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Strategies for Managing Large, Complex Problems
[#permalink]
16 Oct 2015, 16:43
I have been going through the Magoosh Quant videos and something that Mike said really stuck out to me. He said, "Every large problem has a smaller problem waiting to get out." In other words, a large, seemingly complex problem can more easily be solved by realizing the smaller, more manageable, problems within it. I have come across a few tips while working problems that have helped me break down larger problems and I hope others can share some as well :-D
1. Factoring out a common factor For example, when given 2^20 - 2^15, rewrite it as 2^15 (2^5 - 1) Or, when given a complex fraction in the prompt, see if you can reduce it before even starting to solve the problem
2. Combining like bases with different exponents (similar to #1) For example, when given Is X^5/X^2 > Y^4/Y^2 ? rewrite it as Is X^3 > Y^2 ? When possible, rewrite a number as two powers in order to be able to reduce the expression by canceling and make it more manageable
3. Convert units in the beginning to match the unit given in the answer choices. For example, if a prompt gives information in minutes, but the answer choices are in seconds, it may be easier to convert units in the beginning
4. For word problems, create an expression with the given information For example, if you are told that males have some characteristic and females have some characteristic and that the total number of people is 100, you can write m+f=100 An expression like this gives us "free information" that we can use to further break down the problem. Especially helpful in DS when looking to solve for n variables and need n different equations
Hope these are a starting point for others to post some ways that they break down large problems!
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Re: Strategies for Managing Large, Complex Problems
[#permalink]
28 Oct 2015, 14:32
Expert Reply
tennisballa wrote:
I have been going through the Magoosh Quant videos and something that Mike said really stuck out to me. He said, "Every large problem has a smaller problem waiting to get out." In other words, a large, seemingly complex problem can more easily be solved by realizing the smaller, more manageable, problems within it. I have come across a few tips while working problems that have helped me break down larger problems and I hope others can share some as well :-D
1. Factoring out a common factor For example, when given 2^20 - 2^15, rewrite it as 2^15 (2^5 - 1) Or, when given a complex fraction in the prompt, see if you can reduce it before even starting to solve the problem
2. Combining like bases with different exponents (similar to #1) For example, when given Is X^5/X^2 > Y^4/Y^2 ? rewrite it as Is X^3 > Y^2 ? When possible, rewrite a number as two powers in order to be able to reduce the expression by canceling and make it more manageable
3. Convert units in the beginning to match the unit given in the answer choices. For example, if a prompt gives information in minutes, but the answer choices are in seconds, it may be easier to convert units in the beginning
4. For word problems, create an expression with the given information For example, if you are told that males have some characteristic and females have some characteristic and that the total number of people is 100, you can write m+f=100 An expression like this gives us "free information" that we can use to further break down the problem. Especially helpful in DS when looking to solve for n variables and need n different equations
Hope these are a starting point for others to post some ways that they break down large problems!
tennisballa -
Very good advice. One thing I have always tried to stress, and you have summarized this well above, if you recognize the relationships or patterns between numbers, you can simplify your work immensely on the exam. For example, if you recognize that 120% can be re-written as 6/5, you can simplify your computations on problems. Similarly, if you recognize the relationships betweens ratios, percents and fractions, you can move between them to assist with complex problems.
You have hit upon one of the strategy keys on the exam - the more you can "reason" your way to answers, the fewer calculations you need to do.
Good luck.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.