Additional VICs Test

MGMAT Additional VICs Test (8/11) - 73%
Last two were RTD problems which I haven't studied yet so I didn't every really try on those.

Advanced Inequalities

MGMAT Advanced Inequalities Test (9/15) - 60%

Grammar, Meaning, Concision Test

MGMAT Grammar, Meaning, Concision Test (10/15) - 67%

Grammar, Meaning, Concision

    Evaluate problems in this order
    1) Grammar

    2) Meaning
    3) Concision

• If a word has more than one meaning, is the author using that word correctly, to indicate the right meaning?
  - Guide 8 p20 for examples
  - Pay attention to helping verbs (such as may, will, must and should) - only change them if the original sentence is obviously nonsensical.
• Changing the position of a single word can alter the meaning of an entire sentence.
  - Look out especially for short words (such as only and all)
  - Pay attention to overall word order.
• Make sure that words that are connected, such as subjects and verbs or pronouns and antecedents, always make sense together.
• Concise is better.
• Don't use a phrase where a single word will do.
• If two words in a sentence mean the same thing, check the sentence for redundancy. Only one of the words might be necessary.
  - Pay attention to expressions of time.
  

Advanced Formulas & Functions

MGMAT Advanced Formulas & Functions Test (9/14) - 64%

Sentence Correction Strategy

• Strategy for SC:
  1. Write down "A B C D E" on your paper.
  2. Read the sentence, nothing any obvious errors as you read.
  3. Scan the answer choices vertically - do not read them - looking for differences that split the answer choices.
  4. Choose a split for which you know the grammatical rule and which side of the split is correct.
  5. Cross out the answer choices that include the incorrect side of the split.
  6. Compare the answer choices by re-splitting.
  7. Continue to split remaining choices until you have one answer left. 
• Make sure you read the entire sentence, as often important words are placed far from the underlined portion.
• Double check that your answer works in the context of the entire sentence.
  

Advanced Equations

MGMAT Advanced Equations Test (12/17) - 71%

Data Sufficiency for Equations, Inequalities and VICs

Things one must know:

• Solved through algebraic manipulations. Sometimes you will need to manipulate the original equation, other times you will need to manipulate the statements, sometimes both. Remember MADS.
• As you rephrase, always keep in mind the variable or variable combo you are trying to isolate.
• Sometimes, even when the variables have multiple potential values, the answer to the question stays the same.
• Frequently, the combos are "hidden": they are not asked about directly, in these cases, you must rephrase the question to find the hidden combo.
• Be on the lookout for hidden meaning in certain statements as you rephrase a question. Sometimes a particular piece of information has an intuitive interpretation that you will not see by simply plodding through the algebra.
  

VICs

MGMAT VIC Test (14/15) - 93%

VICs (Variable Expressions in the Answer Choices)

Things one must know:

• Four most common types:
  1) Word Translations
  2) Algebra
  3) Percent
  4) Geometry

Direct Algebra Strategy
Direct algebraic translation/manipulation as needed until the solution is obtained. Might become too difficult or dangerous as problems become more challenging, however, can be very fast.

•  Break the problem down into manageable parts.
  

Pick Numbers and Calculate a Target
When you don't see a way to do it algebraically.
1) Pick numbers for all or most of the unknowns in the problem
2) Use those numbers to calculate the answer to the problem - the "Target"
3) Plug the numbers you have picked into each answer choice to see which answer choice yields the same value as your Target.

You may accidentally pick numbers that result in two or more answer choices yielding the Target value. Can be slow because it requires a lot of computation.

• Never pick the numbers 1 or 0, for percent problems, also avoid 100, but usually should pick multiples of 10 that are easy to work with.
  Make sure all the numbers you pick are different.
  Pick small numbers.
  Try to pick prime numbers.
  Avoid picking numbers that appear as a coefficient in several answer choices.
• You should ideally test every answer choices, even if you have already found one that equals your Target value. Stop calculating once you realize that an answer choice cannot equal your Target value.
• When variables are related to each other through an equation, you cannot pick a value for each variable. Pick a value for all but one of the variables and then solve for the value of the remaining variable.
  

The Hybrid Method
Pick numbers to help you think through the problem. However, rather than plug these numbers into the answer choices, use the numbers to think through the computations, and therefore the matching algebra, step by step.

