Lines & Angles Test

MGMAT Lines & Angles Test (14/15) - 93%

Circles and Cylinders Test

MGMAT Circles and Cylinders Test (13.5/15) - 90%

Geometry

     Quadrilaterals

• Quadrilaterals
  - Parallelogram - Opposite sides and opposite angles are equal
  - Rectangle - All angles are 90°, and opposite sides are equal
  - Rhombus - All sides are equal. Opposite angles are equal
  - Square - All angles are 90°. All sides are equal
  - Trapezoid - One pair of opposite sides is parallel
• Sum of Interior Angles of a Polygon = (n - 2) × 180, where n is the number of sides 
• Perimeter is the sum of the lengths of all sides
• Area
  - Triangle = (Base × Height) / 2
  The base refers to the bottom side of the triangle. The height always refer to a line that is perpendicular (at a 90° angle) to the base
  - Rectangle = Length × Width
  - Parallelogram = Length x Height
  - Cut more complex shapes into rectangles and right triangles, then find the areas of these individual shapes.
  - See p16 in MGMAT Geometry for less common area formulas
• Surface Area = The SUM of the areas of ALL of the faces
• Volume = Length × Width x Height
  - Remember, when you are fitting 3-dimensional objects into other 3-dimensional objects, knowing the respective volumes is not enough. You must know the specific dimensions (l,w,h) of each object to determine whether the objects can fit without leaving gaps.
  
  Triangles & Diagonals
• The sum of the three angles of a triangle equals 180°
• Angels correspond to their opposite sides. The largest angle is opposite the longest side, the smallest angle is opposite the shortest side. If two sides are equal, their opposite angles are also equal.
• Length of sides: (x-y)<(x+y)
• Use Pythagorean Theorem to find the hypotenuse (the side opposite the right angle) of a right triangle: a² + b² = c²
• Common right triangles
  3-4-5                6-8-10
  3² + 4² = 5²      9-12-15
  (9 + 16 = 25)    12-16-20
  5-12-13            10-24-26
  5² + 12² = 13²
  25 + 144 = 169
  8-15-17
  8² + 15² = 17²
  64 + 225 + 289
• An isosceles triangle is one with two equal sides, the two angles opposite these two sides are also equal.
  45° 45° 90°
  leg leg hypotenuse
   x :  x  :  x√2
• An equilateral triangle is one with all three sides (and all three angles) equal.
  Two 30-60-90 triangles make up an equilateral triangle
  30°    60°  90°
  short long hypotenuse
     x  :  x√3 : 2x
• Diagonal of a square: d = s√2, where s is a side of a square
• Main diagonal of a cube: d = s√3, where s is an edge of the cube
• To find the diagonal of a rectangle, you must know either the length and the width or one dimension and the proportion of one to the other
• To find the diagonal of a rectangular solid, you can use the Pythagorean theorem twice or the Deluxe Pythagorean Theorem: d² = x² + y² + z²,where x,y and z are the sides of the rectangular solid and d is the main diagonal.
• Triangles are defined as similar if all their corresponding angles are equal and their corresponding sides are in proportion. Once you find that two triangles have two pairs of equal angles, you know that the triangles are similar, furthermore, if two right triangles have one other angle in common, they are similar triangles.  
• If two similar triangles have corresponding side lengths in ratio a:b, then their areas will be in ratio a²:b² 
• Be able to see any side of a triangle as the base, not just the side that happens to be drawn horizontally, also be able to draw the height from that base. 
• The area of an equilateral triangle with a side length of S is equal to (S²√3) / 4
• Right triangle/Rectangle DS tips, knowing any two of these will allow to solve for the rest:
  1. Side length 1
  2. Side length 2
  3. Diagonal/Hypotenuse
  4. Perimeter
  5. Area
  
