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Guiding Principles:
- Read Carefully
- Answer the proper question
- Pick the best approach
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Different type of approaches
- Algebra and conceptual thinking
- Back Solving
- Number picking
- Maintain mental agility
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In ratio problems
they almost never ask for multipliers
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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.
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When to use number picking
- Variables in answer choices
- Percent/Ratio problems
- Parallel small number problems to unlock the concept
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When number picking go through all the answer choices. If there are two answer
choices that match change the numbers and try again.
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Common type of problems
- Venn diagram
- Matrix box problems
- Scenario Min/Max problems
- Weighted average problems
- Mixture problems
- Work/Rate problems
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Venn diagrams general equation
Total = Group A + Group B -Both +Neither
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Matrix box questions
The question deals with complementary events.
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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
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When encountered with percents, ratios or proportions
convert them into whole numbers by figuring out the common number.
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Scenario driven min/max problems
Cannot be typically solved by an equation but reward strategic use of math
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What is smallest number with which A could win an election?
To minimize the winner, maximize the loser
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With what number is he a guaranteed winner?
Maximize the second place.
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A guaranteed loser?
Minimize the winner and maximize the loser.
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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.
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Weighted average concept
The weighted average will skew more closer to the value that has more weight
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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.
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Mapping average is more useful for ratios, percentages and whole numbers when
percentages and ratios are required
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Many mixture problems are weighted average problems. So use mapping strategy
for mixture problems.
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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
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Common rate problems are
- Combined rates
- Conditions when rates change
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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
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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.
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