on one side of the equation. Do this by applying the same math to both sides of the equation. Can check the solution by susbsituting it into the original equation to see if it satisfies it. Solving Two Linear Equations with Two Unknowns If the two equations are equivalent, there are infinetely many solutions. If they are not, they either have a unique solution or no solution. When solved, a contradiction is no solution, 0=0 is equivalency, and a unique solution is just that. Solve for x or y in one equation and then plug that into the other to solve the equation with one variable. When that variable is found, you can plug it into either of the original equations to find the value of the other variable. Can also solve by making the coefficients of one of the unknowns equal
f(x) or g(x) = algebraic expression. Read like f of x or g of x. x is the input, f(x) or g(x) is the corresponding output. There is only one output for a given input, but two or more inputs could give the same output. The set of all allowable inputs for a function is called the domain of the function. Defined like o< or = x < or = 10. If there is no restriction, the domain is assumed to be all values of xthat result in a real number when subsituted into the function. A domain like 0, 1, 2, 3, ... n is called a sequence and instead of being denoted a(n) is denoted a subscript n. Lines A line is a straight line that extends in both directions without end. Notation is line PQ or line Q, etc. A line segment is the area between two endpoints of a line. Line above PQ is the notation and PQ is used to denote the length of the segment. Intersecting Lines and Angles If two lines intersect, the opposite angles are called verticle angles and have the same measure. If the lines are straight the angles next to one another on the same line = 180 degrees. Perpendicular Lines A right angle measures 90 degrees. Two lines intersecting at right angles are perpendicular. This is usually indicated by a right angle symbol in the angle of an intersection. Parallel Lines Two lines in the same plane that don't intersect. If a third line runs through both parallel lines, the angle rules are the same as with other intersecting lines. Polygons (Convex) A polygon is a closed plane figure formed by 3 or more line segments called its sides. The points of intersection of the sides are vertices. The term polygon should be assumed to mean convex, with each interior angle measuring < 180 degrees. The sum of the interior angle measures of a triangle is 180 degrees. The sum of the interior angle measures of a polygon with n sides is (n-2) x 180.
The perimeter of a polygon is the sum of the lengths of its sides. The area of a polygon is the region enclosed in that figure. Triangles The sum of the lengths of any two sides of a triangle is greater than the length of the third side. An equilateral triangle has sides all of equal length. All angles of an equilateral triangle have equal measure. An isosceles triangle has at least two sides of the same length. If two sides of a triangle have equal length, then the two angles opposite those sides have equal measure. Likewise, if two angles of a triangle have equal measure, the two sides opposite those angles have the same length. A triangle with a right angle is a right triangle. The side opposite the right angle is the hypotenuse, and the other two sides are the legs. The pythagorean theorem states that in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. Any triangle in which the lengths of the sides are in ratio 3:4:5 is a right triangle. In 45-45-90 triangles the ratio is 1:1:sqrt(2). In 30-60-90 triangles the lengths of the sides are in the ratio 1:sqrt(3):2. The altitude (height) of a triangle is the segment drawn from a vertex perpendicular to the side opposite that vertex. The opposite side is called the base. The area of a right trangle is BH/2. In an isoceles triangle the altitude could bisect the base if the two other sides are equal. In an equilateral triangle the altitude always bisects the side to which it is drawn. Quadrilaterals Polygons with 4 sides. A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. The opposite sides of a parallelogram have equal length. The diagonals of a parallelogram bisect one another. The area of a parallelogram is equal to BH. where H is height/length of altitude.
The volume is equal to LWH or (area of the base x H). The surface area of a right cylinder is [2(pi(r^2))] + [2(pi(rh))]. The volume of a cylinder is pi(r^2)h. Coordinate Geometry One way to find the distance between two points in the coordinate plane is to the the pythagorean theorem. In y=mx+b, m is the slope and b is the y-intercept. The slope is the difference in the y-coordinates/difference in the x-coordinates. The x-intercept can be found by setting y=0 and solving for x. Can use the slope to find the equation with the formula y-y1 = m(x-x1) by plugging in one of the points used to calculate the slope. If the slope is 0 the line is horizontal and the equation is y=b. For a vertical line slope is undefined and the equation is x=a, where a is the x-intercept. For two linear equations with two unknowns, the lins will intersect is there is one solution, will be the same if there are infinetely many solutions, and will be parallel if there is no solution. Functions can be expressed as y= the function, where y is equated with the value of the function. They can also be expressed as f(x)=y, where any x in the domain of the function f is the point (x, f(x)), which will be on the graph of f. The graph of a quadratic function is a parabola. The roots of the quadratic equation will be the x-intercepts on the graph, and the value of f(0) will be the y-intecept. Rate Problems D=RxT. Can solve some w ratios. If 5 shirts cost $44, then, at this rate, what is the cost of 8 shirts? 5/44= 8/x. Cross multiply and solve. Work Problems
Usually gives the rate at which two things work alone and asks you to compute the rate at which they work together (or vice versa). The formula for these is 1/r + 1/s = 1/h. Will have to cross multiply and solve once you get fractions on either side. Mixture Problems Combine two things of different characteristics and ask you to determine the characteristics of the resulting mixture. Interest Problems Simple annual interest=PRT. If compounded must be computed on principal
- any interest already earned. Discount Problems If a price is discounted by n percent then the price becomes 100-n percent of the original price. Profit Problems GP= revs-exp or selling price-cost. Problems with Sets Sets are written S(or whatever the name is)={numbers}. They can be represented by Venn Diagrams in that the relationship among members of sets can be represented by circles. For the Venn Diagrams, create an equation for each part of the population in question, and then set it equal to the total number of people and solve for x. For the table ones fill in a table with all info, use the one number given with the percentages in the table to solve for the total, and then multiply that by the percentage the problem is asking for. Measurement Problems Could use metric or english units, but, except for units of time, if conversion is required they will always give the relationship. Learn More You can also click the terms or definitions to blur or reveal them Review with an activity