  
• Circles & Cylinders
• A radius is any line segment that connects the center point to a point on the circle
• A chord is any line segment that connects two points on the circle. Any chord that passes through the centre of the circle is called a diameter
• The distance around the circle is termed the circumference: C = 2πr
  A full revolution or a turn of a spinning wheel is equivalent to a wheel going around once, a point on the edge of the wheel travels one circumference in one revolution
• A portion of a distance on a circle is termed an arc. Use the central angle to determine what fraction an arc is of the entire circle (out of a total of 360°)
• The boundaries of a sector are formed by the arc and two radii. Slice of pizza.
• Area of a circle: A = πr² 
• You can find the area of a sector by determining the fraction of the entire area the sector occupies, you can do this by looking at the central angle that defines the sector
• An inscribed angle has its vertex on the circle itself. An inscribed angle is equal to half of the arc it intercepts
• If one of the sides of an inscribed triangle is the diameter of the circle, then the triangle must be a right triangle. Conversely, any right triangle inscribed in a circle must have the diameter of the circle as one of its sides.
• Surface area of a cylinder = 2 circles + rectangle = 2(πr²) + 2πrh
• Volume of a cylinder: πr²h
• If you know the circumference, the radius, the diameter, or the area of a circle, you can use one to find any of the other measurements.
• Sphere
  Surface area: 4πr²
  Volume: 4/3πr³
  
  
• Lines and Angles
• Parallel lines are lines that lie in a plane and that never intersect
• Perpendicular lines are lines that intersect at a 90° angle
• Intersecting lines:
  - the interior angles form a circle, so the sum is 360°
  - angles that combine to form a line sum to 180°
  - angles found opposite each other where two lines intersect are equal. These are called vertical angles.
• An exterior angle of a triangle is equal in measure to the sum of the two non-adjacent (opposite) interior angles of the triangle.
• Parallel lines cut by a transversal:
  - All acute angles (less than 90°) are equal
  - All obtuse angles (more than 90° but less than 180°) are equal
  - Any acute angle is supplementary to any obtuse angle (they sum to 180°) 
• Complementary angles sum to 90°
• Supplementary angles sum to 180°

Geometry Test

1. MGMAT Polygons Test (13/15) - 87%

AWA

Issue
Focus on:
• Clear thesis (main idea - expressed clearly)
• Persuasive examples
• Logical structure (distinct paragraphs)
• Transitional words and structure (while, for example, however, in addition)

Strategy:
1. Read the prompt
    - Summarize the main idea and write it down in the prompt
2. Examples + Thesis = Outline
    - Figure out and type up the examples before you decide to agree or disagree (strong points first)
    - Agree or disagree based on how many and how good your arguments are to support that side
3. Write the intro
    - Summarize the issue (what you wrote down earlier, now just use more sophisticated language) (some.. believe, many.. must decide)
    - State your thesis from the outline
4. Write the body
    - One paragraph per example, three examples is optimal
    - Write with purpose - describe examples with supporting details
    - Tie each example to the thesis (restate it) (This shows the folly of, Clearly, the decision.. is the right choice)
    - Conclusion can be a separate paragraph or at the end of the last body paragraph. Clearly restate your argument by looping back to the thesis. Don't summarize the examples.
    - Use transitional words
5. Proofread
    - Add transitional words
    - Make sure examples are tied to the thesis

Argument
• Argument is always flawed.
• Dedicate more time to outlining than you do on issue essays
• Don't develop a separate argument of your own!
• Statements presented as aevidence can themselves depend on questionable assumptions. Look for logical leaps in every sentence. 

Strategy:
1. Read the argument, identify the conclusion
    - Summary is not so important as it is on issue essays, just give it a read - pay attention to recommendations which are common conclusions
2. Identify assumptions
    - Write down counterexamples or alternative causes (same as prephrasing weakeners for assumptions) - this will be the outline 
3. Write the introduction
    - describe the argument from the prompt, state that it is flawed (the argument rests on a questionable chain of logic; without additional evidence this argument cannot stand up to scrutiny), use the word assumption (the author relies on an assumption), briefly state one or two assumptions
4. Write the body paragraphs 
    - use the outline
    - one paragraph per assumption, describe the assumption, cite alternative causes and/or counter examples
    - show insight - conclude by noting info that might support the argument
5. Proofread 
    - logic - make sure you have identified assumptions, alternative causes/counterexamples
    - structure - paragraph breaks, transition
    - grammar - erros, vary syntax (long sentence followed by a shorter sentece)

Common assumptions:

Generalizations - True in one case, so true in general

Questionable analogies - True in one case, so true in a "similar case"

Past vs Present - Something true in the past is still true today

Correlation vs Causation - Events occur together, so one caused the other

Trends - What has been happening recently will continue

Advanced strategies:

• Don't change ideas halfway
• Strengthens can be positioned at the end of the assumption paragraph or at the end of the essay
• Issue essays - discredit opposing evidence

