UNIVERSITA’ BOCCONI UNDERGRADUATE SCHOOL

Guide to the

Entrance Test for Bachelor Programs 

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MATHEM MATICS questionss 1. What is thhe centre of thhe circle that passes p throughh points (1,2 2), (4,1) and (11,4)? (1,1) 1 (0,1) 2 (1,1) 3 (0,0) 4 (1,0) 5

Answer t same for the t three poin nts and so muust lie on The distancee from the cenntre must be the the axis of seegment AB annd on the axiss of segment BC; it therefo ore coincides with the point of interrsection (1,1) of these two axes. a The correct answer, a thereffore, is numbeer 3.

2. What is the t minimum value that asssumes the function g(x) = x2  2x? 2 1 1 2 0 3 1 4 2 5

Answer g is a quadrattic function: itss graph is a paarabola that op pens upward (the ( coefficiennt of x2 is positive), so the minimum m value of g iss the ordinate of the vertex of the parabola; given

that the absciissa of the verrtex is

the ordinate is i a thereffore, is numbeer 2. The correct answer,

3. P is the point p of coordiinate x.

And so thhe point of cooordinate 1/x iss: A 1 B 2 C 3 D 4 E 5

Page 3 Answer ween 0 and 1 and so 1/x is necessarily n grreater than 1 ((it cannot be A); A if we lookk As we can seee from the grraph, x is betw more closelyy, we see that x is strictly leess than 1/2 annd so 1/x must strictly be grreater than 2. The only poin nt compatiblee with this infoormation is E.. The correct answer, a thereffore, is numbeer 5. 4. What is thhe equation of the line in thhe graph below w?

1 2 3 4 5

Answer 0). The slope (or ( gradient) oof the line is th herefore: The line crossses the y-axiss at point (0,4)) and the x-axiis at point (8,0

The interceptt is 4 and so thhe correct ansswer is option 4.

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5. The chart below shows the frequency of family member numbers for a certain number of families. If we choose one of these families at random, what is the likelihood of it being composed of 3 members?

450 400 350 300 250 200 150 100 50 0 0

1

2

3

4

5

About 65% 1 About 75% 2 About 85% 3 About 95% 4 The data given is insufficient 5

Answer The bar chart shows the frequencies given in the following table: No. of members

1

2

3

4

5

Frequency (approx.)

50

200

400

280

70

Around 1000 families were analysed in total. Families composed of at least three members accounted for approximately 400 + 280 + 70 = 750. The relative frequency of families with at least three members is therefore about 75%. The correct answer, therefore, is number 2.

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WORD RELATIONSHIPS questions In this type of question you will be asked to work with the words and spot the relationships between them. In some cases, the question will consist of a series of words, all of which will be related to each other except for one. You will therefore be asked to identify the "odd one out", i.e. the word which does not follow the same logic that brought all the other words together (in terms of their meaning, function, classification, etc.). In other questions you will be asked to identify the relationship that exists between certain words. This relationship will be in the form of a ratio ( X : Y = W : Z or “X and Y are linked

together by the same logic that links W and Z”) from which two words have been omitted; choosing the words that complete the ratio will lead you to the correct answer. The relationship between the first and the second word must be equal to the relationship between the third and the fourth word. 6. Which word is the odd one out? Vest 1 Jumper 2 Tee-shirt 3 Shoes 4 Shirt 5

Answer All of the words listed are items of clothing; four of these, however, (vest, jumper, tee-shirt and shirt) are garments designed to dress the upper part of the body; shoes, on the other hand, dress the lower part of the body. In this case, the common logic that brings these words together relates to their function, and so the correct answer is number 4. 7. ……… is to NABOB as UPRISING is to ………. HE 1

A. BARKING

B. PROCESSION

C. BEAUTIFUL

D. POOR

E. IMPOSTOR

F. RICH

G. MOVING

H. REVOLT

AG 2 DB 3 CE 4 FH 5

Answer In this case, we arrive at the correct answer by finding the synonyms of the two words above ("nabob" and "uprising"). Indeed, of all the alternatives suggested, the only one that can resolve the given ratio correctly is FH: rich is to nabob (the first word is synonymous with the second) as uprising is to revolt (the relationship is the same, i.e. the third word is synonymous the fourth). The correct answer, therefore, is number 5.

