海归人才网投行Brain Teaser面试问题&答案总结.docx

海归人才网投行Brain Teaser面试问题&答案总结 海归求职网-专注留学生海归求职培训辅导服务 投行Brain Teaser面试问题&答案总结 你进了投行final round？这个时候就不仅仅是看你会多少technical question，和你的resume了。你也会被问到Brain Teaser。 说是智力问题，其实考察的是你遇到之前没有碰到过的问题的反应和你的Thinking Process。也就是说：答案不重要，但是你得有逻辑的告诉我你怎么想的！ QUESTION You invest $100 today in a company. You earn 10% in your first year but lose 10% in the second year. At the end of the second year do you have more, less or the same as you started with? This is another question that isnt really a brainteaser, but it was asked in a Barcap analyst interview so we should give it a look. ANSWER The instinctive response is to say the same. But lets take this step by step. T = 0: you have $100. Between T = 0 and T = 1 you earn 10% on what you started with. 10% of $100 is $10, so now you have $110. T = 1: you have $110. Between T = 1 and T = 2 you lose 10% and 10% of $110 is $11.T = 2: you have $99! So you have less than what you started with. Sometimes interviewers use different numbers but the general idea is the same. Well be asking a question with a similar structure later, lets see if you can spot it! QUESTION There are three boxes of eggs. In each box is either big eggs, small eggs or big and small eggs. The boxes are labelled: Big, Small and Mixed but every box is labelled incorrectly. What is the least number of boxes you can open to know which eggs are in which box and why? ANSWER 海归求职网-专注留学生海归求职培训辅导服务 The key here is to read the question carefully; remember that all boxes are marked incorrectly.Lets start with a hypothetical situation. What happens if you open the box marked “Small”? Either the eggs will be big or they will be mixed (since the boxes are labelled incorrectly). Lets say that they are mixed. Then we have two boxes left. One labelled “Big” and the other labelled “Mixed” and the contents are either small eggs or big eggs. We are told in the question that the boxes are all labelled incorrectly so the big eggs cant be in the box marked “Big”. The big eggs are in the “Mixed” box; the mixed eggs are in the “Small” box and the small eggs are in the “Big” box. Whatever scenario you choose, you will always be able to work out which eggs are in which box by only opening one box. QUESTION How many disposable nappies were sold in the UK last year? This is another standard estimation problem. More specifically, it is a market-sizing question, since we are estimating the number of nappies sold every year. This is exactly the kind of question that the top management consultancies like to ask. ANSWER My first impression is that we need to estimate: · Population of the UK · Proportion that wear disposable nappies · Number of nappies worn per day · Number of days in a year To get our estimate we multiply these numbers together. The population of the UK is about 60 million. More precisely, it is about 62 million but 60 million will do just fine. In your interview you may be asked about countries other than the US or the UK, so having a good general knowledge of populations is helpful. 海归求职网-专注留学生海归求职培训辅导服务 Now how many of those people wear disposable nappies? There are three parts to this question. Firstly, at what age do people wear nappies? I know nothing about kids. If youve got a younger sibling you might be able to put a more accurate estimate together here. From personal experience I can never remember wearing a nappy, and I reckon my earliest memories go back to when I was 6 or 7. So Im going to estimate that nappies are worn between the ages of 0 and 5 (Im also assuming no one over the age of 5 wears a nappy!). Secondly, what proportion of the population is in that age group? Im not familiar with the demographics of the UK. We could assume that people are evenly distributed between 0 and 100, but I dont think that is accurate enough. There tends to be more younger people than older people. There are certainly more people between the ages of 0 and 5, then 95 and 100. Moreover, this answer looks like it is going to be reasonably straight forward so it might help to throw in a little extra detail. Lets say that 60% of the UK is under 40 and 40% is over 40. The “baby-boomers” might weight that more towards the over 40s but I think this is adequate for our purpose. Now we can assume that the under 40s are evenly distributed throughout their group. 60% of the population is 36 million. People aged 0-5 are one eight of the number of people aged 0-40. 36 million/8 = 4.5 million nappy wearers. Finally, how many of them are wearing disposable nappies? Again, my knowledge of babies is limited, but I would guess well over 90%, so Im not going to adjust the estimate. Does that number make sense? 4.5 million out of a population of 60 million is 7.5% of the population. That might be too big but its not absurd. If we had gotten a figure of 20%+ then that would have been absurd. How many nappies does a child wear in a day? Well, the purpose of a nappy is to act as a surrogate toilet, and lets say that one uses a toilet 3 times a day on average. Perhaps children eat more and 海归求职网-专注留学生海归求职培训辅导服务 therefore use the toilet more. I dont know. We wont get into too much analysis here well just stick with 3. In that case a child wears three nappies a day. So we have 4.5 million children wearing 3 nappies a day which means 13.5 million nappies are used every day. How many nappies used in a year? 365*13.5 million = uuuh. Lets think of it as 365*1.35 which is roughly 366*1.33 = (11/3*100)*4/3 = 44/9*100 which roughly = 500. Now we reintroduce the 10 million to get 5 billion. Thats a lot of nappies! QUESTION You have 5 pots of coins. One of the pots contains only fake coins. The normal coins weigh 10 grams. The fake coins weigh 9 grams. You are given a weighing scales (one you would use to weigh yourself,not a balancing scales) and allowed to make only one measurement. How do you determine which pot contains the fake coins? This is a very popular question, and it was most recently asked at a Deutsche Bank interview. It seems to be particularly in programming interviews. But I wouldnt assume that it couldnt be asked anywhere else. ANSWER We want to select a group of coins such that it will always tell us which pot the fake coins came from. We have 5 pots so there needs to be 5 different possible outcomes. Each outcome is a weight so we need to select a group of coins that will give us 5 different weights depending on which pot contains the fake coins. If we take one coin from each pot and weigh them we will get 49 grams irrespective of which pot contains the fakes. 4 coins are normal and weigh 10 grams and one coin is fake. If we choose 2 coins from each pot we have the same problem. We cant discern where the fake coin came from so that doesnt help us. If choosing the same number of coins from each pot doesnt help, then maybe choosing a different number from each pot would. If we take 1 from the first, 2 from the second, and so on and weigh them then what happens? 海归求职网-专注留学生海归求职培训辅导服务 If the first pot contains fakes then the weight will be 149 grams (1*9 + (2+3+4+5)*10). If the second pot contains fakes then the weight will be 148 grams (2*9 + (1+3+4+5)*10). If we continue these calculations we can see that every time we calculate the weight we get a different answer, because in every scenario there are a different number of fake coins. In the first scenario there is one fake coin so the first pot contains the fakes. In the second scenario there are two fake coins so the second pot contains the fakes etc. Note that this will work for any group of numbers that are different, they dont have to be consecutive. You just need to be able to remember your 9 times tables. Try a different combination for yourself. 文档来源：专业留学生海归求职培训辅导机构 海归求职网AceCareer