Overlapping Sets Test

MGMAT Overlapping Sets Test (12/15) - 80%

Overlapping Sets

• For problems involving only two categorizations or decisions use the Double-Set Matrix: a table whose rows correspond to the options for one decision, and whose columns correspond to the options for the other decision. The last row and the last column contain totals, so the bottom right corner contains the total number of everything in the problem.
• Make sure the columns and rows correspond to mutually exclusive options for one decision.
• If no amounts are given, pick smart numbers for total, for problems involving percents pick 100, for problems involving fractions, pick a common denominator for the total.
• Read the problem very carefully to determine whether you need to use algebra to represent unknowns.
• You can extended the Double Set Matrix if a decisions requires you to consider more than two options as long as each set of distinct options is complete and has no overlaps.
• Problems hat involve three overlapping sets should be solved using a Venn Diagram. Remember to work from the inside out.
  1) Fill in the innermost circle, items on all three teams.
  2) Fill in circles for items on two teams, remember to subtract the items on all three teams.
  3) Fill in circles for items only on one team, remember to subtract items on two teams and on all three teams.
  To determine the total, just add all numbers together. 
• The union of two sets is the set of all elements that are found in either of the two sets (or in both of them).
• The intersection of two sets is the set of all of the elements that are found in both sets.
  
  

Statistics Test

MGMAT Statistics Test (12/15) - 80%

Statistics

• Arithmetic mean:
  Average = Sum / # of terms
  Sum = Average x (# of terms)
  To keep track of two average formulas in the same problem, you can set up an RTD style table.
• The average of an evenly spaced set is the middle number (or the arithmetic mean of two middle numbers). All you need to do to find the middle number is to find the arithmetic mean of the first and last terms.
• Weighted averages:
  Weighted average = (weight/sum of weights) x (data point) + (weight/sum of weights) x (data point) + ..
  or
  Weighted average = (weight)(data point) + (weight)(data point) / sum of weights
• Having just the ratios of the weights will allow you to find a weighted average. Simply write the ratio as a fraction, and use the numberator and the denominator as weights. If you know the weighted average you know the ratio of weights.
• If you know the two sub-group averages and you know the overall weighted average, then you can solve for the relative weightings of the two sub-groups. 
• If you are finding a weighted average of rates (whose units are fractions), then the "weights" correspond to the units appearing in the denominator of the rate.
• Median is the unique middle value of a set containg an odd number of values arranged in increasing (or decreasing) order, or the arithmetic mean of the two middle values of a set containing an even number of values arranged in increasing (or decreasing) order.
  You may be able to determine a specific value for the median of a set even if one or more unknowns are present.
• Solve problems involving both the arithmetic mean and the median by writing expressions for both.
• You may be required to construct and manipulate a completely abstract set, you can use alphabetical order to make it a little more concrete, or you can place the variables on an abstract number line in order to visualize their relationships, or you can create a column chart.
• Standard deviation indicates how far from the average (mean) the data points typically fall. The more spread out the numbers, the larger the SD.
  If you see a problem focusing on changes in the SD, ask yourself whether the changes move the data closer to the mean, farther from the mean, or neither. If the problem requires comparisons, ask yourself which set is more spread out from its mean.
  The term "variance" is the square of the SD.
• The mode of a set of numbers is the number that occurs most often.
• The range of a set of numbers is the difference between the largest number and the smallest number.
  
  

Sentence Correction

• Subject and verb must agree in number
  - find the subject and the verb through filler
  - verb might come before subject, ask what?
  - identify each subject and verb in the underlined part and pair them
• Unusual subjects
  - compound subjects - and means plural (two things)
  - collective nouns (i.e. group, team) are singular
  - verbals that function as nouns (gerunds aka -ing words or infinitives) are singular
• Fragments
  - looks like a complete sentence, but doesn't express a complete thought
  - check to see that the sentence has a main verb
• Run-on sentence
  - combines two sentences that could stand on their own without proper punctuation, must be separated by a semicolon or a comma and a fanboys word:
  For
  And
  Nor
  But
  Or
  Yet
  So
  - Make sure there are full sentences on both sides of these conjunctions
• Pronouns
  - have to refer to a specific antecedent
  - must agree in number with the antecedent
  - both is plural; each is singular
  - watch out for answer choices that introduce new pronouns
• Modifiers
  - When a sentence starts with a modifier, the object that it is modifying should be the first word after the comma
  - Modifiers should be close to what they modify
• Verb tense indicates the time of verb's action
  - Auxiliary verbs express more complex tenses:
    Past perfect (had) - event in the past preceding another event in the past, (X had before Y was)
    Present perfect (has) - started in the past continuing to present (doesn't need to continue to into the future)
  - Actions in the same time frame should be expressed in the same tense
  - Keywords: as, until, before, since
• Parallel construction:
  - Lists
  - Correlative conjunction: not only.. but also, neither.. nor.. 
  - Comparisons and contrasts - unlike, just as...so, like, as...as, than.., compared with.., in contrast..,
  - "like..., word directly after the comma" 
  - Make sure items are logically comparable