• Break the problem down into manageable parts.

Misc

• Always draw a diagram for geometry VIC problems.
• Create intermediate variables to represent key unknowns when solving a VIC problem, just remember that your solution cannot contain these intermediate variables.
• If you are trying to figure out the algebraic manipulation but you get stuck, you should immediately switch to a number picking strategy
• If the variables in a VIC problem are already defined as numbers, find the equation that relates the numbers. This will be the same equation that relates the variables.
  

Inequalities

MGMAT Inequalities Test (11/15) - 73%

Inequalities

Things one must know:

• When you multiply or divide an inequality by a negative number, flip the inequality sign.
• You cannot multiply or divide an inequality by a variable, unless you know the sign of the number that the variable stands for.
  Set up two cases - the positive and the negative case - and solve each one separately to arrive at two possible scenarios.
• When taking reciprocals flip the sign unless the two sides have different signs. If you don't know the signs of both sides, you cannot take reciprocals. 
• You can only square inequalities when both sides have the same sign.
  If both sides are known to be positive, then do not flip the inequality sign when you square.
  If both sides are known to be negative, then flip the inequality sign when you square.
  If the sides are unclear or different, then you cannot square.
  
• Combining inequalities:
  1) Solve
  2) Simply so that all the inequality symbols point in the same direction
  3) Line up the common variables
  4) Combine by taking the more limiting upper and lower extremes
  
• You can perform operations on a compound inequality as long as you remember to perform those operations on every term in the inequality.
• You can add inequalities together as long as the inequality signs are pointing in the same direction. You can multiply inequalities together only if both sides of inequalities are positive. You can never subtract or divide two inequalities. 
• Use extreme values for problems that involve multiple inequalities and the potential range of values for variables in the problem
• You should know how to solve problems involving both equations and inequalities by: (1) plugging the inequality into the equation using extreme values, and (2) plugging the equation into the inequality using standard algebra.
• Extreme value arithmetic operations (MGMAT 3rd book, p92)
  Flip the extreme value when subtracting, dividing and multiplying a negative number by an extreme value. Multiply two extreme values if you know that both are positive.
• Use extreme values to solve minimization and maximization problems - focus on the largest and smallest possible values for each of the variables. Set up a table with extreme values for all the variables. 
  Set terms with even exponents equal to zero when trying to solve optimization problems.
  
• When you see inequalities with zero on one side of the inequality, you should consider using positive/negative analysis to help solve the problem.
  Common inequality statements:
  xy > 0 implies that x and y are both positive or both negative
  xy < 0 implies that x and y have different signs
  x² - x < 0 or x² < x or 0 < x < 1
• Inequalities and absolute value
  | x + b | = c means the center point of the graph is -b and that x must be exactly c units away from -b.
  | x + b | < c means the center point of the graph is -b and that x must be less than c units away from -b.
  Solve algebraically:
  1) First scenario, simply remove the absolute value brackets and solve
  2) Second scenario, reverse the signs of the terms inside absolute value brackets, remove the brackets, and solve again.
  3) Combine the scenarios into one range of values
• Inequalities involving even exponents require you to consider two scenarios.
  √x² = |x| likewise consider that x can be negative or positive (i.e. positive x < 2 and negative x > -2
• If you have an inequality with zero on one side, see if you can factor the either side to create two factors that can be used for positive/negative analysis.
• Be wary of answer choices A or B on problems involving inequalities and variables. A seemingly in consequential statement, such as "x is positive" or "a is negative" if often crucial on inequality problems.
  
  

Functions

MGMAT Functions Test (12/15) - 80%

After almost a week of studying - every day very little - I'm done with this chapter.

