ECUR-E15
CA’ FOSCARI UNIVERSITY OF VENICE
Degree in Business Administration - Economics and
Management (curriculum Economics and Management)
UNIVERSITY OF TRIESTE
Degree in Economics, International Trade and Financial
Markets (curriculum in Economics of Financial and Insurance
Markets and Economics and Management of Innovation)
QUESTIONNAIRE
DO NOT OPEN
the plastic envelope until you are told
the test is starting
1
2
PROVA P00000
1.
Mario left his house and walked towards Enrico's house, 48 km away. Two hours later, Enrico left his house and
ran towards Mario's house. If Mario's speed was 4 km per hour and Enrico's 6 km per hour, how many km had
Mario walked when he met Enrico?
A.
8
B.
11
C.
22
●D. 24
2.
Six people travel for work during the first six months of the year. Knowing that:
- each person leaves on a different month;
- Silvano leaves in January;
- Paolo leaves after Luigi and Carlo;
- Luigi and Carlo leave on two consecutive months (not necessarily in that order);
- Mario and Dario will not leave on two consecutive months;
which is the latest month for Carlo to leave?
A.
May
●B. April
C.
June
D.
February
3.
A 20m high pole projects a 5m shadow. If, at the same time of the day, a building projects a 20m shadow, how
high is the building?
A.
4m
B.
400m
C.
100m
●D. 80m
4.
The sum of 200 consecutive natural numbers, the first of which is 200, equals to:
A.
19900
●B. 59900
C.
39900
D.
80200
5.
A.
●B.
C.
D.
6.
Three clocks chime as follows: the first every 3 hours, the second every 4 hours and the third every 5 hours.
Today, Tuesday, they will chime contemporarily at 16:00 Hrs.
When and at what time will they chime again at the same time?
A.
Thursday, at 04:00
B.
Friday, at 12:00
C.
Wednesday, at 16:00
●D. Friday, at 04:00
7.
Say which of the numbers below is the next in the sequence 10, 11, 13, 16 …
A.
17
B.
18
C.
19
●D. 20
8.
At the nearest “Do-it-yourself” shop you buy 1432 m of a metallic net to outline the straight boundary of a field.
Every 4 m you need to place also support poles. How many poles do you need to purchase?
A.
360
B.
358
C.
356
●D. 359
ECUR-E15 - Prova P00000
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9.
Two oil cans have a total capacity of 19 litres. The biggest contains three times more oil than the smaller plus one
litre. How many litres does each can contain?
A.
14 and 6
B.
12 and 7
C.
14 and 5
●D. 14.5 and 4.5
10. In Italy, the average grade in the first level degree in Engineering is 98.1/110, while the average grade of exams
is 24.6/30. Knowing that the difference between the degree grade and the average grade, is equal to the value
(in scale 1/110) of the thesis, which is the average value of the thesis?
A.
79
B.
26.75
C.
2.15
●D. 7.9
11. In a class, 10 students play football, 10 play basketball and 10 swim. Of those, only one plays all three sports
while the others play only one. By how many students is the class composed?
A.
30
B.
29
●C. 28
D.
27
12. A car importer is planning on increasing the price of a specific model by 1,000€. At this new price 5 fewer cars per
month will be sold, but the total revenues will rise by 26,000€, amounting to a total of 594,000€. What is the
number of cars the manufacturer would sell at this new price?
A.
51
B.
61
●C. 66
D.
71
13. If a + b = 55 and a * b = 666, then:
●A. a − b = 19
B.
a + b = 54
C.
a = 12
D.
a/b = 2
14. Of the answers given to a questionnaire, 8 are wrong and 80% are exact. How many questions does the
questionnaire contain?
A.
160
B.
72
C.
48
●D. 40
15. The SPAR supermarket offers to all customers a 10% discount on listed prices, plus a further 5% discount if the
sum exceeds 100 euros. Hence, for a 200 euros total, a customer pays:
●A. 171 euro
B.
180 euro
C.
170 euro
D.
169 euro
16. A capital sum of 400,000 Euro, deposited in a bank, is subject to a 4% annual interest rate. What is its future
value in one year time?
A.
404,000 Euro
B.