Checklist

• Phrases and clauses
  Find subject and main verb of sentence
  Do subject and verb agree in number?
  Is the sentence a fragment?
  Do phrases/clauses create wordiness?
• Lists 
  Is each item parallel?
• Verbals
  Do verbals violate parallelism?
  Any misplaced/dangling modifiers?
  Are verbals wordy/awkward?
• Pronouns
  Match pronouns to antecedents
  Does each pronoun have one ant.?
  Do pronouns and ant. agree? 
  Is pronoun unnecessary and wordy?
• Comparisons
  Identify items that are compared
  Are items logically able to be compared?
  Are compared items parallel?
  Are comparison idioms correct?
• Quantity Words
  Is correct word used (e.g. fewer/less)? Any redundancy in quantity words?
• “Tell” Words“
  Had” / “if” – tense errors?
  “Being” / “having been” – wordiness?
  Passive verbs – awkward style?
  “There are” / “there is” – wordiness?

Coordinate Plane Test

MGMAT Coordinate Plane Test (13/15) - 87%
One careless mistake.

Coordinate Plane

• Slope of a line is defined as "rise over run" - how much it rises vertically divided by how much it runs horizontally.
  rise / run = y₁-y₂ / x₁-x₂ 
• A point where a line intersects a coordinate axis is called an intercept.
  - The x-intercept is the point on the line at which y = 0
  - The y-intercept is the point on the line at which x = 0
  Plug in 0 for x or y to find the intercepts.
• All lines can be written as equations in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept of the line.
• Finding the equation of a line:
  1) Find the slope of the line by calculating the rise over run.
      Remember that y-intercept is a point as well
  2) Plug the slope in for m in the slope-intercept equation.
  3) Solve for b, the y-intercept, by plugging the coordinates of one point into the equation. Either point's coordinates will work.
  4) Write the equation in the form of y = mx + b
• Determining which quadrants a given line passes through can be done in two ways:
  1) First, rewriting the equation in form of y = mx + b and then sketching the line
  2) Finding two points on the line by setting x and y equal to zero in the original equation. 
• The perpendicular bisector has the negative reciprocal slope of the line segment it bisects.
  1) Find the slope of the line it bisects
  2) Find the negative reciprocal by flipping the fraction and changing the sign (product must be -1)
  3) Find the midpoint of the line, by finding the midpoints of the x and y coordinates separately.
  4) To find the value of b of the perpendicular bisector substitute the coordinates of the midpoint for x and y. 
• Parallel lines have equal slopes. 
• If two lines in a plane intersect in a single point, the coordinates of that point solve the equations of both lines. To find the find the intersection point of two equations, turn them into slope-intercept form and set them equal to each other.
• When faced with an inequality in the coordinate plane:
  1) Draw the line either by converting to slope-intercept form or using the x and y intercepts
  2) Plug in a point on one side of the line. If this point makes the inequality true, that point is in the solution set. If not, the solution set is on the other side of the line.
• Distance between two points
  Square root of (x₁-x₂)²+(y₁-y₂)²
  
  Need to finish this.
  

Probability

Probability = Number of desired or successful outcomes / Total number of possible outcomes

• All the outcomes must be equally likely - you can use a counting tree
• To determine the probability that independent events X and Y will both occur, multiply the two probabilities together.
• To determine the probability that mutually exclusive events X or Y will occur, add the two probabilities together.
  - if the events cannot occur together, add the probabilities of individual events
  - if the events can occur together, use the formula: P(A or B) = P(A) + P(B) - P(A and B)
• Probability of success + Probability of failure = 1
• If success contains multiple possibilities - especially if the wording contains phrases such as "at least" and "at most" - then consider finding the probability that success does not happen.
• Be careful of situations in which the outcome of the first event affects the probability of the second event, i.e. picking things out of a box.
• When you use a probability tree, multiply down the branches and add across the results.
  

