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- 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
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.