LOGIC questions from "getting into oxbridge guide"

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Amrad
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#41
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#41
IIRC this question was on an E&M admissions paper. I agree that the expected value of the car must be calculated mathematically and is £2000.

b) You can make as many offers for the car as you like, but want to be wary of continually upping your offer as the salesman might see this and choose a strategy accordingly. At this stage you do not know at what values the salesman will sell a good/bad car at, and we may assume that he would want more than £1000 for a bad car. You need to discern through your bidding whether or not the car is good or bad, but I would say this is too risky as you have no idea of the salesman's values. For example he may want £1500 for a bad car and you may end up offering £3500 for a bad car. I would therefore bid incrementally from a value below £1000, say £500 up to a value of £1000. It is too risky to try and guess what type of car you have in front of you, so I would settle for a bad car as the majority are likely to be bad and you are less likely to lose money this way. A risk minimisation strategy, but the one I would opt for.

c) Make an offer of £500. If it is not accepted the car is good, so make an offer of £4000. This assumes the salesman will not get involved in any sort of mindgames.

d)If he knows you know his strategy then he could easily reject an offer of £500 for a bad car and sell it to you for £4000. However we assume that he will stick to what is suggested in the question for part c). By deviating from this strategy he could easily throw you and portray a bad car as good. You are using his minimum selling prices as indicators, and if these indicators are moved then your judgement and strategy will not be so effective.
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Amrad
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#42
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As for the cheque question, whoever currently holds the cheque is paying for the man's holiday. I am assuming here that the "Pay" part of the cheque is left blank otherwise it would not be legal tender if made payable to someone else. The obvious implication here is the interest that the man will accrue as his cheque is being passed around. Eventually the cheque will get back to the source of the supply chain and be banked.
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noctivaga
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#43
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(Original post by tomcoolinguk)
Your approach, I feel, is the seeming 'obvious' approach that these problems lead up the garden path.
I can easily agree with you on that, my approach might seem rudimentary, and until it is taken a couple of steps further and developed into a more complete answer, it is not worth much.

rockindemon: There is nothing in your answer I would disagree with as such, but the question is still asking what you expect the value of 'the car you are buying' (ie. one car). I guess both points of view are valid in their own sense, as long as their limitations are taken into account.
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Lucky number 8
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#44
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Ok i think that between us we have receached soem form of conclusion on the first question about the cars, however opinions do seem to differ about the answer to part (a). However i think that it is time to move on with the next question, so please, no more posts about the car question. On the other hand, answers to the cheque question are still welcome.
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Hellsbells
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#45
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(Original post by Lucky number 8)
Rachel and Peter have no sport in common, though each has a sport shared with Jemima.

Jemima, Peter and William have no game in common.
Erm, this doesn't work!

EDIT: Hmm maybe I've misunderstood the second sentence?
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Amrad
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#46
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(Original post by Hellsbells)
Erm, this doesn't work!

EDIT: Hmm maybe I've misunderstood the second sentence?
I hit the same wall...
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Hellsbells
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#47
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(Original post by Lucky number 8)
Having just tried it, I agree it doesn't work. If there are only four sports and four students, and each student plays two sports, then it is impossible for only one sport to be played by more than two of them.
Surely?
Yes - so saying that three of them have no game in common is a pointless statement. But as there are only 4 games, at least one set of two people must have a game in common with each other.
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Lucky number 8
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#48
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#48
Stupid book giving question which are impossible, or maybe that is the answer which they were looking for in the interview, that the question is impossible to solve! what do you think
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Lucky number 8
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#49
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#49
Lets forget that one. Anyone up for attempting another one?
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Amrad
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#50
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(Original post by Hellsbells)
Yes - so saying that three of them have no game in common is a pointless statement. But as there are only 4 games, at least one set of two people must have a game in common with each other.
And how can one game be played by more than two students if Peter, Jemima and William have no game in common. If three or four students are playing the same game then it would have to include two/three of these.
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Hellsbells
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#51
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(Original post by Lucky number 8)
Stupid book giving question which are impossible, or maybe that is the answer which they were looking for in the interview, that the question is impossible to solve! what do you think
I'm working on it! Maybe there is an answer...
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Amrad
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#52
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(Original post by Hellsbells)
I'm working on it! Maybe there is an answer...
Well now he has removed the question I can't work on it... so post another one.
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Hellsbells
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#53
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(Original post by Lucky number 8)
Lets forget that one. Anyone up for attempting another one?
Aww, did you delete it?
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fishpaste
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#54
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#54
Can you repost the question please? I want to check something.
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Hellsbells
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#55
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#55
(Original post by fishpaste)
Can you repost the question please?
Seconded!
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fishpaste
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#56
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#56
(Original post by Hellsbells)
Seconded!
Though my answer was wrong I've realised.
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Hellsbells
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#57
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#57
(Original post by fishpaste)
Though my answer was wrong I've realised.
I was half-way to my second attempted answer... please re-post the question!
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Amrad
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#58
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#58
I'm waiting too...
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Lucky number 8
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#59
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#59
Economists try this one:

Pooh bear and Rabbit like honey and plan to begin producing by errecting beehives in a meadow. Only Eeyore has the skill to craft the beehives, and he agrees to make the hives for Pooh and Rabbit in exchange for two pots of honey for each hive he makes. As more hives are errected in a meadow the yield from each new hive decreases according to teh formula (50 - (n squared) ), where n is the number of hives in the meadow. Assume motivation is self interest.

(a) How many beehives should Pooh and Rabbit buy from Eeyore?

(b) How many pots will they each have?

(c) Pooh and Rabbit fall out and decided to produce seperately, and Eeyore sells to them seperately. What may now happen? How many beehives will each put up? Discuss answers with explaination.
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Lucky number 8
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#60
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#60
a and b seem straight forward.

For (a) i get 6. For part (b) i get 209 for Pooh and Rabbit and 12 for Eeyore. Still working on (c)
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