Reading Comprehension

• Read for the big picture, don't dwell on the details, translate ideas and terms into simpler words, ask "why" for each new idea, create a Passage Structure
• Use PS and keywords in the passage to find:
  Main Idea: What? The point or idea that the author expresses in the passage.
  Attitude: How? The feeling or opinion the author expresses about the main idea.
  Purpose:Why? The author's reason for writing
• Pay attention to soft and extreme wordings: some vs all
• Keywords: must, if, then, like
• Read the passage first, don't look at the question before
• Main idea or title should capture the whole passage, not just one paragraph
  
• Global questions
  - Use MAPs
  - Prephrase an answer
  - Look for a match
• Detail question
  - Use MAPs to locate the detail
  - Paraphrase and scan answer choices for the paraphrasing of the passage language
  - Read the complete idea to provide context
• Inference question
  - Think must be true (and are concretely supported by the passage)
  - Eliminate answers one by one using the passage to invalidate
  - (Don't prephrase)
• Distinguish between the author's voice and others
• Common wrong answer choices - out of scope, too broad, distorted details, extreme. 

Combinatorics Test

MGMAT Combinatorics Test (11/15) - 73%
This is tough!

Combinatorics

• Fundamental Counting Principle: If you must make a number of separate decisions, then multiply the number of ways to make each individual decision to find the number of ways to make all the decisions.
• For problems in which certain choices are restricted and/or affect other choices, choose the most restricted options first.
• The number of ways of putting n distinct objects in order, if there are no restrictions, is n!
• When you have repeated items, divide the "total factorial" by each "repeat factorial" to count the different arrangements. 
• To count possible groups, divide the total factorial by two factorials: one for the chosen group and one for those not chosen.
• If you are required to choose two or more sets of items from separate pools, count the arrangements separately - perhaps using a different anagram grid each time. Then multiply the number of possibilities for each step.
• If the problem has unusual constraints, try counting the arrangements without constraints first. Then subtract the forbidden arrangements.
  - for problems in which items or people must be next to each other, pretend that the items "stuck together" are actually one large item.
  - keep in mind that stuck together items can be XY and YX so multiply the result by two.
• A combination is a selection of items from a larger pool, the order of items does not matter.
• A permutation is also a selection of items from a larger pool, the order of items matters.
• If switching the elements in a chosen set creates a different set, it is a permutation. If not, it is a combination.
  

Ratios Test

MGMAT Ratios Test (13/15) - 87%
Two careless errors.

Ratios

• Expresses a part-part relationship or a part-whole relationship.
• If there are only two parts in the whole, you can derive a part-whole ratio from a part-part ratio and vice versa.
• If two quantities have a constant ratio, they are in direct proportion to each other.
• Always write units on either ratio itself or the variables you create, or both.
• Simple ratio problems:
  1) Set up a proportion
  2) Cross multiply to solve
  Note that you can cancel factors either vertically within a fraction or horizontally across an equals sign, but never diagonally across an equals sign.
• Unknown Multiplier
  M/W which is 3/4 becomes 3x/4x which cancel out
  M + W becomes 3x+4x
  Can be used once per problem, you can never have two unknown multipliers in a problem.
  Should be used when neither quantity in the ratio is already equal to a number or a variable expression.
• You can multiply each ratio to make a common term in order to combine ratios.
  
  

Rates & Work Test

MGMAT Rates & Work Test (14/15) - 93%

Rates & Work

Rate x Time = Distance
Rate x Time = Work

• All the units in your RTD chart must match up with one another.
• Always express distance rates as "distance over time" (i.e. 50 km per hour) or work rates as jobs per time unit.
  
• When you have more than one traveler on trip, make a row in your RTD chart for each traveler or trip.
• Sample translations/problems (MGMAT WT p35-38)
  - moving toward each other (add the rates)
  - chasing and catching up (subtract the rates)
  - chasing and falling behind (subtract the rates)
  - faster means lower time
  
• The numbers in the same row of an RTD table will always multiply across. However, the specifics of the problem determine which columns will add up into a total row.
• Use variables to stand for either Rate or Time, rather than Distance.
• Average rate: find the total combined time for the trips and the total combined distance for the trips. You can actually pick any number for the distance. 
• If two or more agents are performing simultaneous work, add the work rates. Only exception is when one agent's work undoes the other agent's work, in this case subtract the rates.
• Use population chart for problems where populations double or triple in size over constant intervals of time.
  

