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Domanda 1 di 20
1. Domanda
In answering the next question consider the following passage.
“One relevant aspect is that concerning stock options: while in the AngloSaxon world they are still the largest source of profit for top managers of companies, in Italy the impact due to the use of stock option plans is definitely limited. In fact, consider that in the twoyear period 20122013, only 43 companies (accounting for 20.98% of the issuers analyzed here) issued option plans for their top managers. Considering instead the directors who used this tool to have extra compensation, only 15 (7.32 percent of the sample) CEOs actually exercised at least some of the options in their possession, averaging 1,014,364 options.”
The tone taken by the author in comparisons of the use of stock options in Italy tends to be:
Corretto
Solution: A. The author, in describing the adoption of stock options for managers of Italian companies, appears to have a critical tone as evidenced by the use of the following expressions: ‘definitely limited’, ‘only 43 companies’, ‘only 15’. The article does not have an investigative tone, but it does not appear to be completely descriptive or analytical, as it as it inserts judgments/expressions of merit within the passage.
Non corretto
Solution: A. The author, in describing the adoption of stock options for managers of Italian companies, appears to have a critical tone as evidenced by the use of the following expressions: ‘definitely limited’, ‘only 43 companies’, ‘only 15’. The article does not have an investigative tone, but it does not appear to be completely descriptive or analytical, as it as it inserts judgments/expressions of merit within the passage.
Risposta non fornita
Solution: A. The author, in describing the adoption of stock options for managers of Italian companies, appears to have a critical tone as evidenced by the use of the following expressions: ‘definitely limited’, ‘only 43 companies’, ‘only 15’. The article does not have an investigative tone, but it does not appear to be completely descriptive or analytical, as it as it inserts judgments/expressions of merit within the passage.

Domanda 2 di 20
2. Domanda
Knowing that the arc of a circular sector measures 8π and that its area is equal to 4/9 of the full circle, how large is the area of the circle?
Corretto
Solution: C. If the circular sector corresponds to 4/9 of the entire circumference, then the circumference measures 2πr = 8π x (9/4) = 18π, from which r = 9. The area of the circle being equal to πr^{2} = 81π (answer C).
Non corretto
Solution: C. If the circular sector corresponds to 4/9 of the entire circumference, then the circumference measures 2πr = 8π x (9/4) = 18π, from which r = 9. The area of the circle being equal to πr^{2} = 81π (answer C).
Risposta non fornita
Solution: C. If the circular sector corresponds to 4/9 of the entire circumference, then the circumference measures 2πr = 8π x (9/4) = 18π, from which r = 9. The area of the circle being equal to πr^{2} = 81π (answer C).

Domanda 3 di 20
3. Domanda
How many pairs of positive integers (m,n) are there such that m^{n} = 6^{4} ?
Corretto
Solution: C. We see that 6^{4} can also be rewritten as 36^{2} = 1296. The pairs of numbers are therefore 3 (answer C).
Non corretto
Solution: C. We see that 6^{4} can also be rewritten as 36^{2} = 1296. The pairs of numbers are therefore 3 (answer C).
Risposta non fornita
Solution: C. We see that 6^{4} can also be rewritten as 36^{2} = 1296. The pairs of numbers are therefore 3 (answer C).

Domanda 4 di 20
4. Domanda
In answering the next question, consider the following passage.
“It was decided to limit the location of the target companies of the survey to the area of Northern Italy, which was considered representative of the national system. As a methodology of survey, it was appropriate to use a multiplechoice questionnaire to be submitted to companies through phone interviews.
The reference sample was selected from the AIDA database produced by the Bureau Van Dijk Publishing, which contains information from more than 200,000 corporations operating in Italy. The empirical survey involved 207 companies out of an initial sample of 676 attesting to an overall response rate of 31 percent.”Which of the following tools/methods is not mentioned in the text?
Corretto
Solution : C. Since it is a telephone interview, the web questionnaire is not cited by the author.
Non corretto
Solution : C. Since it is a telephone interview, the web questionnaire is not cited by the author.
Risposta non fornita
Solution : C. Since it is a telephone interview, the web questionnaire is not cited by the author.

