Integers = negative or positive numbers. Do not include fractions.
= odd or even.

a=b x q + r (q=quotient r=remainder)
Distinct numbers = cannot be equal
Prime numbers = a positive integer that has exactly 2 different positive divisor (1 and itself). 0 and 1 are not prime numbers
Absolute value of 5 is |5|

Divisibility rules:

• 6 is divisible by 2
• the factors of 20 are 1,2,4,5,10
• 20 is a multiple of 4

Remember:
Most problems at GMAT require more than one step in getting the right answer!
If you are not a native English speaker learn the technical terms!

Incoming search terms:

If a question asks “what is x?” it means: can a single value for x be found?

For data sufficiency GMAT problems, when see the word “percent” think part/whole

For a data sufficiency statement to be sufficient there must be as many equations as there are variables.

• A single equation with two variables cannot be solved
• Two distinct equations with the same two variables can be solved, using simultaneous equations

Just because there is only one variable does not mean an equation has just one solution.

• An equation with a variable raised to an even power may have more than one solution
• An equation with a variable raised to an odd power will have only one solution

Data sufficiency yes or no: if a statement answers the question in the affirmative or in the negative, it is sufficient.

The answer can be no!!!

Never assume!!!

Just because one statement seems to agree with the other does not mean they are necessarily saying the same thing. !!!

When you look at Statement 2 always cover up Statement 1 and think like you never saw it. !!!

Incoming search terms:

Paragraphs (as in the post about analysis of an issue):

1. Write the argument (copy/paste) and point the three weak points you identified.
2. Write the first weak point and write one reason ore more reasons why it is not true.
3. Write the second weak point and write one reason ore more reasons why it is not true.
4. Write the third weak point and write one reason ore more reasons why it is not true.
5. Write again the three weak points and say that because of those the argument is not “entirely logically persuasive”.

As an example:

1. The argument that … is based on … but omits certain important concerns that must be addressed to make this argument logically persuasive. The declaration that follows the explanation of what … simply explain …. This alone does not support the main argument.
2. First the argument assumes that … But …
3. Second the argument never concentrates on … Although …
4. Finally, the argument also does not deal with … However …
5. Thus the argument is not completely persuasive. The argument would have been more comprehensive and compelling if …

Incoming search terms:

What you need to remember is:

• Nobody cares what your opinion really is
• Be superficial

Tips & tricks:

• When an entire paragraph contradicts with another use expressions like: on the one hand/on the other hand, the traditional view/the new view.
• When you support the main idea use: for example, to illustrate, for instance, because.
• When you use a second argument to support the main idea: furthermore, in addition, similarly, just as, also, moreover.
• The most important idea that you write must be introduced by one of the following words: surely, truly, undoubtedly, clearly, certainly, indeed, as a matter of fact, in fact, most important.
• The conclusion starts with: therefore, in summary, consequently, hence, in conclusion, in short.
• When you talk about the opinion that you argue against, start with: admittedly, certainly, obviously, undoubtedly, one cannot deny that, true, granted, of course, to be sure, it could be argued that.

Incoming search terms:

Basically you just replace with number the unknown data represented with letters. Sounds stupid, but it works and you gain time.

Plugging in a number in the question:

1. Pick one or more numbers to replace the letters in the problem (question)
2. Using your numbers, find an answer to the problem
3. Plug your numbers into the answer choices to see which choice equals the answer you found in step 2

Plugging in a number in the answers:

1. Always start with answer C. Plug that number into the problem and check if it gives you a solution.
2. If choice C is too small, choose the next larger number
3. If choice C is too big choose the next smaller number

If the question contains “must be”, “could be” or “cannot be”, the problems can be solved by plugging in but you may need to plug more than one number.
You must have at least as many distinct equations as you have variables for the equation to be solvable.

ax² + bx + c = 0

x = [-b +/- √ (b²-4ac)] / 2a

Also, simultaneous equation can be solved an addition or subtraction of one equation from the other. This way you can eliminate one of the unknowns.