Critical Reasoning

Evidence + Assumption = Conclusion

Evidence - explicit stated support for conclusion
Assumption(s) - unstated support for conclusion
Conclusion - main point

Assumption Strategy:
1) Identify the conclusion
• sounds most important and general
• sounds like an opinion
• preceded by conclusion keywords (therefore, thus, so)
2) Identify the evidence
• sounds like factual info
• sounds like it is contributing to believability of something
• keywords (because, claimed, as)
• is always true (no need to question it)
3) Identify the assumption
• fills the gap between the evidence and the conclusion, a general rule that ties the two
• must be true, if the author didn't believe it, the conclusion would be invalid

Red flags in answer choices:
• extreme statements (keywords: only, never, always)
• opposite
• irrelevant (often irrelevant comparison)
• out of scope (introduces new information)

Stem based approach:
1) Identify the question type
2) Untangle stimulus (read the stimulus)
3) Predict an answer (before looking at the answer choices)
4) Match the prediction with an answer choice

Strengthen / Weaken:
Manipulate the assumption. Correct answer doesn't need to fully prove or disprove the conclusion, just strengthen or weaken it.
Denying an assumption invalidates the conclusion.
Strengthening argument must cause the conclusion to make sense.

Causation:
If X & Y happen at the same time and it is assumed that X causes Y, it could be argued that:
- the reverse is true, Y causes X
- something else caused Y, Z causes Y
- it is just a coincidence

Logical opposite of X is not X

Inference:
What must be true based on what was said in the statement.

Inference Strategy:
1) Logically link each sentence
2) Paraphrase the argument
3) Go through answer choices one by one (difficult to predict an answer)

Degrees of certainty:
- Must be true
- Must be false
- Could be true
Think of what is being asked! All true except - means that can be either 'must be false' or 'could be true'


Some - Most
- Some - at least one
- Most - more than half
Cannot be determine which is greater
Most + Some = Some

Common Wrong AC:
- extreme
- could be true (new info that wasn't mentioned in the stimulus)
- opposite

Formal Logic
X -> Y
not Y -> not X

Algebraic Translations Test

Algebraic Translations Test (11/15) - 73%

Algebraic Translations

• Translating English into algebra:
  1) Assign variables
      - Try to minimize the number of variables
      - Make use of a relationship given in the problem.
  2) Write equations
  3) Solve algebraically
  4) Evaluate the algebraic solution in the context of the problem - make sure you answer the question asked
• You can check your translations with easy numbers.
• Write an unknown percent as a variable divided by 100
• Translate bulk discounts and similar relationships carefully
• When a problem involves several quantities and multiple relationships, it is often a good idea to make a chart or a table to organize the information, i.e. age problems:
  - Put people in rows and times in columns.
  - Use variables to indicate the age of each person now, fill other columns by adding or subtracting time from the now column.
  - Write equations that relate the individuals' ages together
• In a typical Price-Quantity problem, you have two relationships:
  - the quantities sum to a total
  - the monetary values sum to a total
• Look out for hidden constraints (i.e. whole number, positive)
  - Think about what is being measured or counted and whether a hidden constraint applies.
  - To solve algebra problems that have integer constraints, test possible values systematically in a table.
  - When all quantities are positive in a problem, certain algebraic manipulations are safe to perform: 1) dropping negative solutions of equations; 2) dropping negative possibilities with inequalities (see MGMAT WT p21)
  

Subject - Verb Agreement

• Every sentence must have a subject and a (working) verb (a verb that can run a sentence by itself).
• Subject and verb must make sense together.
• Subject and verb must agree in number.
• A noun in a prepositional phrase cannot be the subject of the sentence.
• Compound plural subjects are formed with the word and, additive phrases do not form compound subjects. 
• Phrases such as or, either... or, neither nor - must agree to in number to the nearest noun. Either and neither in a sentence alone (without or or nor) are singular.
• Collective nouns are almost always considered singular.
• Confusing subjects are more often singular than plural. 

This list might not be final.

Subject - Verb Agreement

MGAMT Subject - Verb Agreement Test (9/15) - 60%