Functions

Things one must know:

• A function rule describes a series of operations to perform on a variable.
• The "domain" of a function indicates the possible inputs, or the x-coordinate. The "range" of a function indicates the possible "outputs", or the y-coordinate.
• Input the value in place of the variable to determine the value of the function. When substituting a variable expression into function, keep the expression inside parentheses.
• The key to solving compound function problems is to work from the inside out - i.e. use the result from the inner function as the new input variable for the outer function. 
• Changing the order of the compound functions changes the answer, to find a value of x for which f(g(x)) = g(f(x)), use variable substitution.
• Finding an unknown constant:
  1) Use the value of the input variable and the corresponding output value of the function to solve for the unknown constant.
  2) Rewrite the function, replacing the constant with its numerical value.
  3) Solve the function for the new input variable.
• Direct proportionality means that the two quantities always change by the same factor and in the same direction: y = kx, where x is the input value, y is the output value and k is the proportionality constant. Can also be written as y / x = k. Set up ratios for the before case and the after case, and then set the ratios equal to each other to solve.
• Inverse proportionality means that the two quantities change by reciprocal factors: y = k / x, where x is the input value, y is the output value and k is the proportionality constant. Can also be written as xy = k. This time set up products to solve the problem. 
• Linear growth - growth at a constant rate, same constant added each period: y = mx + b, where slope m is the constant rate at which the quantity grows, the y-intercept b is the value of the quantity at time zero and the variable x stands for time. Initial time is 0.
• Exponential growth - a quantity is multiplied by the same constant each period of time: y(t) = y₀·k^t, where y₀ represents value at time zero, k represents the constant multiplier (commonly in percentage form), and t represents time. Maybe it is y = k(R^t)
  
• Symmetry, the property that two seemingly different inputs to the function always yield the same output. Solve algebraically or it might be easier to pick a number.
• Pick numbers for advanced function problems that test whether certain functions follow certain properties of mathematics.
• Optimization
  1) Linear functions have straight line graphs. The extremes (max and min) of linear functions occur at the boundaries: at the smallest possible x and at the largest possible x, as given in the problem.
  2) Quadratic functions form parabolas. A parabola has either a peak (a max value) or a valley (a min value) that you need to find. The key is to make the squared expression equal to 0. Whatever value for x makes the squared expression equal to zero is the value of x that minimizes or maximizes the function. The sign of the squared term determines whether the extreme point is a minimum (positive sign) or a maximum (negative sign).
  

Formulas

MGMAT Formulas Test (12/15) - 80%

Formulas

Things one must know:

• Plug-In formulas: simply write the equation down, plug in the numbers carefully, and solve for the required unknown. Be sure to write the formula as a part of an equation.
• Strange Symbol formulas: The symbol is irrelevant. All that is important is that you carefully follow each step in the procedure that the symbol indicates. Watch out for symbols that invert the order of an operation.
• Formula problems that involve unspecified amounts should be solved by picking smart numbers for the unspecified variables.
• Sequences are defined by function rules: each term is a function of its place in the sequence. 
• You must be given the rule in order to find a particular number in a sequence. 
• Recursive formulas - each item of a sequence is defined in terms of the value of the previous items in the sequence. You need to be given the recursive rule and also the value of one of the items in the sequence to solve for the values of a recursive sequence. The subscript n - 1 means "the previous term", and the subscript n means "this term.
  
• Linear sequence, the difference between successive terms is always the same.
  Direct formula: Sn = kn + x, where k is the constant difference between successive terms and x is some other constant.
  Recursive formula: Sn = Sn₋₁ + k and S₁ = k + x
  Compute the difference between two terms to find k, you can then solve for x.
  
• Exponential sequence, each term is equal to the previous term times a constant k, the ratio between successive terms is always the same.
  Direct formula: Sn = x(kⁿ), where x and k are real numbers.
  Recursive formula: Sn = kSn₋₁ and S₁ = xk
  You can find k by combing equations, then solve for x.
  
• If a problem seems to require too much computation, look for a pattern to find an easier way to solve it.
  

Quadratic Equations

MGMAT Quadratic Equations Test (12/15) - 80%

Quadratic Equations

Things one must know:

• Quadratic equations are equations with one unknown and two defining components:
  1) a variable term raised to the second power
  2) a variable term raised to the first power
• Factoring quadratic equations:
  1) Move all the terms to the left side of the equation, combine them, and put them in the form ax² + bx + c (where a, b, and c are integers). The right side should equal 0.
  2) Factor the equation: find two integers whose sum equals b and whose product equals c.
  3) Rewrite the equation in the form (x + ?)(x + ?), where the question marks represent the two integers you solved for in the previous step.
  4) Since this product equals 0, one or both of the factors must be 0. Set each factor independently to 0 and solve for x.  The two solutions for x have the opposite signs of the integers we found in step three.
• If you have a quadratic expression equal to 0, and you can factor an x out of the expression, then x = 0 is a solution of the equation. Be careful not to just divide both sides by x, this eliminates the solution x = 0. You are only allowed to divide by a variable (or any expression) if you are absolutely sure that the variable or expression does not equal zero.
• FOIL - First, Outer, Inner, Last
• Some quadratics have only one solution, these are called perfect square quadratics.
• When zero appears in the denominator of an expression, then that expression is undefined. Making the the denominator of the fraction equal 0 would NOT make the entire expression equal zero.
• Three common quadratic expressions:
  #1 x² - y² = (x + y)(x - y)
  #2 x² + 2xy + y² = (x + y)(x + y) = (x + y)²
  #3 x² - 2xy + y² = (x - y)(x - y) = (x - y)²
• If the other side of the equation is a perfect square quadratic, the problem can be quickly solved by taking the square root of both sides of the equation. Be sure to consider both the positive and the negative square root. 
• You can substitute a variable to create a quadratic.
• Determining the number of solutions a quadratic has: b² - 4ac
  If the result is greater than zero, there will be two solutions. If it is equal to zero, there will be one solution. If it is less than zero, there will be no solutions.
  

Equations with Exponents

MGMAT Equations with Exponents Test (11/15) - 73%

Equations with Exponents

Things one must know:

• Equations that involve variables with even exponents can have two solutions: both a positive and a negative solution.
• If exponential expressions appear on both sides of the equation, rewrite the bases so that either the same base or the same exponent appears on both sides of the exponential equation. You can then eliminate the identical bases and rewrite the exponents as an equation. Be careful if 0, 1, or -1 is the base.
  
• Square both sides of the equation to solve problems that involve variables underneath radical symbols. Be sure to check the solution in the original equation.
  

Basic Equations

MGMAT Basic Equations Test (14/15) - 93%
If I remember correctly, the score I got the first time was pretty horrible.

Basic Equations

Things one must know:

• Solve simultaneous equations by substitution or combination:
  Substitution
  1. Solve the first equation for x
  2. Substitute this solution into the second equation wherever x appears
  3. Solve the second equation for y
  4. Substitute your solution for y into the first equation in order to solve for x
  Combination
  1. Line up the terms of the equations
  2. If you plan to add the equations, multiply one or both of the equations so that the coefficient of a variable in one equation is the opposite of that variable's coefficient in the other equation. If you plan to subtract them, multiply one or both of the equations so that the coefficient of a variable in one equation is the same as that variable's coefficient in the other equation.
  3. Add or subtract the equations to eliminate one of the variables
  4. Solve the resulting equation for the unknown variable
  5. Substitute into one of the the original equations to solve for the second variable.
• Look especially for shortcuts or symmetries in the form of the equations to reduce the number of steps needed to solve the system.
• A master rule for determining whether 2 equations involving 2 variables will be sufficient to solve for the variables:
  1) If both of the equations are linear - that is, if there are no squared terms (such as x² or y²) and no xy terms - the equations will be sufficient unless the two equations are mathematically identical (e.g., x + y = 10 is identical to 2x + 2y = 20)
  2) If there are any non-linear terms in either of the equations (such as x², y², xy or x/y), there will usually be two (or more) different solutions for each of the variables and the equations will not be sufficient.
• Try to manipulate the given equation(s) so that the combo (e.g. x + y) is on one side of the equation.
  Four easy manipulations (MADS):
  M: Multiply or divide the whole equation by a certain number
  A: Add or subtract a number on both sides of the equation
  D: Distribute of factor an expression on one side of the equation
  S: Square or unsquare both sides of the equation
• If after manipulating the given equations in question or statements in DS so that the combo is isolated on one side of the equation, if the other side of an equation from a statement contains a value, the equation is sufficient. If the other side contains a variable expression, that equation is not sufficient.
• Avoid trying to solve for the individual variables in combo questions. 
• Equations involving absolute value:
  1. Isolate the expression within the absolute value brackets
  2. The rule, once we have an equation of the form |x|= a with a > 0, is that x = ± a. Remove the value brackets and solve the equation for two cases:
  CASE 1: x = a (x is positive)
  CASE 2: x = -a (x is negative)
  3. Check to see whether each solution is valid by putting each one back into the original equation and verifying that the two sides of the equation are in fact equal.
• In case of integer constraints, there might be many possible solutions among all numbers, but only one integer solution. Solve for one variable and then test numbers (answer choices)
• You can multiply or divide two complete equations together, because you are doing the same thing to both sides of the equations. Multiply the left sides of the two equations together and also multiply the right sides of the equations together. Set those products equal to each other. You can also divide two equations. Do this when it seems that you can cancel a lot of variables in one move.
  