GMAT’ “most wanted”:

• (x + y) ² = x² + 2xy + y²
• (x + y)(x – y) = x² – y²

Incoming search terms:

Now, arithmetic:

1.Rate x Time problems: The only formula you need is rate x time = distance         r x t = d

2. Work problems: ALWAYS think of how much of the job can be done in one hour.

3. Mix problems:

Interest = principal x interest rate x time.
Discount = if a price is discounted by n percent, the price becomes 100-n percent of the original price.|
Profit = revenues minus expenses = selling price minus cost.

4. Functions:

The strange character * or # is part of a fix unit not a formula. What you replace with numbers are letters like x or y.
Domain = the set of all allowable inputs for a function.
Sequence = a function defined only for input values that are the positive integers and possibly 0.

5. Probability.

An event is a particular set of outcomes.
Numerator = the number of possibilities that match what you want.
Denominator = the total number of possibilities.

Six-sided die:

1. one side, one time 1/6
2. two sides, one time 2/6
3. one side, both times 1/6 x 1/6 = 1/36
4. one side or another chosen first 1/6 + 1/6 = 2/6 = 1/3
5. the odds that one side does not happen 5/6
6. the odds that at least one side will happen 1- 5/6 = 1/6

6. Permutations and Combination.

Different source, order does not matters:

• When a problem ask you to choose a number of items to fill specific spots and each spot is filled from a different source, all you multiply the number of choices for each of the spots.

Single source, order matters:

• When a problem asks you to choose from the same source to fill specific spots, you multiply the number of choices for each of the spots. Attention: the number of choices keeps getting smaller. n! = n(n-1)(n-2) … x3x2x1

Single source, order matters but only for a selection:                An/k = n!/(n-k)!

Single source, order does not matters:       C n/k = n!/k!(n-k)!

7. Sets

Set = collection of numbers (elements) or other objects.
T = {1, 2 , 3, 4, 5}                   S = {1, 2, 3}.
|S| = 3 (number of elements).
S = subset of T

Union S U T = {1, 2 , 3, 4, 5}.
Intersection S ∩ T = {1, 2, 3}.
Disjoint or mutually exclusive = no elements in common.

Venn diagrams = google!
|S U T| = |S| + |T| – |S ∩ T|
If S and T are disjoint then |S U T| = |S| + |T| since |S ∩ T| = 0.

Incoming search terms:

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First, some definitions:

• Noun = a word that is used to name a person, place, thing or idea
• Verb = a word that expresses action
• Adjective = a word that modifies a noun
• Adverb = a word that modifies a verb, adjective or adverb
• Preposition = a word that notes the relation of a noun to an action or a thing
• Phrase = a group of words acting as a single part of a speech. A phrase is missing either a subject or a verb or both
• Prepositional phrase = a group of words beginning with a preposition
• Pronoun = a word that takes the place of a noun
• Clause = a group of words that contains a subject and a verb

Pronoun errors that you meet in the GMAT problems can be identified asking the following questions:

• It is completely clear who or what the pronoun is referring to?
• Does the pronoun agree in number with the noun it is referring to?

Common pronouns:

• Singular: I, me, he, him, she, her, you, it, each, another, one, other, such, mine, yours, his, hers, ours, this, either, neither, each, everyone. Everybody, nobody, no one.
• Plural: we, us, they, them, both, these, those.
• Can be singular or plural: some, any, you, who, which, what, that.

Misplaced modifiers

• When a sentence begins with a participial phrase (a phrase that starts with a verb ending in “ing”), that phrase is supposed to modify the noun or pronoun immediately following it.
• Check that the noun is modified comes directly after the modifying phrase.

Parallel construction

If a sentence contains a list of things, or actions or is broken up into two halves, check to make sure the parts of the sentence are parallel.