Domanda 5 di 20
5. Domanda
Let A, B and C be three sets of the setuniverse U, let us denote by A^{c}, B^{c} and C^{c} their complements. Which of the following is the set of elements that belong to A but not to B and/or C?
Corretto
Solution: B. To find the set of elements that belong to A but not to B and/or C, it is first necessary to find the elements that belong to B or C, that is to say B∪C. The elements that do not belong to them is (B∪C)^{c}, that is, its complement. Of this set, not all elements belong to A, so to find the elements only belonging to A, we have to make their intersection, i.e. A∩(B∪C)^{c} (answer B).
Non corretto
Solution: B. To find the set of elements that belong to A but not to B and/or C, it is first necessary to find the elements that belong to B or C, that is to say B∪C. The elements that do not belong to them is (B∪C)^{c}, that is, its complement. Of this set, not all elements belong to A, so to find the elements only belonging to A, we have to make their intersection, i.e. A∩(B∪C)^{c} (answer B).
Risposta non fornita
Solution: B. To find the set of elements that belong to A but not to B and/or C, it is first necessary to find the elements that belong to B or C, that is to say B∪C. The elements that do not belong to them is (B∪C)^{c}, that is, its complement. Of this set, not all elements belong to A, so to find the elements only belonging to A, we have to make their intersection, i.e. A∩(B∪C)^{c} (answer B).

Domanda 6 di 20
6. Domanda
In a test, 1 point is assigned for each answer not given, 3 points are assigned for each incorrect answer, and 3 points for each correct answer.
Knowing that there are 10 questions, what scores strictly above 25 are possible?
Corretto
Solution: D. Let’s study the possible combinations, starting with the one with the highest score. If I get 10 correct answers, I will take 3 x 10 = 30. The second more positive situation is one in which I get 9 correct answers and one not given. In that case the score is 3 x 9 + (1) x 1 = 271 = 26. From here we deduce that the scores 27 to 29 can never be obtained. Hence answer D.
Non corretto
Solution: D. Let’s study the possible combinations, starting with the one with the highest score. If I get 10 correct answers, I will take 3 x 10 = 30. The second more positive situation is one in which I get 9 correct answers and one not given. In that case the score is 3 x 9 + (1) x 1 = 271 = 26. From here we deduce that the scores 27 to 29 can never be obtained. Hence answer D.
Risposta non fornita
Solution: D. Let’s study the possible combinations, starting with the one with the highest score. If I get 10 correct answers, I will take 3 x 10 = 30. The second more positive situation is one in which I get 9 correct answers and one not given. In that case the score is 3 x 9 + (1) x 1 = 271 = 26. From here we deduce that the scores 27 to 29 can never be obtained. Hence answer D.

Domanda 7 di 20
7. Domanda
In answering the next question consider the following passage.
“The State, as asset manager, is failing to achieve appreciable results. Currently, its management absorbs double the resources it is able to earn. As mentioned above, the exact amount of assets is not known. “The Newspaper” speculates that a conservative estimate, including buildings of the central government, those of local authorities and those of public bodies, would be 500 billion euros, although 80 percent of them are owned by local governments, which have no interest in following general lines. Instead, they prefer to manage this lot independently. The way forward could be to entrust an important role to the State Property Agency by involving major investors and banks to achieve what is expected.”
How much of the state’s real estate assets are not in local government hands, according to the text?
Corretto
Solution: D. The text mentions that state real estate is worth about 500 billion of which 80% is in the hands of local governments. 20% consequently is not in the hands of local governments and this corresponds to 500 x 20% = 100 billion (answer D).
Non corretto
Solution: D. The text mentions that state real estate is worth about 500 billion of which 80% is in the hands of local governments. 20% consequently is not in the hands of local governments and this corresponds to 500 x 20% = 100 billion (answer D).
Risposta non fornita
Solution: D. The text mentions that state real estate is worth about 500 billion of which 80% is in the hands of local governments. 20% consequently is not in the hands of local governments and this corresponds to 500 x 20% = 100 billion (answer D).