440,000 Euro
●C. 416,000 Euro
D.
1,600,000 Euro
17. The sum of two consecutive integer numbers is 127. They may be:
A.
62, 65
B.
64, 65
C.
100, 27
●D. 63, 64
ECUR-E15 - Prova P00000
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18. An admission exam consists of two tests: 2/3 of the candidates pass the first test and only 1/6 of these pass also
the second. Of 180 candidates, how many are admitted?
A.
40
B.
30
C.
120
●D. 20
19. “All bicycles have two wheels. Marc’s vehicle has two wheels”. What CANNOT be derived from the previous
statements?
●A. Marc has a bicycle
B.
Marc does not have a car
C.
If Marc has a bicycle, then it has two wheels
D.
Marc’s vehicle might be a bicycle
20. You may choose between Option 1: receive 100 euro today and invest them at 11% annual interest rate for one
year; Option 2: receive 110 in one year. What is preferable?
A.
Options 1 and 2 are indifferent
●B. Option 1 is preferable
C.
Option 2 is preferable
D.
The question cannot be answered
21. In a class of 40 students, 12 enrolled for both Italian and Greek. 22 enrolled for Greek. If the students of the class
enrolled for at least one subject (Italian or Greek), how many students enrolled for only Italian and not Greek?
A.
16
B.
30
C.
20
●D. 18
22. If A is the set of the prime numbers between 1 and 10 and B is the set of the odd numbers between 1 and 10,
which of the following statements is true?
A.
AÍB
●B. A Ç B = {1,3,5,7}
C.
A= B
D.
A È B = {1,3,5,7}
23.
●A.
B.
C.
D.
all other sentences are false
24. Given the sets A, B, C we know that A and C have no elements in common and that A is contained in B. Which of
the following deductions is true in general?
A.
B and C have no elements in common
B.
The elements of B not in A are contained in C
C.
B and C have nonempty intersection
●D. B and C may have empty intersection or not
25. If a is a positive integer and the square of a is divisible by 72, then it is certainly true that a is divisible by:
A.
72
●B. 12
C.
24
D.
36
26. Assuming that x equals the product of integers from 1 to 9, exclusive. The number of different prime factors of x
larger than 1 is:
A.
3
●B. 4
C.
5
D.
7
ECUR-E15 - Prova P00000
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27. Select the answer in which the following numbers appear in ascending order:
A.
●B.
C.
D.
28. Calculate the least common multiple of the following numbers 15, 27 e 45.
A.
75
●B. 135
C.
45
D.
3
29. What is the result of (15/4) : (3/64)?
A.
45/256
B.
5/64
●C. 80
D.
5/12
30. The number 1250 is divisible:
●A. by 2 and by 5
B.
by 11 and by 18
C.
by 5 and by 13
D.
by 3 and by 4
31. Which is the value of x satisfying 7 : 3 = x : (x + 2) ?
●A. −7/2
B.
3/7
C.
−6/7
D.
−14/3
32. Determine the degree of the polynomial 2a2 + a3x4 + x5 + 9.
●A. 7
B.
6
C.
4
D.
5
33. Simplify the expression [− 48x + 30x − 2(2x − 7x − 3x)]:2.
●A. −x
B.
21x
C.
−21x
D.
x
34. If 6n is an integer factor of (10!)2, the largest possible value of n is:
A.
2
B.
6
●C. 8
D.
24
35. If ab+c = a(b+c), which of the following must be true?
●A. a=1 or c=0
B.
a=0 and b=0
C.
a=1 and b=1
D.
b=1 and c=0
36. The solution of the equation 3x−6(1−2x)=45−3x is:
●A. 17/6
B.
15/3
C.
19/3
D.
5/6
ECUR-E15 - Prova P00000
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37. The equation (x− 3)/(x− 2) = 7 has solutions:
A.
3
B.
2 and 3
●C. 11/6
D.
it has no solutions
38. The solutions of the equation x4+4x2−21=0 are:
●A. −
,
B.
− 3, 3
C.
± 3, ± 3
D.
− 2, 1
39. The solution of the inequality 16x - x3 > 0 is:
●A. x < −4 or 0 < x < 4
B.
x < −2 or 0 < x < 2
C.
