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24 Apr 2016, 13:53
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I am writing this post as an attempt to help those struggling with CR. As per my de-brief ( 790-q51-v51-debrief-with-various-tips-211734.html ), I had Verbal score 51 and the only theoretical preparation I did was for SC - for CR and RC I just practiced on the difficult OG questions. And I am not a native English speaker.
So I tried to do a bit of introspection about some of the reasoning techniques I use and present them here in a practical, accessible way. The framework I will take here is to describe briefly a general principle and then illustrate it in practice with one or two actual GMAT questions. I recommend that you try answer the question first and then you can compare your thinking to mine.
Emotions in critical reasoning? No I am not smoking weed
You can discern nonsense answers much easily if you take a very involved attitude to the question. I do this by nature, but you can probably practice it easily. Say the question asks "Which of the following is a possible cause of company ABC's fall in revenue?". Well, imagine you are not the CEO, you are the 100% owner of ABC, and by the current looks you have about a month to turn the business around before you go bankrupt. If you feel like this, you really, really do not have time for BS causes, you just need substance to act on. So answers like "TV stations stopped advertising product X" when the question initially says that the vast majority of revenue comes from product Y will not just be obviously irrelevant, but will get you annoyed, and you will detect them faster.
Equating correlation with causation is one of the most common reasoning mistakes I see people make. Just because A and B occur together, it does not follow that A causes B. It could be that B causes A, or that there is another cause, C, that causes both A and B.
In the spirit of emotionalizing your attitude, here are some controversial practical examples:
1) Global Warming: The fact that the amount of greenhouses gases has been increasing at the same time that the mean global temperature has been increasing need not necessarily imply the increase of greenhouse gases causes the increase in temperatures. Could be that they are just co-incidental - and there's been a lot of controversy about whether they are or not.
2) Racial discrimination in the workplace: Say an employer's workforce is 90% white and 10% non-white in a country where 40% of population is non-white. Does that employer necessarily take race into account when evaluation job applicants? Not necessarily. There could well be million other causes - simplest one being that the employer requires applicants qualified in a field where for whatever reasons the proportion of experts is in fact 90:10 white:non-white.
Try this question:
guidebook-writer-have-visited-hotels-throughout-the-country-80358.html#p603511
When I read the intro and the quick judgment based on correlation, I immediately get suspicious. There are million possible causes for the difference, and this writer just picks his/her nose and decides it's the quality of the carpenters, just like so? No chance. I am looking for something that will disprove his/her correlation=causation judgment (honestly just reading the 3 lines made me slightly annoyed ).
Going by answers:
A. Irrelevant. Hopefully obvious why.
B. Irrelevant. This tries to make you bring in some of your own assumptions, i.e. "fill-in-the-blank" reasoning. For example, bigger hotels -> more carpentry to be done -> lower quality per unit of work. But you don't really know that the second implication is true - more carpenters could have been fhired for example. So as it stands this answer gives us nothing.
C. Strengthens authors hypothesis - hopefully don't need to say why. Point is, because you now really *WANT* to prove the author's shallow judgment wrong, you will detect the irrelevance of this answer in split second.
D. Right answer. How does this help? Because it brings an alternative exaplanation of why hotels built before 1930 have better carpentry, namely by allowing us to accuse the author (keep the emotions up!) of selection bias. The hotels built before 1930 have, according to this answer, been through a much longer "survival of the fittest" race, and thus by now only the ones with really good carpentry have survived. Meanwhile, hotels built after 1930 have not been through such selection process for as long. So the author is comparing a group which has been filtered through a selection process with a group that has not been through that process for as long, and thus in the latter group it is natural that the variance of the quality of carpentry is much greater.
E. Irrelevant. This tries to make you bring in your own implications like in B: shorter apprenticeship -> apprentice has worse skills -> as a carpenter he/she does poorer work. But you don't know that shorter apprenticeship leads to worse skills - the learning methods could have gotten more effective the compensate for the shorter length.
og-2016-intellectual-activities-202263.html#p1552945
Hmm. So some researchers have put mental scores against reported social contact into a spreadsheet and concluded that...they are correlated? Nope, straight away they put their assumptions into work and concluded that increased social contact causes increased mental scores.
We are looking for either something that shows that either the reverse is true (increased mental scores cause increased social contact) or that there is an external factor that causes both.
A. Irrelevant. Hopefully obvious.
B. Right answer. This question doesn't actually say what it is, but it implies that there is some external factor that drives both mental sharpness and social involvement, thus providing evidence that it is not the case that one causes the other.
C. Irrelevant. The fact that in a big enough sample there are individuals with high score on both factors means nothing.
D. Irrelevant. This probably tries to make you think that the study is dodgy because it doesn't use its own data but again, that would be your own opinion you are bringing in from the outside, rather than a general fact or something stated in the question.