Domanda 8 di 20
8. Domanda
The following figure shows the graph of the function f(x) in a certain interval. How many real solutions does the equation f(x) = 5 admit in that interval?
Corretto
Solution: D. Imagine cutting with a line parallel to the xaxis and passing through y=5, we see that the line meets the function in three points, there are therefore three solutions (answer D).
Non corretto
Solution: D. Imagine cutting with a line parallel to the xaxis and passing through y=5, we see that the line meets the function in three points, there are therefore three solutions (answer D).
Risposta non fornita
Solution: D. Imagine cutting with a line parallel to the xaxis and passing through y=5, we see that the line meets the function in three points, there are therefore three solutions (answer D).

Domanda 9 di 20
9. Domanda
Adele has a collection of stamps; she knows she has a little less than 100, but certainly at least 30. She arranges them in rows of 7 and has 1 stamp left over; then she arranges them in rows of 10 and this time she has 2 stamps left over.
How many stamps does she have in total?
Corretto
Solution: A. From the information we have, we know that the number of stamps is between 30 and 100, dividing by 7 gives a remainder of 1 and dividing by 10 gives a remainder of 2. Knowing that dividing it by 10 will give a remainder of 2, it means that the number of units is equal to 2.
Among the proposed solutions ending with 2 are 32, 62 and 92. Let’s see which among these numbers divided by 7 gives remainder 1. 32:7 = 4 with remainder of 4, 62:7 = 8 with remainder of 6, 92:7 = 13 with remainder of 1. From which, we deduce the answer A.Non corretto
Solution: A. From the information we have, we know that the number of stamps is between 30 and 100, dividing by 7 gives a remainder of 1 and dividing by 10 gives a remainder of 2. Knowing that dividing it by 10 will give a remainder of 2, it means that the number of units is equal to 2.
Among the proposed solutions ending with 2 are 32, 62 and 92. Let’s see which among these numbers divided by 7 gives remainder 1. 32:7 = 4 with remainder of 4, 62:7 = 8 with remainder of 6, 92:7 = 13 with remainder of 1. From which, we deduce the answer A.Risposta non fornita
Solution: A. From the information we have, we know that the number of stamps is between 30 and 100, dividing by 7 gives a remainder of 1 and dividing by 10 gives a remainder of 2. Knowing that dividing it by 10 will give a remainder of 2, it means that the number of units is equal to 2.
Among the proposed solutions ending with 2 are 32, 62 and 92. Let’s see which among these numbers divided by 7 gives remainder 1. 32:7 = 4 with remainder of 4, 62:7 = 8 with remainder of 6, 92:7 = 13 with remainder of 1. From which, we deduce the answer A. 
Domanda 10 di 20
10. Domanda
In answering the next question consider the following passage.
“As seen, takeorpay contracts are indexed to the price of oil and its derivatives, these have the function of “underlying”; this means that it does not reflect the correct supply and demand trends in the real gas market, but is instead influenced by the volatility and contingencies of oil dynamics. An efficient market with a good level of flexibility and thus liquidity would overcome all these limitations; the liquidity would then be traded on a spot at the relevant hub.”
What does the term “volatility” mean, as used in the text?
Corretto
Solution: A. The term “volatility” means, in the text, the variability (i.e., the amplitude of fluctuations) in the oil price. Trend and tendency do not describe variability but the slope of the oil price over a certain period.
Non corretto
Solution: A. The term “volatility” means, in the text, the variability (i.e., the amplitude of fluctuations) in the oil price. Trend and tendency do not describe variability but the slope of the oil price over a certain period.
Risposta non fornita
Solution: A. The term “volatility” means, in the text, the variability (i.e., the amplitude of fluctuations) in the oil price. Trend and tendency do not describe variability but the slope of the oil price over a certain period.

