Word problems
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Guiding Principles:
 Read Carefully
 Answer the proper question
 Pick the best approach

Different type of approaches
 Algebra and conceptual thinking
 Back Solving
 Number picking
 Maintain mental agility

In ratio problems
they almost never ask for multipliers

When to use back solving
 when algebra is messy or tough
 answer choices are clean numbers
 age,distance rate problems
 Answers choices are
 generally in ascending order or descending order. So always start in the
 middle.

When to use number picking
 Variables in answer choices
 Percent/Ratio problems
 Parallel small number problems to unlock the concept

When number picking go through all the answer choices. If there are two answer
choices that match change the numbers and try again.

Common type of problems
 Venn diagram
 Matrix box problems
 Scenario Min/Max problems
 Weighted average problems
 Mixture problems
 Work/Rate problems

Venn diagrams general equation
Total = Group A + Group B Both +Neither

Matrix box questions
The question deals with complementary events.

Guiding principles of matrix problems
 When to use them(complementary information)
 Be careful with mixing and matching percent information with absolute number data
 Proper information for that box

When encountered with percents, ratios or proportions
convert them into whole numbers by figuring out the common number.

Scenario driven min/max problems
Cannot be typically solved by an equation but reward strategic use of math

What is smallest number with which A could win an election?
To minimize the winner, maximize the loser

With what number is he a guaranteed winner?
Maximize the second place.

A guaranteed loser?
Minimize the winner and maximize the loser.

Guiding principles for min/max problems
 Understand which value you want to minimize/maximize and what you want to do with other values
 Remember that in almost all cases all values must be integers(which is what makes the scenarios tick)
 These problems are tricky because of the potential values hug one border.
 Usually its easy to either minimize or maximize the value in question, but to do the other is where you have to do the work.

Weighted average concept
The weighted average will skew more closer to the value that has more weight

Alternative method for weighted average is mapping strategy
 Find the distances between the weighted average and the individual average.
 Then flip the ratio to answer the question.
 Mapping strategy gives the inverse of the ratio. So flip the ratio.

Mapping average is more useful for ratios, percentages and whole numbers when
percentages and ratios are required

Many mixture problems are weighted average problems. So use mapping strategy
for mixture problems.

Guiding principles for rate problems
 Always convert rates to time
 Rates are additive(when 2 or more entities are working together)
 Know the formula for rates(w=rt or r=d/t)
 Reset when conditions change

Common rate problems are
 Combined rates
 Conditions when rates change

Guiding principles for catching up problems
 Determine how far behind the faster train is before it starts
 Take the distance that the faster train is behind and divide it by the differential in rates between the two trains

Guiding principles for collision problems
 Make sure that the 2 entities are starting at the same time. If not, account for the hour head start and reset the equations.
 Add the rates of the 2 trains with which they are covering the distances.
 Divide the distance between the 2 trains by their combined speed
 Once you have the time to collision, go back to either train to see how farthey went.
 Lastly account for any distance traveled by the train that started first.