8. Which word is the odd one out? Bright 1 Sharp 2 Discounted 3 Shrewd 4 Answer

Witty 5

Four of the words given (bright, sharp, shrewd and witty) contribute to the description of a common quality, generally referred to as intellect, intelligence or mental alertness. Discounted is therefore the odd one out, because it has an entirely different meaning to all of the other words. The correct answer, therefore, is number 3.

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CRITICAL REASONING questions This type of question is made up of two parts: the first part describes a situation that our protagonist believes to be true. The second part provides additional information (highlighted by the symbol Å). In answering these questions, the last piece of information given must be carefully considered in order to determine what effect it might have on our protagonist's belief. The new information might confirm the protagonist's belief beyond any doubt, it might go completely against the protagonist's belief and therefore contradict it, or it might have no effect at all on the protagonist's belief because the information provides no concrete evidence to confirm or contradict it.

Only three answer options are given for this type of question: 1 the new information confirms their belief; 2 the new information goes against their belief; 3 the new information does not influence their belief.

9. Marianna believes that very soon she will be given a pay rise. Å Marianna's company chief has very often complimented her for her reliability and punctuality.

Answer Despite Marianna having been shown respect and appreciation, this is not enough to conclude that her positive attitude will, besides verbally, also be rewarded economically, i.e. with a pay rise. The new information does not give her enough evidence to draw firm conclusions and it is therefore likely that Marianna's belief will not be affected; i.e. it will be neither confirmed nor contradicted. The correct answer, therefore, is 3.

10. Andrea believes that his colleague Marianna is better than him with the computer. Å Whenever Andrea has had a serious problem with the computer, he has asked Marianna for help. She has always

helped to solve the problem, whether it be hardware related or software related. Answer In this case the information highlighted by the symbol (Å) can only confirm Andrea’s belief: he is indeed convinced that

Marianna is more capable than him when it comes to using computers. The information enables us to say with certainty that, because she has solved a number of various kinds of problems for him, Marianna is more competent than Andrea. The correct answer, therefore, is 1. 11. Marianna thinks that the company she works for is about to go bankrupt. Å Marianna found out from the Managing Director that, in the last 3 years, the company has grown by 5% each year

compared to the previous year and that a 10% growth is forecast for the coming year. Answer On the one hand we have Marianna, who thinks that the company is about to go bankrupt (opinion). On the other we have an unequivocal fact: that the company is growing and is in good health. This last piece of information patently contradicts and is incompatible with Marianna's opinion. The correct answer, therefore, is 2.

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NUM MERICAL REASON NING queestions The followingg are exampless of questions that are designned to assess your y numericall reasoning skills. No advancced knowledgee of mathematics is required because b each time t the task will w be to solvee the problem primarily p throuugh reasoning and by payingg d to perform sums, these willl generally bee simple. Moree attention to thhe data you haave been givenn. Whenever yoou are required often than nott, the biggest challenge c lies in being able too read a chart or o table correcttly, understandd it and differen ntiate betweenn information thhat is critical and a informationn that is superffluous to solvin ng the problem m.