0<x<2
D.
x < −8
40. The solution of the inequality 3x2 − 4x − 7 < 0 is:
●A. − 1 < x < 7/3
B.
1/4 < x < 9/4
C.
+1 < x < + 7/3
D.
x<− 2
V
x > 1/4
41. Compute the solution of the inequality (2x − 8)/(1 − x) > 0.
●A. 1 < x < 4
B.
0<x<4
C.
2<x<4
D.
1<x<2
42.
A.
B.
C.
●D.
ECUR-E15 - Prova P00000
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43. The graphic representation of the function y = (−2x + 10)2 is:
A.
●B.
C.
D.
44. Which of the following equations represents an ellipse?
A.
y = (x -1)2
B.
y = 3x2
●C. x2 + 4y2 = 1
D.
x2 - y2 = 1
45. y-coordinates of Parabola y2 = x + 2 and circle x2 + y2 = 4 points of intersection are given by:
A.
2,−2
B.
0
●C. 0 ,
D.
,−
1 , 2 , -1
ECUR-E15 - Prova P00000
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10
11
12
ECUR-14
CA’ FOSCARI UNIVERSITY OF VENICE
Degree in Business Administration - Economics and
Management (curriculum Economics and Management)
UNIVERSITY OF TRIESTE
Degree in Economics, International Trade and Financial
Markets (curriculum in Economics of Financial and
Insurance Markets and Economics and Management of
Innovation)
QUESTIONNAIRE
DO NOT OPEN
the plastic envelope until you are told
the test is starting
1
Prova P0001
2
Prova P0001
1.
It’s wrong to affirm that it’s not true that some cat is not four-legged.
If this sentence is true, it follows that:
X
A.
there is at least one cat that isn’t four-legged
B.
no cats are four-legged
C.
no cats aren’t four-legged
D.
there is at least one four-legged cat
2.
X
During a meeting, 10 businessmen agree that each of them will write a reference for every member of
the group who has had a higher turnover than themselves over the previous year. If none of the
businessmen had the same turnover, how many references are written?
A.
10
B.
30
C.
45
D.
55
Answer the following two questions in accordance with the table below, which provides a breakdown of spending
patterns in relation to annual family income.
3.
A family belonging to the 4th income brackets spends € 8,200 on health. What is its annual income?
A.
€ 40,000
B.
€ 42,000
C.
€ 38,000
X
D.
€ 41,000
4.
Which of the following statements is NOT true?
X
A.
All of the families in the second income bracket spend less than € 9,000 on housing.
B.
A family with an income of € 13,000 spends the same amount on food as a family with an income of € 39,000
spends on clothing.
C.
A family with an income of € 14,000 spends the same amount on food as a family with an income of € 42,000
spends on clothing.
D.
A family with an income of € 40,000 spends € 16,400 on food.
5.
X
6.
X
Which of the numbers below is related to the following?
24 42 63 18 69
A.
46
B.
78
C.
52
D.
68
Choose the alternative that is a logical equivalent of the following sentence:
Some European state is member of NATO.
A.
Most European states are not members of NATO
B.
At least one European state is a member of NATO
C.
Most European states are members of NATO
D.
At least one European state is not a member of NATO
Prova P0001
3
7.
Three friends have 80, 90 and 100 euro each. Their first names are John, Philip and Nick. Their
surnames are Smith, Bell and Collins. Given that:
Philip has less than Mr. Bell;
John has 90 euro;
Neither Nick nor Mr. Smith has 80 euro
which of the following is correct?
X
8.
A.
John Bell has 90 euro
B.
Nick Collins has 100 euro
C.
Nick Bell has 100 euro
D.
John Collins has 90 euro
Five exporters each have, respectively, a turnover of 5, 10, 15, 20 and 25 million euro. Each one only
has one office, which are found in the cities of Boston, Madrid, Amsterdam, Genoa and Frankfurt,
although not necessarily in that order. Moreover, each of them only handles one specific merchandise.
If we know that:

The coffee exporter has his office in Madrid

The corn exporter has a turnover of 10 million euro

The Boston office has a turnover of 5 million euro and deals in barley

The exporter with a 20 million euro turnover deals in cocoa and has an office in Genoa.

