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%