The num mber and kin nd of books soold by the on--line store Go oBooks s.r.l. during d the m month of Janu uary 2011 per books Pap Type of boook

E-b books

Sold items

%

Sold item ms

%

Fiction

45

25.7

5

3.6

Crime

28

16.0

33

23.6

Horror

10

5.7

21

15.0

History

13

7.4

44

31.4

Children’s

32

18.3

17

12.1

Manuals

24

13.7

10

7.1

Nonfiction

23

13.1

10

7.1

Distributtion of GoBooks s.r.l. custtomers per agge bracket (2010 data) Ag ge < 21 7% Age > 50 A 20%

Age 41-50 4 33 3%

Agee 21-30 1 15%

Agee 31-40 2 25%

Revvenues collectted by the on n-line store GoBooks G s.r.l. since its open ning Sales (in n thousands of o Euros)

* forecassted figures

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12. In January 2011, the difference between paper book sales and e-book sales, as reported by the on-line store GoBooks s.r.l., was: 35 more paper books than e-books 1 44 more paper books than e-books 2 approximately 10 more e-books than paper books 3 0 insofar as the number of paper books sold and the number of e-books sold was exactly the same 4 The question cannot be answered on the basis of the data presented here 5

Answer The table contains all the data we need to answer the question. We start by calculating the total number of paper books (45 +

28 + 10 + 13 + 32 + 24 + 23 = 175) and the total number of e-books (5 + 33 + 21 + 44 + 17 + 10 + 10 = 140) sold by the shop. Once we have these values, we can work out the difference between the two by doing a subtraction: 175 – 140 = 35. We can therefore conclude, based on the data that we have been given, that the difference between the number of paper books sold and the number of e-books sold was 35. The correct answer, therefore, is 1. 13. If we know that the on-line store GoBooks s.r.l. had 300 customers over the age of 50 in 2010, how many customers under the age of 21 did the online store GoBooks s.r.l. have in the same year? 350 1 70 2 105 3 90 4 140 5

Answer As we can see from the labels and title, the pie chart contains figures relating to the distribution of GoBooks s.r.l. customers per age bracket for the year 2010. We know from the graph that, for 2010, customers over the age of 50 made up 20% of the total. The wording of the question gives us a vital clue: the exact number of customers who fall into the 50+ age group. Given that 20% corresponds to a fifth of the total, we can calculate the total number of customers by completing the multiplication 300 ¯ 5 = 1500 customers. To answer this question, we must now calculate 7% of 1500; we start by working out what 1% is (1500/100 = 15) before multiplying this value by 7 (15 ¯ 7 = 105). In 2010, the online store GoBooks s.r.l. had 105 customers under the age of 21. The correct answer, therefore, is 3.

14. Which of the following statements is correct? Revenues collected by the on-line store GoBooks s.r.l. will certainly be higher in 2014 than in 2013 1 The store's profits fell to an all-time low in 2008 2 2006 was the best year in terms of revenue 3 The best-selling genre of books in 2009 was Horror 4 Revenue amounted to 300 Euros in 2009 5

Answer The bar graph on the previous page shows the revenue collected by the store since it opened. It also contains a revenue forecast for 2012 and 2013 (these figures are hypothetical and not based on recorded sales). It tells us that revenue collections reached an all-time high in 2006 [3]. We have no data for 2014 and the 2013 figures are only forecast revenues: we

cannot say anything about the future with total certainty [1]; likewise, we do not have any information on how many horror books were sold in 2009 [4]. Option [2] may be misleading in that it claims profit was minimal in 2008: the graph shows a drop for this year, but we must remember that the graph relates to revenue, not profit! Option [5] might trick us into making a mistake: the amounts expressed in the graph are in Euro thousands, so the revenue for 2009 amounted to300,000 Euros and not just 300 Euros. The only correct statement, therefore, is 3.