Domanda 11 di 20
11. Domanda
To answer the question consider the following data:
“The Central Bank prints only 10, 30 and 50cent coins.”
Carlo paid 90 cents using at least two coins of equal value.
How many coins did Carlo use?
Corretto
Solution: E. Marco will be able to pay 90 cents using one of the following options: (1) pay with nine 10cent coins, (2) pay with one 50cent coin and four 10cent coins, (3) pay with one 30cent coin and six 10cent coins, (4) pay with two 30cent coins and three 10cent coins, and (5) pay with three 30cent coins. All these solutions are acceptable and lead to 9, 5, 7, 5 and 3 coins respectively. Therefore, all the answers are possible solutions (answer E).
Non corretto
Solution: E. Marco will be able to pay 90 cents using one of the following options: (1) pay with nine 10cent coins, (2) pay with one 50cent coin and four 10cent coins, (3) pay with one 30cent coin and six 10cent coins, (4) pay with two 30cent coins and three 10cent coins, and (5) pay with three 30cent coins. All these solutions are acceptable and lead to 9, 5, 7, 5 and 3 coins respectively. Therefore, all the answers are possible solutions (answer E).
Risposta non fornita
Solution: E. Marco will be able to pay 90 cents using one of the following options: (1) pay with nine 10cent coins, (2) pay with one 50cent coin and four 10cent coins, (3) pay with one 30cent coin and six 10cent coins, (4) pay with two 30cent coins and three 10cent coins, and (5) pay with three 30cent coins. All these solutions are acceptable and lead to 9, 5, 7, 5 and 3 coins respectively. Therefore, all the answers are possible solutions (answer E).

Domanda 12 di 20
12. Domanda
At what speed should I go as a minimum to travel 30 km in less than 40 minutes?
Corretto
Solution: A. 40 minutes corresponds to 2/3 of an hour (40 minutes divided by 60 minutes per hour). To travel 30 km in 40 minutes then I must travel at a speed of 30/(2/3) = 30 x 3/2 = 45 km/h (answer A).
Non corretto
Solution: A. 40 minutes corresponds to 2/3 of an hour (40 minutes divided by 60 minutes per hour). To travel 30 km in 40 minutes then I must travel at a speed of 30/(2/3) = 30 x 3/2 = 45 km/h (answer A).
Risposta non fornita
Solution: A. 40 minutes corresponds to 2/3 of an hour (40 minutes divided by 60 minutes per hour). To travel 30 km in 40 minutes then I must travel at a speed of 30/(2/3) = 30 x 3/2 = 45 km/h (answer A).

Domanda 13 di 20
13. Domanda
In answering the next question, consider the following passage.
“Analyzing how the Italian banking sector is responding to the crisis, it can be noticed that since the onset of the financial crisis in 2008, the number of Italian banking branches has decreased by about 4,000 units, at an annual rate of 1.7 percent. Before that date, banks believed that in order to be more competitive, it was necessary to increase the penetration of branches in the cities. That was perceived as the optimal strategy to better serve the existing customers and to acquire new ones, thanks to the marketing of the capillary branches. The turnaround began in 2008 starting with the largest banks, but quickly affecting smaller ones as well.”
How did Italian banks respond to the 2008 crisis, according to the text?
Corretto
Solution: C. As the text quotes, “the number of Italian banking branches decreased by about 4,000 units.” So banks have decreased the number of branches as a result of the crisis. We can infer from the following sentence that increasing the number of branches in cities corresponds to increasing territorial penetration in cities. Conversely, reducing the number of branches reduces the penetration. The correct answer is C.
Non corretto
Solution: C. As the text quotes, “the number of Italian banking branches decreased by about 4,000 units.” So banks have decreased the number of branches as a result of the crisis. We can infer from the following sentence that increasing the number of branches in cities corresponds to increasing territorial penetration in cities. Conversely, reducing the number of branches reduces the penetration. The correct answer is C.
Risposta non fornita
Solution: C. As the text quotes, “the number of Italian banking branches decreased by about 4,000 units.” So banks have decreased the number of branches as a result of the crisis. We can infer from the following sentence that increasing the number of branches in cities corresponds to increasing territorial penetration in cities. Conversely, reducing the number of branches reduces the penetration. The correct answer is C.