E. Irrelevant. All this says is "high mental sharpness = good in mathematics problems". Yet we don't care how to detect high mental sharpness - we care about what to do to increase it. Even if this statement is true, it could be that someone solves 0 math problems in 10 years, but chats with people non-stop 20 hours a day, and does really well on math problems, and hence is judged to have high mental sharpness.
I am going to write and post Part 2 of this when I have time to write it up. In the meanwhile, if you have feedback about whether this was helpful or not, I would be glad to hear it. In particular, I would be interested if there is anything that you didn't see before that made things clearer for you, and if there is any explanation that you found particularly confusing (I might beef it up then).
As background reading, I recommend the writings of the economist Thomas Sowell, because he explains the basic reasoning mistakes people make in very clear and vivid detail. I most recommend his book "Basic Economics". Yes, he is what is called in the US right wing, but it doesn't matter. If you don't agree with him, then you should work to the point where you are able to find the logical errors in his arguments. I did that even though I agree with him, mostly thanks to the very clear logic I learnt from him
So I tried to do a bit of introspection about some of the reasoning techniques I use and present them here in a practical, accessible way. The framework I will take here is to describe briefly a general principle and then illustrate it in practice with one or two actual GMAT questions. I recommend that you try answer the question first and then you can compare your thinking to mine.
Emotional Attitude
Emotions in critical reasoning? No I am not smoking weed
You can discern nonsense answers much easily if you take a very involved attitude to the question. I do this by nature, but you can probably practice it easily. Say the question asks "Which of the following is a possible cause of company ABC's fall in revenue?". Well, imagine you are not the CEO, you are the 100% owner of ABC, and by the current looks you have about a month to turn the business around before you go bankrupt. If you feel like this, you really, really do not have time for BS causes, you just need substance to act on. So answers like "TV stations stopped advertising product X" when the question initially says that the vast majority of revenue comes from product Y will not just be obviously irrelevant, but will get you annoyed, and you will detect them faster.
Principle 1: Correlation is not causation
Equating correlation with causation is one of the most common reasoning mistakes I see people make. Just because A and B occur together, it does not follow that A causes B. It could be that B causes A, or that there is another cause, C, that causes both A and B.
In the spirit of emotionalizing your attitude, here are some controversial practical examples:
1) Global Warming: The fact that the amount of greenhouses gases has been increasing at the same time that the mean global temperature has been increasing need not necessarily imply the increase of greenhouse gases causes the increase in temperatures. Could be that they are just co-incidental - and there's been a lot of controversy about whether they are or not.
2) Racial discrimination in the workplace: Say an employer's workforce is 90% white and 10% non-white in a country where 40% of population is non-white. Does that employer necessarily take race into account when evaluation job applicants? Not necessarily. There could well be million other causes - simplest one being that the employer requires applicants qualified in a field where for whatever reasons the proportion of experts is in fact 90:10 white:non-white.
Example question 1
Try this question:
guidebook-writer-have-visited-hotels-throughout-the-country-80358.html#p603511
When I read the intro and the quick judgment based on correlation, I immediately get suspicious. There are million possible causes for the difference, and this writer just picks his/her nose and decides it's the quality of the carpenters, just like so? No chance. I am looking for something that will disprove his/her correlation=causation judgment (honestly just reading the 3 lines made me slightly annoyed
).Going by answers:
A. Irrelevant. Hopefully obvious why.
B. Irrelevant. This tries to make you bring in some of your own assumptions, i.e. "fill-in-the-blank" reasoning. For example, bigger hotels -> more carpentry to be done -> lower quality per unit of work. But you don't really know that the second implication is true - more carpenters could have been fhired for example. So as it stands this answer gives us nothing.
C. Strengthens authors hypothesis - hopefully don't need to say why. Point is, because you now really *WANT* to prove the author's shallow judgment wrong, you will detect the irrelevance of this answer in split second.
D. Right answer. How does this help? Because it brings an alternative exaplanation of why hotels built before 1930 have better carpentry, namely by allowing us to accuse the author (keep the emotions up!) of selection bias. The hotels built before 1930 have, according to this answer, been through a much longer "survival of the fittest" race, and thus by now only the ones with really good carpentry have survived. Meanwhile, hotels built after 1930 have not been through such selection process for as long. So the author is comparing a group which has been filtered through a selection process with a group that has not been through that process for as long, and thus in the latter group it is natural that the variance of the quality of carpentry is much greater.
E. Irrelevant. This tries to make you bring in your own implications like in B: shorter apprenticeship -> apprentice has worse skills -> as a carpenter he/she does poorer work. But you don't know that shorter apprenticeship leads to worse skills - the learning methods could have gotten more effective the compensate for the shorter length.