The Frankfurt office has a turnover of 15 million euro

One of the exporter deals in soya
which of the following statements is wrong?
X
A.
The exporter with a turnover of 10 million euro isn’t in Madrid
B.
The Madrid office has a turnover of 25 million euro
C.
The soya exporter has a turnover of more than 20 million euro
D.
The Amsterdam office has a turnover of 10 million euro
9. Which of the diagrams illustrates the relationship between the given terms?
Scandinavians, people with fair hair, women
X
A.
Diagram 3
B.
Diagram 5
C.
Diagram 1
D.
Diagram 4
10. The McCann company makes boxes. To assemble 1,000 boxes, machine “x” takes 3 days, whereas
machine “y” needs a third of the time it takes machine “x”, and machine “z” only needs half the time it
takes machine “x”. How many days would it take the McCann company to assemble the 1,000 boxes if
it has one each of the machines?
X
A.
One day
B.
Half a day
C.
A day and a half
D.
Two days
11. Which of the following inequalities is verified if and only if x > 3 ?
X
A.
6x + 7 > 3x + 16
B.
6x + 5 > 2x - 7
C.
6 (x + 4) < 2x + 1
D.
6x - 7 > 3x - 8
A.
x4
B.
x≥2
C.
x≥4
D.
x  -2
12.
X
Prova P0001
4
13. Through two distinct points in the plane:
X
A.
more than two distinct lines pass
B.
infinite distinct lines pass
C.
only two distinct lines pass
D.
only one line passes
14. Given a triangle with sides AB and BC of the same length and a 70° angle in B, what is the angle in A?
X
A.
65°
B.
55°
C.
50°
D.
60°
15. Divide the following polynomial into factors 2x 3 - 3x2y - 2x2z - 2xz + 3xyz + 3yz.
X
A.
(2x + 3y) (x2 - xz - z)
B.
(2x - 3y) (x2 - x2z - z2)
C.
(2x + 3y) (x - x2z + z2)
D.
(2x - 3y) (x2 - xz - z)
16. In the Cartesian plane, which of the following straight lines passes through the point P of coordinates (3 , 5)?
X
A.
y = 2x + 1
B.
y = 2x - 1
C.
D.
17. In the Cartesian plane , the lines 3x + 5y - 17 = 0 and 6x + 10y + 5 = 0 are:
X
A.
parallel
B.
perpendicular
C.
coincident
D.
incident
18. The polynomial 4x4y - 5x2y4 + 7x3y2 is:
X
A.
second degree with respect to the x, first degree with respect to the y and has a total degree equal to 5
B.
third degree with respect to the x, fourth degree with respect to the y and has a total degree equal to 8
C.
fourth degree with respect to the x, second degree with respect to the y and has a total degree equal to 4
D.
fourth degree with respect to the x, fourth degree with respect to the y and has a total degree equal to 6
19. If X = {b,c,e,f,g,t} and Y = {a,b,e,f,i}, then:
X
A.
X⊂Y
B.
X ∪ Y = {a,b,i}
C.
X ∩ Y = {a,c,g,i}
D.
X ∩ Y = {b,e,f}
20. Given the sets A = ( - ∞; 4], B = (-2 ; + ∞) and C = (-2 ; 4] it is true that:
X
A.
C=A+B
B.
C=AB
C.
C=AB
D.
C=A-B
21. What is the arithmetic average of the natural numbers 4, 5, 6, 9, 13, 14, 19?
X
A.
9
B.
14
C.
12
D.
10
Prova P0001
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22. The equations system :
3x  2y  12

x  2y  4
has the solution :
A.
X
B.
x = -2; y = 3
C.
D.
x = 2; y = -3
23. The solution of the equation 6x - 41 = 4x - 19 is:
X
A.
11
B.
9
C.
13
D.
-13
24. When A = (7 , 3) and B = (-3 , -5) are the extremes of a segment, determine the middle point M.
X
A.
M = (1 , -2)
B.
M = (2 , -1)
C.
M = (4 , -2)
D.
M = (10 , 8)
25. Which of the following sequences of numbers is arranged in a strictly increasing order?
A.