Again, if your native language is not English, verify your knowledge tenses:

• Present
• Simple Past
• Present Perfect
• Past Perfect
• Future

Subject-verb agreement

• “The number of …” – singular
• “A number of …” – plural
• Singular pronouns: each, everyone, everybody, nobody

Quantity words

• If two items: between, more, better, less.
• If more than two items: among, most, best, least.

• Countable items: fewer, number, many.
• Non-countable items: less, amount, quantity, much.

Incoming search terms:

The texts are in form of an argument with three parts:

1. Conclusion = what the author is trying to convince you of.
2. Premises = pieces of evidence the author gives to support the conclusion.
3. Assumptions = unstated ideas or evidence without which the entire conclusion might be invalid.

To describe the eight questions types I will use the classification that I found in the book Cracking the GMAT (The Princeton Review):

Assumption questions = ask you to identify an unstated premise of the passage from among the answer choices.

• Gaps of logic:
  • Causal assumption = takes an effect and suggest a cause for it.
  • Analogy assumption = compares one situation to another, ignoring the question of whatever the two situations are comparable.
  • Statistical assumption = uses statistics to prove its point.
• Contain one of the following wordings:
  • Which of the following is an assumption on which the argument depends?
  • The argument above assumes which of the following?
  • The claim above rests on the questionable presupposition that …
• Guideline:
  • Assumptions are never stated in the passage. If you see an answer choice that comes straight from the passage, it is not correct.
  • Assumptions support the conclusion of the passage.
  • Assumptions frequently turn on the gaps of logic (see up).

Strengthen-the-argument questions = ask you to find the gap in the logic of the argument and then fix it with additional information.

• Contain one of the following wordings:
  • Which of the following, if true, most strengthens the author `s argument?
  • Which of the following, if true, most strongly supports the author` s hypothesis?
• Guideline:
  • The correct answer will strengthen the argument with new information.
  • The new information you are looking for will support the conclusion of the passage.

Weaken-the-argument questions = ask you to find a hole in the argument and expose it.

• Contain one of the following wordings:
  • Which of the following, if true, most seriously weakens the conclusion drawn in the passage?
  • Which of the following indicates a flaw in the reasoning above?
  • Which of the following, if true, would cast the most serious doubt on the argument above?
• Guideline:
  • The statement you will look for should weaken the conclusion of the passage.
  • Frequently trade on the gaps of logic: cause for an effect, the representative of the statistics, analogy of a situation.

Inference questions = they do not really ask you to make an inference.

• Contain one of the following wordings:
  • Which of the following can be inferred from the information above?
  • Which of the following must be true on the basis of the statements above?
  • Which of the following conclusions is best supported by the passage?
  • Which of the following conclusions could most properly be drawn from the information above?
• Guideline:
  • The answer is basic
  • Search for a situation described in the passage but do not go too far
  • These questions will concern the premises, not the conclusion

Mimic-the-reasoning questions = ask you to recognize the reasoning in the passage and follow the same line of reasoning in one of the answer choices.

• Contain one of the following wordings:
  • Which of the following most closely parallels the reasoning used in the argument above?
  • Which of the followings supports its conclusion in the same manner as the argument above?
  • Which of the following is most like the argument above in its logical structure?
• Guideline:
  • If A, then B

Resolve-the-paradox questions = ask you to resolve an apparent paradox or explain a possible discrepancy.

• Contain one of the following wordings:
  • Which of the following, if true, resolves the apparent contradiction presented in the passage above?
  • Which of the following, if true, best explains the discrepancy described above?
  • Which of the following, if true, forms a partial explanation for the paradox described above?
• Guideline:
  • Find the answer choice that allows both of the facts from the passage to be true

Evaluate-the-argument questions = ask you to ‘evaluate” or “assess” part of an argument.

• Contain one of the following wordings.
  • The answer to which of the following questions would be most useful in evaluating the significance of the author `s claims?
  • Which of the following pieces of information would be most useful in assessing the logic of the argument presented above?

