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LOGIC questions from "getting into oxbridge guide"
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tomcoolinguk
it is made clear that the car must be worth £1000 or £5000!
No, you are prepared to pay £1000 for a bad car and £5000 for a good car, it does not say anything about the real market value of the car. However, I would agree with you final answer, as I would expect the car to be in a bad condition, and I would also expect that the £1000 I am prepared to pay for a car in a bad condition is a reasonable price.
A good start at thinking about problems like these would be "Logic" in the Oxford "very short introduction" series, I've only read parts of it (yet), but I've read many others in the series. All the other books have been brilliant, and from what I have read in this one, it seems to me that it is of the same, very high, standard.
I apologise for my grammatical slip, but the meaning was there- I was just rushing! What book(s) are you talking about by the way?
tomcoolinguk
I do think the first part is a right or wrong answer question; it is made clear that the car must be worth £1000 or £5000! As three quarters of cars cost £1000 this must be most common. Can't believe so many people have been tricked... tee hee. I feel a bit better about myself
"Expected" is a loaded term though, especially if you do Stats.
tomcoolinguk
I apologise for my grammatical slip, but the meaning was there- I was just rushing! What book(s) are you talking about by the way?
Yes, it was nothing major, maybe I'm just being pedantic, but I thought it was worth pointing out. These questions are, from what I feel and understand, mostly designed to test one's ability to think cognitively, analytically and laterally, and being somewhat pedantic tends to help in answering them as precisely as possible.
Here are the full details of the book:
Priest, G., 2000. Logic. Oxford : Oxford University Press.
It's only just over 100 (small) pages short, and is a terrific little book that really consolidates your ability to think about questions like these, and your ability to justify your reasoning. There are probably loads of other books that would do the same job, but I haven't come across any other books that are as concise and interesting as this. By the way, the RRP is £6.99.
The way which i understand the question, it implies that the cheque is never actually cashed. Therefore who payes for the mans holiday. Surely not the man as the money never gets deducted from his account. So who?
8 Lucky number
The way which i understand the question, it implies that the cheque is never actually cashed. Therefore who payes for the mans holiday. Surely not the man as the money never gets deducted from his account. So who?
Say the holiday costs £1000, and he has £1500 in his bank. If the bank knew of his cheque, then they could limit his account so that he can now only withdraw/pay £500, but if the cheque is never cashed, then technically he still has £1500 in his account (although he shouldn't have access to £1000 of it).
Of course, with cheques, the bank doesn't know you've made one until it gets cashed in, so if it's never cashed then the man never pays for the holiday, but he has a £1000 IOU slip floating around. However, it doesn't seem like that big of a deal. Money is created and destroyed every day.
the question was asked in an economics interview. i personally do not feel that the answer is related to the way in which the financial system of banks works and how cheques are cashed. If we assume that the cheque is never cashed, then the man doesn't pay for the holiday, agreed? Neither does the holtelier as he uses it to pay his supplier. The cheque is effectively being used as a new broad form of money is it not? However who pays for the holiday? Help please from fellow economists, perhaps i am on the wrong track?
tomcoolinguk
I do think the first part is a right or wrong answer question; it is made clear that the car must be worth £1000 or £5000! As three quarters of cars cost £1000 this must be most common. Can't believe so many people have been tricked... tee hee. I feel a bit better about myself
But it says the "expected value" of the car - a maths student would certainly calculate this to be £2000.
E(X) = sum(P(X=x)for all values of x)
i.e. 5000*0.25+1000*0.75 = 2000
So they have not been tricked.
i agree with you hitch hiker, you used the same method as myself.
If one's 'willingness to pay' for a car is defined as what the person buying the car think it is worth, your line of thought does not seem logical at all. After all, a car is, according to you worth either £1000 or £5000. How can you expect a car to be worth £2000? The exercise does not mention anything about cars being 'somewhat good' etc.
Of course, there are no objectively right answers to the question, and as long as you are able to explain how you found your answer and how that answer is reasonable, you should be fine.
Of course, there are no objectively right answers to the question, and as long as you are able to explain how you found your answer and how that answer is reasonable, you should be fine.
noctivaga
If one's 'willingness to pay' for a car is defined as what the person buying the car think it is worth, your line of thought does not seem logical at all. After all, a car is, according to you worth either £1000 or £5000. How can you expect a car to be worth £2000? The exercise does not mention anything about cars being 'somewhat good' etc.
Of course, there are no objectively right answers to the question, and as long as you are able to explain how you found your answer and how that answer is reasonable, you should be fine.
Of course, there are no objectively right answers to the question, and as long as you are able to explain how you found your answer and how that answer is reasonable, you should be fine.
I don't believe it is illogical.