X
B.
C.
D.
26. The set of all the solutions of the inequality x2 - 5x + 6 > 0 is:
X
A.
x < -3; x > 2
B.
x < 2; x > 3
C.
2<x<3
D.
x < -2; x > 3
A.
x < -5
B.
x > -5
C.
x>6
D.
x<6
27.
X
28. Given the numbers 429, 517, 726, 858, 979 we can say that:
X
A.
they are all divisible by 11
B.
they are all divisible by 3 and by 4
C.
they are all divisible by 3
D.
they are all divisible by 3 and by 11
29. A player rolls a dice and wins if he gets an odd number that is less than 5. What
winning ?
X
A.
1/6
B.
1/2
C.
1/3
D.
2/3
Prova P0001
is the probability of
6
30. If the population of a town composed of 15.000 inhabitants increases by 10% a year , three years
later the population will amount to :
X
A.
19.555 inhabitants
B.
19.795 inhabitants
C.
19.965 inhabitants
D.
18.765 inhabitants
31. In the Cartesian plane, the intersecting point of the lines 2x - 3y - 4 = 0 and 3x + 2y - 6 = 0 has coordinates:
X
A.
(0, 1)
B.
(0, -2)
C.
(-2, 0)
D.
(2, 0)
32. The point common to the two lines 2x - y + 1 = 0 and x + y - 7 = 0 is:
A.
B.
X
C.
D.
33. The parabola y = ax2 + bx + c is a symmetrical curve with respect to equation line r:
A.
B.
C.
X
D.
34. In the Cartesian plane, for what value of q does the equation line y = 2x + q pass through the point of
coordinates (5, 2)?
A.
q = -4
B.
X
C.
q = -8
D.
q=8
35. Which of the following expressions is equal to the polynomial (a3 + b3) ?
X
A.
(a - b) (a2 + ab + b2)
B.
(a + b) (a2 + 2ab + b2)
C.
(a + b) (a2 + ab + b2)
D.
(a + b) (a2 - ab + b2)
36. Determine the set among the following that does NOT contain fractions that are all equivalent to each
other.
X
A.
{ 9/27; 27/81; 3/9; 108/324 }
B.
{ 13/52; 39/156; 117/468; 65/260 }
C.
{ 2/16; 4/32; 12/96; 48/384 }
D.
{ 4/20; 8/40;12/72;16/80 }
37. In the Cartesian plane, what is the equation of the line passing through point A = (2 , 3) and parallel to line
2x - 4y + 3 = 0 ?
X
A.
2x - 3y + 5 = 0
B.
x - 2y + 4 = 0
C.
x + 2y + 6 = 0
D.
x + 2y - 4 = 0
38. What is the result of the expression (x 4y5)3 (x2y4) ?
X
A.
x14y19
B.
x9y12
C.
x24y60
D.
x10y11
Prova P0001
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39. Which of the following triads cannot represent the measurements of the sides of a triangle?
X
A.
3 , 7 , 11
B.
6 , 8 , 10
C.
3,4,6
D.
5 , 12 , 15
40. The set of all the solutions of the equation x2 + 8x + 15 = 0 is:
X
A.
{5 ; 3 }
B.
{-5 ; -3 }
C.
{-5 ; 3 }
D.
{5 ; -3 }
41. Determine the distance between points A = (2 , 3) and B = (-4 , -5).
X
A.
10
B.
8
C.
37
D.
42. How many real solutions exist to the equation (x2 - 4) (x2 + 9) (x - 1) = 0 ?
X
A.
4
B.
2
C.
1
D.
3
43. The distance between the centres of two secant circumferences is:
X
A.
equal to the difference of the radii
B.
equal to the sum of the radii
C.
less than the sum of their radii and greater than their difference
D.
greater than the sum of the radii
44. When a set consists of 5 elements, how many subsets of 3 elements does it contain?
X
A.
6
B.
10
C.
8
D.
5
45. Indicate, among the following, the pair of numbers that verifies the identity 2x - 3y = 5.
X
A.
(-2, 1)
B.
(2, 1)
C.
(-1, 1)
D.
(1, -1)
Prova P0001
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