Domanda 14 di 20
14. Domanda
The following figure shows the volume of transactions in millions of euros by payment method, in four Italian macroregions.
Which of the following statements is true?
Corretto
Solution: E.
Let’s evaluate each answer separately:
Answer A is false because it is the bank check that has the highest transaction volumes (54 > 40)
Answer B is false in that the volume of bank check transactions in Central Italy is 32 million while the total with this method of payment is 108. We can quickly verify that 32 is less than half of 108.
Answer C is false in that it is the Islands that have the lowest volume of transactions (49 < 65).
Answer D is false since the payment method with the highest transaction volume is credit cards (111 > 108).
Therefore, answer E is the true one.
Non corretto
Solution: E.
Let’s evaluate each answer separately:
Answer A is false because it is the bank check that has the highest transaction volumes (54 > 40)
Answer B is false in that the volume of bank check transactions in Central Italy is 32 million while the total with this method of payment is 108. We can quickly verify that 32 is less than half of 108.
Answer C is false in that it is the Islands that have the lowest volume of transactions (49 < 65).
Answer D is false since the payment method with the highest transaction volume is credit cards (111 > 108).
Therefore, answer E is the true one.
Risposta non fornita
Solution: E.
Let’s evaluate each answer separately:
Answer A is false because it is the bank check that has the highest transaction volumes (54 > 40)
Answer B is false in that the volume of bank check transactions in Central Italy is 32 million while the total with this method of payment is 108. We can quickly verify that 32 is less than half of 108.
Answer C is false in that it is the Islands that have the lowest volume of transactions (49 < 65).
Answer D is false since the payment method with the highest transaction volume is credit cards (111 > 108).
Therefore, answer E is the true one.

Domanda 15 di 20
15. Domanda
For which of the following angles does the cosine function take negative values?
Corretto
Solution: B. Remember that the cosine function takes negative values in the second and third quadrants. The angles shown are not known angles, so it is necessary to transform them into degrees in order to place them in the Cartesian plane. In order to transform an angle from degrees to radians (or vice versa) it is necessary to impose the following proportion: angle_{degrees} : 180° = angle_{radians} : π. By doing so, the solutions shown correspond to 51.42°, 108°, 405°, 40° and 43.33°, respectively. Note that answer C answer reports an angle greater than 360°. In that case we have just to subtract 360° from the angle to easily place it. Doing so results in an angle of 45°. The only angle contained in the second or third quadrant is the second (answer B).
Non corretto
Solution: B. Remember that the cosine function takes negative values in the second and third quadrants. The angles shown are not known angles, so it is necessary to transform them into degrees in order to place them in the Cartesian plane. In order to transform an angle from degrees to radians (or vice versa) it is necessary to impose the following proportion: angle_{degrees} : 180° = angle_{radians} : π. By doing so, the solutions shown correspond to 51.42°, 108°, 405°, 40° and 43.33°, respectively. Note that answer C answer reports an angle greater than 360°. In that case we have just to subtract 360° from the angle to easily place it. Doing so results in an angle of 45°. The only angle contained in the second or third quadrant is the second (answer B).
Risposta non fornita
Solution: B. Remember that the cosine function takes negative values in the second and third quadrants. The angles shown are not known angles, so it is necessary to transform them into degrees in order to place them in the Cartesian plane. In order to transform an angle from degrees to radians (or vice versa) it is necessary to impose the following proportion: angle_{degrees} : 180° = angle_{radians} : π. By doing so, the solutions shown correspond to 51.42°, 108°, 405°, 40° and 43.33°, respectively. Note that answer C answer reports an angle greater than 360°. In that case we have just to subtract 360° from the angle to easily place it. Doing so results in an angle of 45°. The only angle contained in the second or third quadrant is the second (answer B).

