1
Logic and Mathematics Mock Exam
You have 60 minutes to complete the test
1.
7
11
−
=
15 30
1
(a) −
2
2. If a, b ≠ 0 then
(b)
1
2
(c) −
4
15
(d)
4
15
12ab3 − 6a2 b
=
3ab
(a) 4b2 − 2a
(b) 4b2 + 2a
(c) −4b2 + 2a
(d) −4b2 − 2a
3. I have paid ¤ 1000 to buy an appliance. Taking into account that the price had already been
discounted by 20% , what was the originale price, prior to the discount?
(a) ¤ 1200
(b) ¤ 1300
(c) ¤ 1250
(d) ¤ 1350
4. Consider the straight lines whose equations are 2x + y = 4 e 2x − 4y = 5. These lines are:
(a) parallel
(b) perpendicolar
(c) surreptious
(d) skew
5. A child eats at first 80% of her candies, then 5% of the remaining ones. What percentage is she left
with of the original stock?
(a) 19%
(b) 20%
(c) 15%
(d) 21%
6. In my class 15 students swim, 20 ride bikes. If 10 students do both activities, how many will just do
only one?
(a) 5
(b) 10
(c) 15
(d) 35
7. A photocopying machine takes 6 minutes to copy a given amount of pages . After
been completed, how many more minutes does it take to end the job?
(a) 2
(b) 3
2
of the job has
3
(c) 2,5
(d) 3,5
(c) 9
(d) 10
(c) 25
(d) 20
8. If x 2 + 2xy + y 2 = 81 then x + y =
(a) 7
9. If
√
(b) 8
x − 5 + 6 = 11, then x =
(a) 5
(b) 30
10. To prepare old granma’s porridge you need 3.5 liters of water for every kilogram of flour. If you
pour 2.8 liters of water in a pot, how much flour do you have to add?
(a) 1.5 kg
(b) 0.8 kg
(c) 0.7 kg
(d) 0.75 kg
(b) 13
(c) 39
(d) 10
11. If 813 = 2x , then x =
(a) 16
Facoltà di Economia Università di Bologna
2
Logic and Mathematics Mock Exam
12. In a university entrance examination 80% of the candidates passed. How many failed the test, if 80
students took the exam?
(a) 16
(b) 64
(c) 80
(d) 20
13. The table here below shows the answers two samples of women and men respectively gave to the
question: ‘ Are you in favour of this law? ’ What is the total number of those not in favour of the
law?
Men
Women
(a) 273
Sample cardinality
250
350
(b) 463
Percentage in favour
24 %
22 %
(c) 137
(d) 190
14. 5 plus the square of a positive number is 86. The number is
(a)
√
5
(b) 81
(c)
√
86
(d) 9
15. In a 7,5 liters mixture of water and vinegar, the percentage of vinegar is 60%. If we add 1.5 liters of
water to the mixture, what is now the percentage of vinegar?
(a) 60 %
(b) 30%
(c) 40 %
(d) 50%
(c) (x − 2)(x + 1)
(d) (x + 2)(x + 1)
(b) 3/2
(c) 2
(d) 4
(b) no x
(c) x = 1
(d) x = ln 2/ ln 3
(b) 22x+2
(c) 4x
16. x 2 − 3x + 2 can be factorized as
(a) (x + 2)(x − 1)
(b) (x − 2)(x − 1)
17. (x − 2)(x − 4) − (x − 3)(x − 1) = 0 if x =
(a) 5/2
18. 2x = 3x if
(a) x = 0
19. (4x )2 =
(a) 4x+2
2
(d) 24x
20. Let A, B, C be numbers between zero and 9. Consider the following multiplication
C
B
A
6
9
A
2
4
C
2
3
3
A
A
−
A
×
=
Then
(a) A = 4, B = 5, C = 1
(c) A = 5, B = 4, C = 1
(b) A = 1, B = 4, C = 5
(d) A = 5, B = 1, C = 4
Facoltà di Economia Università di Bologna
3
Logic and Mathematics Mock Exam
21. Only one of the following straight lines is not parallel to one of the cartesian axes. Which one?
(a) x + y − 1 = 0
(b) 3x + 1 = 5
(c) 3y + 1 = 3
(d) 4x + 1 = 0
22. Given the sets A = {1, 3, 5, 7, 9} and B = {1, 5, 9} then
(a) A ∩ B = A
(b) A ∪ B = B
(c) A ∪ B = A
(d) A ∩ B = ∅
23. If p(x) = −x 3 + x 2 + 9x − 9 it is then true that
(a) p(x) = (3 − x)(x − 1)(x + 3)
(c) p(x) = (3 − x)(x + 1)(x + 3)
(b) p(x) = (x − 3)(x − 1)(x + 3)
(d) p(x) = (3 − x)(1 − x)(x + 3)
24. Only one of the following numbers is the result of a square multiplied by a cube. Which one?
(a) 1323
25.
p
(b) 793
(c) 527
(d) 1155
(b) -1
(c) i
(d) ±1
(b) 0, 8
(c) 0, 008
(d) 0, 0008
(c) 300 523
(d) 258 453
(−1)2 =
(a) 1
26. (0, 2)3 equals:
(a) 0, 08
27. The least common multiple of 2997 and 1431 is:
(a) 300 532
(b) 158 841
28. If a non-leap year begins on a Thursday, on what day will the next year begin?
(a) Thursday
(b) Wednesday
(c) Friday
(d) Saturday
(b) 4
(c) 8
(d) 6
(b) 2545
(c) 545
(d) 257
(b) 930
(c) 311
(d) 910
29. 7776 is the fifth power of …
(a) 2
30. 59 × 55 equals
(a) 2514
31. 310 + 310 + 310 =
(a) 330
1
32.
1+
(a)
=
1
1+
3
5
1
2
(b)
5
3
Facoltà di Economia Università di Bologna
(c)
2
3
(d)
3
2
4
Logic and Mathematics Mock Exam
33. x and y are numbers such that if we increase x by 23% and we decrease y by 19% we eventually end
x
is equal to
up with same number. Then the ratio
y
25
20
27
37
(a)
(b)
(c)
(d)
100
100
41
71
34. If x is both a square and a cube and if 2 ≤ x ≤ 200 what is the value of x?
(a) 8
(b) 125
(c) 64
(d) 16
(b) 425
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449
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(d) 299
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(a) 225
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(c) a + b + c is even
(d) abc is a multiple
of 3
5
Logic and Mathematics Mock Exam
Answers
Facoltà di Economia Università di Bologna