Identify-the-reasoning questions = ask you to identify a method, technique or strategy used in the passage, or identify the role of a bolded phrase in the passage.

• Contain one of the following wordings:
  • The bolded phrase plays which of the following roles in the argument above?
  • The argument uses which of the following methods of reasoning?
• Guideline:
  • Identify the conclusion and the premise and think about how they are related.

Incoming search terms:

Some basic tools refer to remembering number replacement and measurements used by GMAT.

• You need to memorize the following approximations: Π = 3, √1 = 1, √2 = 1.4, √3 = 1.7, √4 = 2
• For those used with the metric system memorize this: 12 inches = 1 foot and 3 feet = 1 yard

Also any drawings that have written next: “not drawn to scale” can not be measured.

Going back to the uses that the people which are not native English speaker:

• Line = straight line that extends without end in both directions
• Line segment = part of a line from one point to another
• Right angle = 90
• Perpendicular lines = two lines intersect at right angles
• Parallel lines = two lines in the same plane that do not intersect
• Polygon = closed plane figure formed by three or more line segments called sides
• Vertices = point of intersection of the sides
• Triangle = 3 sides polygon
• Quadrilateral = 4 sides polygon
• Pentagon = 5 sides polygon
• Hexagon = 6 sides polygon
• 180 degrees = sum of the interior angle measures of a triangle
• (n-2) x 180 degrees = sum of the interior angle measures of a polygon with n sides

Degrees and angles

• 360 degrees = circle.
• 180 degrees = line

When two parallel lines are cut by a third line, there appear to be eight separate angles, but there are really only two.( If you do not understand that, maybe is time for you to “Google” some more)

Triangles

• One side of a triangle can never be longer than the sum of the lengths of the other two sides of the triangle, or less than their difference
• Equilateral = all sides of equal length (the angles are also equal)
• Isosceles = two sides of the same length
• Right triangle = a right angle (opposite side = hypotenuse, the others = legs)
• Perimeter = the sum of the lengths of the three sides
• Area = (base x altitude)

Pythagorean Theorem = in a right triangle, the square of the hypotenuse equals the sum of the squares of the other sides.

a² + b² = c²

3 – 4 – 5; 6 – 8 – 10; 12 – 5 – 13; 12 – 9 – 15

A right isosceles triangle: 45 – 45- 90 = 1: 1: √2

A 30 – 60 – 90 triangle: 1: √3: 2

Circles

• Circle = a set of points in a plane that are all located the same distance from a fixed point (the center)
• Chord = a line segment that has its endpoints on the circle
• Diameter = a chord that passes through the center of the circle
• Radius = a segment from the center of the circle to a point on the circle (r)
• Length of an arc of the circle = the degree of the arc/360
• Tangent to a circle = a line that has exactly one point (point of tangency) in common with a circle
• Circumference = the distance around the circle. C = 2 Π r
• Area A = Πr²

Rectangles, squares and other four-sided objects

• Parallelogram = a quadrilateral with both pair of opposite sides parallel. Area = base x heights
• Rectangle = Parallelogram with right angles. Area = length x width
• Square = rectangle with all sides equal
• Trapezoid = a quadrilateral with two sides that are parallel. Area = small base x big base x height/2

Solids, volume and surface area

• Rectangular solid = a three dimensional figure formed by six rectangular surfaces.
• Area = sum of the areas of all the faces
• Volume = length x width x height

Cylinder

• Area = 2 Π r² + 2 Π r h
• Volume = Π r² h

Coordinate geometry - Coordinate plane

• X – Axis = horizontal line
• Y – Axis = vertical line
• Point 1 = (x1, y1); point 2 = (x2, y2)

Line in a coordinate plane: y = m x + b

b = y- intercept. m = slope.

m (slope) = (y2-y1) / (x2-x1)

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