Domanda 16 di 20
16. Domanda
a, b and c are real numbers such that however two are chosen their sum is greater than or equal to zero.
Which of the following statements is certainly true?
Corretto
Solution: E. Consider the following two cases (triplets of numbers) a = 1, b = 2, c=3 and a = 1, b = 2, c=3. Both of these combinations of numbers satisfy the condition that ” however two are chosen their sum is greater than or equal to zero.” Evaluate each of the answers:
The first is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true. The second is false in that it is not necessary for one of the 3 numbers to be zero.
The third is true for the second triplet, but not for the first, so it is not forcibly true.
The fourth is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true.
We are left with only the fifth. By proving it, we see that both the triplets satisfy the condition and is therefore forcibly true.
Non corretto
Solution: E. Consider the following two cases (triplets of numbers) a = 1, b = 2, c=3 and a = 1, b = 2, c=3. Both of these combinations of numbers satisfy the condition that ” however two are chosen their sum is greater than or equal to zero.” Evaluate each of the answers:
The first is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true. The second is false in that it is not necessary for one of the 3 numbers to be zero.
The third is true for the second triplet, but not for the first, so it is not forcibly true.
The fourth is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true.
We are left with only the fifth. By proving it, we see that both the triplets satisfy the condition and is therefore forcibly true.
Risposta non fornita
Solution: E. Consider the following two cases (triplets of numbers) a = 1, b = 2, c=3 and a = 1, b = 2, c=3. Both of these combinations of numbers satisfy the condition that ” however two are chosen their sum is greater than or equal to zero.” Evaluate each of the answers:
The first is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true. The second is false in that it is not necessary for one of the 3 numbers to be zero.
The third is true for the second triplet, but not for the first, so it is not forcibly true.
The fourth is false, although it holds for the first triplet, it does not hold for the second, so it is not forcibly true.
We are left with only the fifth. By proving it, we see that both the triplets satisfy the condition and is therefore forcibly true.

Domanda 17 di 20
17. Domanda
The figure below shows the number of customers who visited 4 post offices in a certain city on the six working days.
Which of the following statements is true?
Corretto
Solution: E. Let’s evaluate each of the answers. Answer A is false in that the day with the fewest customers for office D is Friday and not Monday.
Answer B is false because the peak day (i.e., with the most customers) is Saturday.
Answer C is false because the number of customers falls between Tuesday and Wednesday, so it is not monotonically increasing. Answer D is false because the number of customers increases between Friday and Saturday, so it is not monotonically decreasing.
None of the answers above is true (answer E).
Non corretto
Solution: E. Let’s evaluate each of the answers. Answer A is false in that the day with the fewest customers for office D is Friday and not Monday.
Answer B is false because the peak day (i.e., with the most customers) is Saturday.
Answer C is false because the number of customers falls between Tuesday and Wednesday, so it is not monotonically increasing. Answer D is false because the number of customers increases between Friday and Saturday, so it is not monotonically decreasing.
None of the answers above is true (answer E).
Risposta non fornita
Solution: E. Let’s evaluate each of the answers. Answer A is false in that the day with the fewest customers for office D is Friday and not Monday.
Answer B is false because the peak day (i.e., with the most customers) is Saturday.
Answer C is false because the number of customers falls between Tuesday and Wednesday, so it is not monotonically increasing. Answer D is false because the number of customers increases between Friday and Saturday, so it is not monotonically decreasing.
None of the answers above is true (answer E).

Domanda 18 di 20
18. Domanda
Marco got three grades. The average of the three grades is 7 and the mode is 8, how much is the smallest number worth?
Corretto
Solution: A. Recall that the mode is the number that appears most often. Since there are three numbers, whose average gives 7, and with mode 8, we can guess that there are 2 grades equal to 8. Now, we need to find the third grade: we know that by adding the grades and dividing them by 3, we should get 7 (i.e., the average). By imposing the equation, we have (x+8+8)/3 = 7, from which x+16 = 21, x=5. The lowest grade is therefore 5 (answer A).
Non corretto
Solution: A. Recall that the mode is the number that appears most often. Since there are three numbers, whose average gives 7, and with mode 8, we can guess that there are 2 grades equal to 8. Now, we need to find the third grade: we know that by adding the grades and dividing them by 3, we should get 7 (i.e., the average). By imposing the equation, we have (x+8+8)/3 = 7, from which x+16 = 21, x=5. The lowest grade is therefore 5 (answer A).
Risposta non fornita
Solution: A. Recall that the mode is the number that appears most often. Since there are three numbers, whose average gives 7, and with mode 8, we can guess that there are 2 grades equal to 8. Now, we need to find the third grade: we know that by adding the grades and dividing them by 3, we should get 7 (i.e., the average). By imposing the equation, we have (x+8+8)/3 = 7, from which x+16 = 21, x=5. The lowest grade is therefore 5 (answer A).