FDPs

Just finished the MGMAT FDPs book and the OG problems that go with it. I feel I could have done better. I have had so little time to study lately and that's really showing. At this pace there is no way I will be ready for 2010 intake.

Back to basics (cont.)

MGAMT Advanced FDPs Test (18/23) - 78%
Didn't get some of the percent word translation stuff.

Data Sufficiency for FDPs

Things one must know:

• Rephrase questions and statements into equations in order to keep track of what you know and what you need to know. Your ultimate goal in writing equations is to combine them in such a way that you are left with a single equation with only one variable. The variable in the equation should represent the quantity you are asked to find in the original question
• Beware of statements that introduce too many variables, these are usually not sufficient to answer the qeuestion.
  

FDPs

Things one must know:

• Common FDP equivalents (MGMAT FDPs p66)
• Prefer fractions for doing multiplication or division, but prefer decimals and percents for doing addition or subtraction, for estimating numbers or for comparing numbers.
• FDPs and word translations (MGMAT FDPs p68) - X percent is (X/100)
  
  Advanced:
• Repeating decimals: Generally, just do the long division to determine the repeating cycle. However, if the denominator is 9, 99, 999 or another power of 10 minus 1, then the numerator gives you the repeating digits (perhaps with leading zeroes).
• Terminating decimals: When written as a fraction and if, after being fully reduced, the denominator has any prime factors besides 2 or 5, then its decimal will not terminate. If the denominator only has factors of 2 and/or 5, then the decimal will terminate.
• Unknown digits problems:
  1) Look at the answer choices first, to limit your search.
  2) Use other given constraints to rule out additional possibilities.
  3) Focus on the units digit in the product of sum.
  4) Test the remaining answer choices.
• When you work with formulas that act on decimals, avoid shortcuts and follow directions precisely.
• Fractions and Exponents & Roots: The effect of raising a fraction to a power varies depending upon the fraction's value, sign and the exponent. Be ready to generate outcomes with test numbers such as 1/2 or 3/2. Not that taking the square root of a proper fraction raises its value toward 1.
• Use a mixture chart for weighted average problems that involve percents and percent change. You can also use the formula, and leave the percents (keeping the % sign) when you solve.
• You can plug a value that is a fraction, a ratio, a decimal or a percent straight into percent change equations as long as you keep the labels straight.
• Estimating decimal equivalents:
  1) Make the denominator the nearest factor of 100 or another power of 10.
  2) Change the numerator or denominator to make the fraction simplify easily.
  3) Small percent adjustment, increase/decrease the result by the same percent you increased/decreased the nominator/ denominator.
  Try not to change both the numerator and denominator, especially in opposite directions.

Percents

Things one must know:

• A part is some percent of a whole:
  PART / WHOLE = PERCENT / 100
  Set up a proportion like above to solve
• Change is the part, while the original is the whole
• 100% plus or minus a percent change equals the percent of the original quantity that the new quantity represents; ORIGINAL +/- CHANGE = NEW
• You can compute the percent change using the ratio of any two of the following: original, change and new.
• To solve successive percent problems choose real numbers, usually 100 is the easiest, and see what happens
• In a percent problem with unspecified amounts, pick 100 to represent the orginal value
• Simple interest: Principal x Rate x Time
• Set up a mixture chart with the substance labels in rows and 'Original', 'Change' and 'New' in the columns, this way you can keep careful track of the various components and their changes.
  

Back to basics (cont.)

3. MGMAT Percents (14/15) - 93%
4. MGMAT FDPs (13/15) -  87%