You have 60 minutes to complete the test. (c) (a) parallel (b) perpendicolar (c) surreptious (d) skew

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1 Logic and Mathematics Mock Exam 1 You have 60 minutes to complete the test = (a) 1 1 (c) If a, b 0 then 1ab 6a b ab = (a) 4b a 4b a (c) 4b a 4b a. I have paid 1000 to buy an appliance. Taking into account that the price had already been discounted by 0%, what was the originale price, prior to the discount? (a) (c) Consider the straight lines whose equations are x y = 4 e x 4y = 5. These lines are: (a) parallel perpendicolar (c) surreptious 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% 0% (c) 15% 1% 6. In my class 15 students swim, 0 ride bikes. If 10 students do both activities, how many will just do only one? (a) 5 10 (c) 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? of the job has (a) (c),5,5 8. If x xy y = 81 then x y = (a) 7 8 (c) If x 5 6 = 11, then x = (a) 5 0 (c) To prepare old granma s porridge you need.5 liters of water for every kilogram of flour. If you pour.8 liters of water in a pot, how much flour do you have to add? (a) 1.5 kg 0.8 kg (c) 0.7 kg 0.75 kg 11. If 8 1 = x, then x = (a) 16 1 (c) 9 10

2 Logic and Mathematics Mock Exam 1. In a university entrance examination 80% of the candidates passed. How many failed the test, if 80 students took the exam? (a) (c) 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? Sample cardinality Percentage in favour Men 50 4 % Women 50 % (a) 7 46 (c) plus the square of a positive number is 86. The number is (a) 5 81 (c) 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 % 0% (c) 40 % 50% 16. x x can be factorized as (a) (x )(x 1) (x )(x 1) (c) (x )(x 1) (x )(x 1) 17. (x )(x 4) (x )(x 1) = 0 if x = (a) 5/ / (c) x = x if (a) x = 0 no x (c) x = 1 x = ln / ln 19. (4 x ) = (a) 4 x x (c) 4 x 4x 0. Let A, B, C be numbers between zero and 9. Consider the following multiplication Then C 4 A = 6 C A B 9 A A A (a) A = 4, B = 5, C = 1 A = 1, B = 4, C = 5 (c) A = 5, B = 4, C = 1 A = 5, B = 1, C = 4

3 Logic and Mathematics Mock Exam 1. Only one of the following straight lines is not parallel to one of the cartesian axes. Which one? (a) x y 1 = 0 x 1 = 5 (c) y 1 = 4x 1 = 0. Given the sets A = {1,, 5, 7, 9} and B = {1, 5, 9} then (a) A B = A A B = B (c) A B = A A B =. If p(x) = x x 9x 9 it is then true that (a) p(x) = ( x)(x 1)(x ) p(x) = (x )(x 1)(x ) (c) p(x) = ( x)(x 1)(x ) p(x) = ( x)(1 x)(x ) 4. Only one of the following numbers is the result of a square multiplied by a cube. Which one? (a) 1 79 (c) ( 1) = (a) 1-1 (c) i ±1 6. (0, ) equals: (a) 0, 08 0, 8 (c) 0, 008 0, The least common multiple of 997 and 141 is: (a) (c) If a non-leap year begins on a Thursday, on what day will the next year begin? (a) Thursday Wednesday (c) Friday Saturday is the fifth power of (a) 4 (c) equals (a) (c) = (a) (c) = (a) 5 5 (c)

4 Logic and Mathematics Mock Exam 4. x and y are numbers such that if we increase x by % and we decrease y by 19% we eventually end up with same number. Then the ratio x y is equal to (a) (c) If x is both a square and a cube and if x 00 what is the value of x? (a) 8 15 (c) The half of 4 50 is: (a) (c)"#$"%&' 4 49 "# 99 "#$%&' (&) 6. In this figure the radius of the bigger circle is twice that of the smaller one, both circles being concentric. The ratio between the shadowed region and the area of the smaller circle is $%&'()%,-.) % /0.- 1# 4 5 (6-7).'8- (% (6-8).6(9 (6-80:)' %7 (6- &08.-8 ;)8;&- ) (<);- (60( %7 (6- =0&&-8 ;)8;&- 57 (6- ;)8;&- 08- ;%;-> "#$%& '()& #& (& ")#,&,-& (& ()..& "/#,01& )")&,& ( 08-0 %7 (6- =0&&-8 # ' G 5 (6-7).'8- (% (6-8).6(9 "#$ ) 0 )%;-&- 8).6( ( ) (8)0.&-9 0: () H(a) G I60( π ) ( %7 (6-60:-: 8-.)% (c) ""#$%&'() )")(#, G 7. In the figure below, if x = 4 then y 1M 1M $% &' (),-./ (0 () /,-)(1, - 1 4MG 45 ", $"%& :5 "#$% ;5 #%" N 5 (6-7).'8- (% (6-8).6(9 ( %7 "%& ) " I60( ) ) # ( %7 %&#? 4" G" <% &' (),-./ (0 () /,-)(1 =),>) 0 () 0??0=,'- >0.?@ G1 ( () >00/@,'B(C 0 B D0,'(,' () C)B@@ "1 75 (a) 1 (c) 4 "# $%&'(# )# (&'$# 5 (6- # 7).'8- $&',# 1 8. (% (6-8).6(9 OPK$ ) 0 Q'08-0: R 0: S ( 0# " ) 08- =):/%)( -# $,&'$.# %7 10 (6-) /-;()T = ):- I60( ) ( %7 Q'0:8)&0(-80& U (a) (c) G 1 () 4 9.,-./ What (0 () /,-)(1 is the =),>) last 0 digit () 0??0=,'- of 5 D0,'(C =,(),' () >,/>?E &#'% 45 9%#1 G%#5 (a) 4 9 (c) 5 0 "# $/&'/# )# $,0&',# # " :5 40. H1 ""5 If a, b, c are consecutive integers such that a < b < c, which of the following is true? ;5 #%#1 F%#5 (a) b c = 1 a b = 1 (c) a b c is even abc is a multiple of G% &' (),-./ (0 () /,-)(1 () -/,@ >0'C,C(C 0.',( CI.B/C% J)B(,C () B/B 0 () D0?K-0'E 45 < 65 G 85 Facoltà "H di Economia Università di Bologna :5 "7 ;5 "#

5 Logic and Mathematics Mock Exam 5 Answers