Domanda 19 di 20
19. Domanda
Read the following data and propositions carefully and answer the next question
DATA
PROPOSITIONS
Andrea is older than Caterina Dario is older than Elena
Caterina is younger than Giulia
Giulia is younger than Elena
A. Caterina is older than Dario
B. Andrea is younger than Caterina
C. Caterina is younger than Elena
D. Dario is younger than Andrea
Based on the above data, which proposition(s) is/are necessarily true?
Corretto
Solution: C. We denote for brevity the ages of Andrea, Caterina, Dario, Elena and Giulia by A, C, D, E and G. From the four sentences we can deduce that A > C, D > E, G > C, E > G. From which we infer that D > E > G > C. We cannot establish relations between A and D/E/G, but only with C (A > C).
Proposition A is false, since D > E > G > C and therefore D > C. Proposition B is false in that A > C. Proposition C is true in that D > E > G > C, and therefore E > C. Proposition D is indeterminate in that we cannot make connections between A and D. Consequently, the correct answer is C.
Non corretto
Solution: C. We denote for brevity the ages of Andrea, Caterina, Dario, Elena and Giulia by A, C, D, E and G. From the four sentences we can deduce that A > C, D > E, G > C, E > G. From which we infer that D > E > G > C. We cannot establish relations between A and D/E/G, but only with C (A > C).
Proposition A is false, since D > E > G > C and therefore D > C. Proposition B is false in that A > C. Proposition C is true in that D > E > G > C, and therefore E > C. Proposition D is indeterminate in that we cannot make connections between A and D. Consequently, the correct answer is C.
Risposta non fornita
Solution: C. We denote for brevity the ages of Andrea, Caterina, Dario, Elena and Giulia by A, C, D, E and G. From the four sentences we can deduce that A > C, D > E, G > C, E > G. From which we infer that D > E > G > C. We cannot establish relations between A and D/E/G, but only with C (A > C).
Proposition A is false, since D > E > G > C and therefore D > C. Proposition B is false in that A > C. Proposition C is true in that D > E > G > C, and therefore E > C. Proposition D is indeterminate in that we cannot make connections between A and D. Consequently, the correct answer is C.

Domanda 20 di 20
20. Domanda
Five friends exchange key chains, so that each of them has a different one from the one they had before.
How many (different) ways can they exchange them?
Corretto
Solution: E. Consider the possibilities: the first one will be able to give it to 4 people. The one who received the first one will be able to give his to one of the other 4 people. The third one, viz. the one who received the second keychain, will be able to give his to one of the three people left without an assigned keychain. The two remaining people will have to forcibly exchange key chains, so each of the two will have only one chance.
The number of possible ways is therefore 4x4x3x1 = 48 (answer E).
Non corretto
Solution: E. Consider the possibilities: the first one will be able to give it to 4 people. The one who received the first one will be able to give his to one of the other 4 people. The third one, viz. the one who received the second keychain, will be able to give his to one of the three people left without an assigned keychain. The two remaining people will have to forcibly exchange key chains, so each of the two will have only one chance.
The number of possible ways is therefore 4x4x3x1 = 48 (answer E).
Risposta non fornita
Solution: E. Consider the possibilities: the first one will be able to give it to 4 people. The one who received the first one will be able to give his to one of the other 4 people. The third one, viz. the one who received the second keychain, will be able to give his to one of the three people left without an assigned keychain. The two remaining people will have to forcibly exchange key chains, so each of the two will have only one chance.
The number of possible ways is therefore 4x4x3x1 = 48 (answer E).