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PASSAGE COMPREHENSION questions The Undergraduate Bachelor’s Degree Courses admission’s test will also feature a series of questions designed to test your understanding of passages and ability to process the information contained therein. Be sure to read the passage carefully. Questions will immediately follow the passage. In order to answer them correctly, you will need to have absorbed the meaning of the text and the information contained therein: some of these questions are designed to assess your understanding of the information that has been clearly presented, while others will relate to the implicit meaning of parts of the passage or the passage as a whole. Carefully read the following passage: “Made-in-Italy products used to enjoy a certain prestige”... But wait, they still do! And the textile industry is pulling out flattering figures to prove it, with some increases even edging into double figures. In fact, according to “Sistema Moda Italia” estimates, turnover for 2010 was up by 11.8% compared to 2009. The industry hasn't yet reached its precrisis level, of course, but positive signs - even signs of stability – are indeed there. It’s a deep breath of fresh air after a crisis that has loomed since 2007; joblessness figures are still sometimes critical and not all businesses have grown in the same way. The industry as a whole, however, is demonstrating that a real upturn might just happen, even though nothing will ever return to how it was before the crisis. What we need is commitment and the ability to conquer new markets; we must even learn how to use a kind of “logic of retaliation”. What to do about the Chinese crowding the Italian market with jeans for just a few Euro? Why don’t we head to the East to sell our best quality textiles to the Chinese? As Michele Tronconi, Chairman of “Sistema Moda Italia”, will tell you, “there’s specific demand for Made-in-Italy products in China”.

15. According to the above passage , which of the following might be a way to support the textile industry's upturn? Sell Italian products in Italy and not abroad 1 Promote the high quality of the Italian product 2 Ban China from selling its products in Italy 3 Produce low-quality clothing at a very low price 4 None of the above is correct 5

Answer Here you must try to find the information in the text, i.e. which of the suggested upturn strategies is the one put forward by the author. The passage states “Why don’t we head to the East to sell our best quality textiles to the Chinese?” According to the author, therefore, there is a need to “promote the high quality of the Italian product”, i.e. the strategy set out in option [2]. It is also easy to see why the other options are considered wrong, either because they simply do not feature in the text [3] or are directly at odds with the overall meaning of the passage [1] and [4]. The correct answer, therefore, is 2. 16. What is the overall tone of the passage? Ironic 1 Neutral 2 Gloomy 3 Optimistic 4 Irreverent 5

Answer The idea is to grasp the overall meaning of theflattering figures”, “positive signs”, “stability”, “breath of fresh air”, “a real upturn might just happen”, etc. The correct answer, therefore, is 4.

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ENGLISH KNOWLEDGE questions Lastly, the test will include questions designed to test your knowledge of English. There will be two types of questions: the first will be a short passage about economics, followed by five statements designed to assess your understanding of what you have just read; the second will be a longer passage but with certain words (prepositions, articles, verbs, pronouns, words, etc.) removed. The task here will be to choose the word from the list of options that best completes the passage. Carefully read the following passage: RyanAir’s Michael O’Leary, the king of low-cost travel, may be unhappy about his recent decision to move some of his operations from France to Spain: a Spanish court has declared he has no right to force customers to print their own boarding passes. A judge in Barcelona said that, under international air travel conventions, RyanAir can neither demand passengers turn up at the airport with their boarding pass, nor make them pay €40 (£34) if they do not. (The Guardian)

17. Why can RyanAir not force customers to print their own boarding passes? It’s a Spanish law 1 All customers do not have printers 2 The customers will be unhappy 3 It is against international air travel conventions 4 A judge in Barcelona does not like RyanAir 5 Answer The correct answer is 4 because, according to international conventions, RyanAir can neither force customers to print out their boarding pass nor make them pay if they do not.

Consider the passage below, parts of which must be completed when answering questions 18 and 19. A: What’s your name? B: Sylvan Carmichael. A: Could you (18)___________ that, please? B: Sure. S-Y-L-V-A-N, new word, C-A-R-M-I-C-H-A-E-L. A: Where do you work? B: I work in Seattle. A: (19)___________ do you work for? B: I work for Citibank.

18. Select the appropriate word to complete the sentence: spell 1 spells 2 write 3 writes 4

Answer The correct answer is 1 because the person is asked how his name is written (spelled out in English).

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19. Select the appropriate word to complete the sentence what 1 where 2 for who 3 who 4 whom 5

Answer The correct answer is 4 because the question asked is "Who do you work for?”. Because for is placed at the end of the sentence, the question must start with who. The other alternatives are meaningless and therefore completely wrong.

© Giunti O.S. and Università Bocconi, 2011

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