Suppose you get a question and have to select an answer with multiple choices to choose from, you can find out the right answer logically using the game theory using the Game Theory. Without even knowing the question.

And the reason I am posting this here, is that I have used a similar method myself a lot of times when I didn’t have the time, or didn’t know how to get the right answer. But I never knew it was related to the Game theory.

Example:

Which of the following is the correct answer?

a) 4π sq. inches

b) 8π sq. inches

c) 16 sq. inches

d) 16π sq. inches

e) 32π sq. inches

Answer:

The odd answer in the series is c. Since it is so different from the other answers, it is probably not right. The fact that the units are in square inches suggests an answer that has a perfect square in it, such as 4π or 16π.
This is a fine start and demonstrates good test-taking skills, but we haven’t really started to use game theory. Think of the game being played by the person writing the question. What is that person’s objective?

He or she wants people who understand the problem to get the answer right and those who don’t to get it wrong. Thus wrong answers have to be chosen carefully so as to be appealing to folks who don’t quite know the answer. For example, in response to the question: “How many feet are in a mile?” an answer of “Giraffe,” or even 16π, is unlikely to attract any takers.

Turning this around, imagine that 16 square inches really is the right answer. What kind of question might have 16 square inches as the answer but would lead someone to think 32π is right? Not many. People don’t often go around adding π to answers for the fun of it. “Did you see my new car — it gets 10π miles to the gallon.” We think not. Hence we can truly rule out 16 as being the correct solution.

Let’s now turn to the two perfect squares, 4π and 16π. Assume for a moment that 16π square inches is the correct solution. The problem might have been: “What is the area of a circle with a radius of 4?” The correct formula for the area of a circle is πr2. However, the person who didn’t quite remember the formula might have mixed it up with the formula for the circumference of a circle, 2πr. (Yes, we know that the circumference is in inches, not square inches, but the person making this mistake would be unlikely to recognize this issue.)

Note that if r = 4, then 2πr is 8π, and that would lead the person to the wrong answer of b. The person could also mix and match and use the formula 2πr2, and hence believe that 32π or e was the right answer. The person could leave off the π and come up with 16 or c, or the person could forget to square the radius and simply use πr as the area, leading to 4π or a. In summary, if 16π is the correct answer, then we can tell a plausible story about how each of the other answers might be chosen. They are all good wrong answers for the test maker.

What if 4π is the correct solution (so that r = 2)? Think now about the most common mistake: mixing up circumference with area. If the student used the wrong formula, 2πr, he or she would still get 4π, albeit with incorrect units. There is nothing worse, from a test maker’s perspective, than allowing the person to get the right answer for the wrong reason. Hence 4π would be a terrible right answer, as it would allow too many people who didn’t know what they were doing to get full credit.

At this point, we are done. We are confident that the right answer is 16π. And we are right. By thinking about the objective of the person writing the test, we can suss out the right answer, often without even seeing the question.

Now, we don’t recommend that you go about taking the GMAT and other tests without bothering to even look at the questions. We appreciate that if you are smart enough to go through this logic, you most likely know the formula for the area of a circle. But you never know. There will be cases where you don’t know the meaning of one of the answers or the material for the question wasn’t covered in your course. In those cases, thinking about the testing game may lead you to the right answer.

BTW, this reasoning was given in the book – The Art of Strategy. My next read.

The  CAT 2008 – the premier MBA entrance examination in India was held today. I will try to post a detailed analysis and the answers / solutions here.

The CAT 2008 Solutions are expected to be out by 5 PM.

The CAT this year has 90 questions in all.

25 Quant
25 DI
40 Verbal

The DI section was a bit complicated and very calculation intensive, while the Quant section was relatively easy. The Verbal section, as always was unpredictable and no one seems to know how they fared. As there were 40 questions in the VA section, it will play a major role in determining the chances of getting into the IIMs.

Solutions:

TestFunda.com has started uploading CAT 2008 solutions and answer keys:

http://cat2008a.testfunda.com/CAT_Answer_Key_Answers_Solutions_Analysis_CAT_2008_Score_ANSWER_KEY.aspx

http://hitbullseye.com/user/key2008.php

http://www.ch-india.com/CAT08_sol/cat08_anskey.htm

http://www.ch-india.com/CAT08_sol/cat08_sum_ana.htm

Check out this PagalGuy’s score card for answers:

http://www.pagalguy.com/scorecard/

>> Career Launcher CAT 2008 Analysis

CL’s Take on the CAT

Overall, the CAT’08 paper was of a moderate difficulty level. The paper was more balanced than previous years, primarily because of more choices in the English section. There have been an increase in the total number of questions – from 75 to 90, with English section accounting for 40 questions (an increase of 15 from last year) and Quant and DI having 25 questions each.

The Quant section was less difficult than last two years, though not in an absolute sense.

DI, however, proved to be a tougher nut to crack this time around.

The English section, with more choices, was easier to handle.

Expected cut-offs:
Quant: 30-32
VA: 46-48
DI: 28-30
Overall: 125+

IMS CAT 2008 Answer Key

>> IMS India CAT 2008 page

IMS’s Take on the CAT

CAT 2008 was easier compared to tha CAT in the last few years. The Verbal section, especially, offered a lot of scoring opportunities to the students. This would mean an increase in the verbal cut-offs. The DI section had quite a few sets with only 3 questions each, thereby increasing the effort required to score higher. Logical reasoning made a come back while Data Sufficiency was out of the DI section. Finally, the PS section was quite easy, and students who had rigorously solved and analysed the SimCATs would have sailed through this section.Overall, an easy CAT with cut-offs that would probably go higher than last year, especially in PS and VA.

Quant Cutoff: 32-35

DI Cutoff: 32-35

Verbal Cutoff: 46-49

Overall Cutoff: 120 – 140

TIME’s CAT 2008 Answer Key

>> T.I.M.E CAT 2008 Analysis

TIME’s take on the CAT:

* QA was similar to CAT07 but of a higher difficulty level. This section had fewer questions on Arithmetic.  Cutoff -> 18 ± 2

* L & DI was of a similar level of difficulty as CAT07. This was a classical DI paper with sets on DI as well as Logic puzzles. Cutoff-> 32 ± 2

* Verbal was less subjective than last year. Level of vocabulary was higher. Cutoff-> 42 ± 2

Overall Cutoff -> 125 ± 3

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Note: This post will be updated dynamically as more information comes out.