Example question 2
og-2016-intellectual-activities-202263.html#p1552945
Hmm. So some researchers have put mental scores against reported social contact into a spreadsheet and concluded that...they are correlated? Nope, straight away they put their assumptions into work and concluded that increased social contact causes increased mental scores.
We are looking for either something that shows that either the reverse is true (increased mental scores cause increased social contact) or that there is an external factor that causes both.
A. Irrelevant. Hopefully obvious.
B. Right answer. This question doesn't actually say what it is, but it implies that there is some external factor that drives both mental sharpness and social involvement, thus providing evidence that it is not the case that one causes the other.
C. Irrelevant. The fact that in a big enough sample there are individuals with high score on both factors means nothing.
D. Irrelevant. This probably tries to make you think that the study is dodgy because it doesn't use its own data but again, that would be your own opinion you are bringing in from the outside, rather than a general fact or something stated in the question.
E. Irrelevant. All this says is "high mental sharpness = good in mathematics problems". Yet we don't care how to detect high mental sharpness - we care about what to do to increase it. Even if this statement is true, it could be that someone solves 0 math problems in 10 years, but chats with people non-stop 20 hours a day, and does really well on math problems, and hence is judged to have high mental sharpness.
To be continued...
I am going to write and post Part 2 of this when I have time to write it up. In the meanwhile, if you have feedback about whether this was helpful or not, I would be glad to hear it. In particular, I would be interested if there is anything that you didn't see before that made things clearer for you, and if there is any explanation that you found particularly confusing (I might beef it up then).
As background reading, I recommend the writings of the economist Thomas Sowell, because he explains the basic reasoning mistakes people make in very clear and vivid detail. I most recommend his book "Basic Economics". Yes, he is what is called in the US right wing, but it doesn't matter. If you don't agree with him, then you should work to the point where you are able to find the logical errors in his arguments. I did that even though I agree with him, mostly thanks to the very clear logic I learnt from him
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16 May 2016, 00:48
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Thanks. That's insightful.
Can you elaborate how do you easily nail down the logical issue in such problems? Many courses recommend finding 'unstated assumptions' before moving onto answer choices. Sometimes it is easy to figure out those assumptions when it is too obvious the gap in reasoning, but for problems involving numbers, percents etc. I end up circling around stimulus and taking more time.
You seem to 'paraphrase' the likely ans without falling in traps which is exactly the things I want to master. I may be doing the same but around wrong areas which won't impact the reasoning much even if weaken/strengthen.
Any suggestions to optimize this process with results? Cheers.
Posted from my mobile device
Can you elaborate how do you easily nail down the logical issue in such problems? Many courses recommend finding 'unstated assumptions' before moving onto answer choices. Sometimes it is easy to figure out those assumptions when it is too obvious the gap in reasoning, but for problems involving numbers, percents etc. I end up circling around stimulus and taking more time.
You seem to 'paraphrase' the likely ans without falling in traps which is exactly the things I want to master. I may be doing the same but around wrong areas which won't impact the reasoning much even if weaken/strengthen.
Any suggestions to optimize this process with results? Cheers.
Posted from my mobile device
jk451
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21 May 2016, 05:24
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HarisinghKhedar
Thanks for the feedback!
Yes most of the time, I make an opinion about what is missing/what is wrong/what I really need before I go through the answers. That way, as I am going through the answers, most I recognize straight away as pointless/irrelevant/wrong and usually one stands out as sensible because I know what I am roughly looking for. This is not always the case, sometimes I hesitate between two answers, but for real GMAT questions, vast majority of the time they make sure that one answer stands out.
Where this is a bigger problem are test questions from other providers like MGMAT, etc. Despite these providers doing really good and hard work on such questions, about 1/5 of the questions, especially harder ones, is just wrong in the sense that none of the answers addresses the real fault/missing piece in the question. So I really recommend practicing CR (and RC) on real GMAT questions vast majority of the time, because otherwise you might find yourself wasting time to develop artificial techniques to find answers that don't actually make sense in reality.
If you have problems finding faults in questions heavy on numbers, percents, etc. then I recommend practicing on problems you care about - it's so much easier to find logical problems when you have motivation to do so compared to when you don't. For most people, this involves political/social topics. Say you are in America and feel super strongly about abolishing guns - it will be much easier for you to find the reasoning problems (assumptions, wrong implications, etc.) than to find what the problem is in an argument why tomatoes should be planted in some greenhouses instead of peppers. For example (numbers made up): "100,000 in the US die due to gun crime compared to 10,000 in Britain" -> "But US has much larger population, so obviously there will be more gun deaths" -> "8.5 people per thousand in the US die due to gun crime compared to 4.5 in Britain" -> "This suffers from selection bias. In Britain, absence of guns means that violence often happens with knives and other tools, which are not included in the statistic" -> "how many people die in the US/Britain due to gun/knife/tool crime" -> so on
