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GMAT(Graduate Management
Admission Test) Exam Prep
Standardized Questions With Correct
Verified Answers 100% Score.
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 1/2 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.
- Verb Form: correct tenses.
- present perfect: has/have + verb.
- past perfect: had + verb.
- future perfect: will have.
- present progressive: ongoing action that is happening now, used with am, is, or are + verb-ing.
- past progressive: was or were + verb-ing.
- future progressive: will be or shall be + verb-ing.
- present perfect progressive: have been or has been + verb-ing.
- past perfect progressive: had been + verb-ing.
- future perfect progressive: will have been + verb-ing.
Properties of Integers
An integer is any number in a set {-1, 0, 1}. If x and y are integers and x >0, x is a factor of y as long as y=xn for some integer n. In other words, y would be divisible by/a multiple of x. A quotient is the number that can be evenly divided into another, the remainder is what is left over if it is not even. y is divisible by x only if the remainder is 0. When a small integer is divided by a large integer, the quotient is 0 and the remainder is the small integer. (5/7= 7(0) + 5).
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, 7. 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) + 2]/3 = 23/3.
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).
Percent change: if a problem asks for a % incr or decr from one quantity to another, divide the amount of the incr/decr by the original amount, and express this quotient as a %.
Powers and Roots of Numbers
k^n is the nth power of k. 2^2= 2 x 2=4.
Raising a number >1 to a higher power creates a larger number. Raising a number between 0 and 1 to a higher power results in a smaller number.
The square root of a number equals the number when squared. The square root of a negative is not a real number. Every positive number has a positive and a negative square root. The two square roots of 9 are 3 and - 3.
Cube roots are like square roots, but the cube root of a number equals the number when cubed. Can have negative cube roots on the inside.
Descriptive Statistics
Mean= sum of n numbers/n.
Median= order numbers from least to greatest and pick the middle one. If there are two, the median is the average of them. It is not always the case that half of the data is less than and half is greater than the median.
Mode= the number that occurs most frequently. There can be more than one.
Range= difference between largest and smallest numbers.
Standard deviation= find the mean, find the differences between the mean and each of the numbers in the data set, square all of the diffs, find the average of the squared diffs, take the square root of this. Smaller standard deviation= numbers being closer to the mean.
Frequency distribution= lists each value and the frequency with which it occurs.
Sets
A set is a collection of numbers or objects. The objects are called elements. The number of elements in set S is denoted |S|. The order of the elements in the set doesn't matter. If all of the elements of set S are also elements of set T, then S is a subset of T.
The union of sets A and B is the set of all elements that are in A or B or both (denoted by U). The intersection is the set of all elements that are in both A and B (denoted by upside down U). Two sets with nothing in common are disjoint/mutually exclusive. The number of elements in the union equals the 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
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 (through multiplying each of the equations by some lcm), and adding/subtracting the equations to eliminate that unknown. Then can solve for the other unknown and plug it into one of the original equations to find the first unknown.
Solving Equations by Factoring
Add or subtract to bring all of the expressions to one side of the equation, with a 0 on the other side. Try to factor the nonzero side into a product of expressions, which can then each by set equal to 0 for simpler equations that possibly can be solved. The solutions of the simpler equations will be the solutions of the factored equation.
A fraction equals 0 only if its numerator equals 0, so if a fraction equals 0 can set the equation in the numerator equal to 0.
Solving Quadratic Equations
ax^2 + bx + c. a can't = 0. Can factor to solve. There will be two roots, one root, or no roots. If a quadratic can't easily be factored, use the quadratic formula, x = - b +/- sqrt(b^2 - 4ac)]/ 2a
Exponents
- (x^r)(x^s) = x(r+s)
- (x^r)/(x^s)=x(r-s)
- (x^r)(y^r)= xy^r
- (x/y)^r = (x^r)/(y^r)
- (x^r)^s = x^(rs) = (X^s)^r
- x^-r = 1/(x^r)
- x^0 = 1
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.
Rectangular Solids and Cylinders
A rectangular solid is a 3d figure formed by 6 rectangles, each of which is a face. Each line segment is an edge, and each point which the edges meet is a vertex. Opposite faces are parallel rectangles that have the same dimensions. A rectangular solid in which all of the edges are of equal length is a cube.
The surface area of a rectangular solid is the sum of the areas of all the faces.
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