Leaving aside the fact that obviously there is a sliding scale for good or bad cars, if we do take it that they are either good (£5000) or bad (£1000) then this is a discrete random variable - it can only take one of two values (I'm sorry if this seems patronising, I don't know what level of maths you have).
Mathematically, the "expected value" is then effectively the weighted mean of the variables.
That is: sum(P(X=x)for all values of x) (as I have said before)
This expected value of x may take a value which is not one of the variables.
And maths is never illogical
hitchhiker_13
And maths is never illogical
Maths is not illogical, however, maths applied in a less than favourable way may not always give a logical answer worth anything in 'the real world.' There is a sliding scale, however, whether you are supposed to take this fact into account when answering the question or not is not stated explicitly. I assumed that I was not supposed to use a sliding scale, hence limiting the complexity of the reasoning.
However, as these are questions one is preparing to being asked in an interview situation, this should be taken into account. If one explains minor details as these, they will be able to understand very clearly how you reach your answer. The point of the exercise is not for you to provide the perfect answer to every question, but to have valid, interesting and analytical ways of attacking questions. Therefore, I would place less emphasis on the minor calculations that have been done than on the basics of the question. Anyone could calculate the 'expected value' of the car, however, not that many would be able to explain clearly and sensibly why they chose to do it that way.
noctivaga
Maths is not illogical, however, maths applied in a less than favourable way may not always give a logical answer worth anything in 'the real world.' There is a sliding scale, however, whether you are supposed to take this fact into account when answering the question or not is not stated explicitly. I assumed that I was not supposed to use a sliding scale, hence limiting the complexity of the reasoning.
However, as these are questions one is preparing to being asked in an interview situation, this should be taken into account. If one explains minor details as these, they will be able to understand very clearly how you reach your answer. The point of the exercise is not for you to provide the perfect answer to every question, but to have valid, interesting and analytical ways of attacking questions. Therefore, I would place less emphasis on the minor calculations that have been done than on the basics of the question. Anyone could calculate the 'expected value' of the car, however, not that many would be able to explain clearly and sensibly why they chose to do it that way.
However, as these are questions one is preparing to being asked in an interview situation, this should be taken into account. If one explains minor details as these, they will be able to understand very clearly how you reach your answer. The point of the exercise is not for you to provide the perfect answer to every question, but to have valid, interesting and analytical ways of attacking questions. Therefore, I would place less emphasis on the minor calculations that have been done than on the basics of the question. Anyone could calculate the 'expected value' of the car, however, not that many would be able to explain clearly and sensibly why they chose to do it that way.
Point taken, and I don't think you would be disadvantaged for approaching it like that, as it is not a mathematical course - although I presume social sciences would involve a fair bit of statistics so maybe calculating the expected value is important.
Explaining it is simple - "expected value" is a mathematical term with a very specific meaning, so you have done exactlywhat has been asked (the quite precise wording of the question would indicate to me that this is what they intended you to do, but I may be mistaken), rather than some roundabout reasoning.
I just reread the question, and spotted a rather important point (how I managed not to specifically point it out in my previous posts, I have no idea, it's rather obvious): you think that 75% of all cars are bad (ie. expected to be worth £1000) and 25% of all cars are good (ie. expected to be worth £5000). There is no sliding scale.
And, since a bad car for you is worth a maximum of £1000 and a good car for the seller is worth a minimum of £4000, it seems pretty unreasonable to me to expect the car to be worth £2000, as there are no cars worth £2000.
Of course, my example does not illustrate a real-world market for cars very well, however, that is not the intention of it. The intention is simply to reason logically based on the information I get in the exercise, at least that's how I choose to see it. Oh, and maths is terribly important, don't get me wrong, but I don't think an admissions tutor would feel too impressed when you place a simple calculation in front of them, and neither do I think that the points of these exercises (nor that of the interviews) is to show basic skills already acquired.
And, since a bad car for you is worth a maximum of £1000 and a good car for the seller is worth a minimum of £4000, it seems pretty unreasonable to me to expect the car to be worth £2000, as there are no cars worth £2000.
Of course, my example does not illustrate a real-world market for cars very well, however, that is not the intention of it. The intention is simply to reason logically based on the information I get in the exercise, at least that's how I choose to see it. Oh, and maths is terribly important, don't get me wrong, but I don't think an admissions tutor would feel too impressed when you place a simple calculation in front of them, and neither do I think that the points of these exercises (nor that of the interviews) is to show basic skills already acquired.
noctivaga
I just reread the question, and spotted a rather important point (how I managed not to specifically point it out in my previous posts, I have no idea, it's rather obvious): you think that 75% of all cars are bad (ie. expected to be worth £1000) and 25% of all cars are good (ie. expected to be worth £5000). There is no sliding scale.
And, since a bad car for you is worth a maximum of £1000 and a good car for the seller is worth a minimum of £4000, it seems pretty unreasonable to me to expect the car to be worth £2000, as there are no cars worth £2000.
Of course, my example does not illustrate a real-world market for cars very well, however, that is not the intention of it. The intention is simply to reason logically based on the information I get in the exercise, at least that's how I choose to see it. Oh, and maths is terribly important, don't get me wrong, but I don't think an admissions tutor would feel too impressed when you place a simple calculation in front of them, and neither do I think that the points of these exercises (nor that of the interviews) is to show basic skills already acquired.
And, since a bad car for you is worth a maximum of £1000 and a good car for the seller is worth a minimum of £4000, it seems pretty unreasonable to me to expect the car to be worth £2000, as there are no cars worth £2000.
Of course, my example does not illustrate a real-world market for cars very well, however, that is not the intention of it. The intention is simply to reason logically based on the information I get in the exercise, at least that's how I choose to see it. Oh, and maths is terribly important, don't get me wrong, but I don't think an admissions tutor would feel too impressed when you place a simple calculation in front of them, and neither do I think that the points of these exercises (nor that of the interviews) is to show basic skills already acquired.
As I said I am ignoring any sliding scale - as we have no data about any one that may exist.
The calculation still stands.
I'm sorry I really don't understand you - this calculation is exactly what the question calls for. I am not saying your way is invalid; it may be as far as it goes.
But for you to say that an admissions tutor would be unimpressed is unfair - a candidate who does that calculation has done exactly what is called for, and any tutor who tried to invalidate this would get a piece of my mind.
I really don't see how saying, "Well, I would expect it to be £1000, because most of them are" is in any way more indicative of a wonderful intellect. Where is the merit in that statement?
I am not necessarily saying that the correct answer is £1000 (nor anything else, as I think there are no correct answers to the question!). However, do you see the logical break in that there are no cars worth between £1000 and £4000, and you expect the value of the car to be £2000? Is the question really asking the potential student to find an answer that must be wrong? My point is as simple as that, and I haven't really provided any decent solution to the question, as I think any solution I would reach would not be a simple number, but an explanation of why I am not able to reach a simple answer, and then just explain what would be reasonable to guess, and within what ranges one is limited to guess.
noctivaga
I am not necessarily saying that the correct answer is £1000 (nor anything else, as I think there are no correct answers to the question!). However, do you see the logical break in that there are no cars worth between £1000 and £4000, and you expect the value of the car to be £2000? Is the question really asking the potential student to find an answer that must be wrong? My point is as simple as that, and I haven't really provided any decent solution to the question, as I think any solution I would reach would not be a simple number, but an explanation of why I am not able to reach a simple answer, and then just explain what would be reasonable to guess, and within what ranges one is limited to guess.
Please go and read a maths textbook.
I understand your calculation (although you are probably right, I should read more maths, however, not for the purpose of understanding your calculation 
). If you read my replies, I am not saying that your calculation as such is wrong. However, how on earth can you expect a car to be worth £2000 when no cars are worth between £1000 and £4000?
). If you read my replies, I am not saying that your calculation as such is wrong. However, how on earth can you expect a car to be worth £2000 when no cars are worth between £1000 and £4000?You have approached the question from one angle, and I have approached it from another. Yet really, amongst the people called for interview at Oxford your approach would not be considered anything special without justification, which have done extremely lucidly, and for this they would give you plaudits. However, if you were to approach it is a probability question,
so what is the value of X= p(A) or p(B), where A is three times as common. The expected value would therefore be £1000. If however, you were buying four cars, the expected mean value would be £2000; because you would expect one high quality good car to be included. You have to treat A and B has concrete values. The question does not call for values AA-AZ in the interim, and in trying to incoprpoate them into your answer you undermime it and would show a lack of appreciating the nature of the problems, as it is made clear the car is either worth £1000 or £5000.
Your approach, I feel, is the seeming 'obvious' approach that these problems lead up the garden path.
so what is the value of X= p(A) or p(B), where A is three times as common. The expected value would therefore be £1000. If however, you were buying four cars, the expected mean value would be £2000; because you would expect one high quality good car to be included. You have to treat A and B has concrete values. The question does not call for values AA-AZ in the interim, and in trying to incoprpoate them into your answer you undermime it and would show a lack of appreciating the nature of the problems, as it is made clear the car is either worth £1000 or £5000.
Your approach, I feel, is the seeming 'obvious' approach that these problems lead up the garden path.
the expected value of £2000 is referring to the expected payout the man would pay if he purchased several cars; the more of which he bought, the more accurate it would be, assuming there are a quarter good cars etc, which there isnt as it is his estimate. I knew decision maths would come in handy. Game Theory ahhh John Nash has done me proud.
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