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# Logic

### N°1: Find the next number of the sequence 12-17-23-30-38….

1. 47
2. 44
3. 38
4. 19

The logical you have to follow to complete the sequence is to add 5 to the first number, 6 to the second…7 to the third, 8 to the fourth and finally 9 to the last number.

12(+5) 17 (+6) 23 (+7) 30 (+8) 38 (+9) = 47

### N°2 : Which of these characters is out of context:

1. Francesco Guccini
2. Rosa Balistreri
3. Luigi Pirandello
4. Mia Martini

Luigi Pirandello was an Italian novelist winner of the 1934 Nobel Prize for Literature. With his invention of the “theatre within the theatre” in the play “Sei personaggi in cerca d’autore” he became an important innovator in modern drama; while the other are singers.

### N°3: Which is the month to discard?

1. December
2. September
3. November
4. October

September, October and November are autumn months, while December is the only winter month of the list.

### N°4: Find the word out of the context:

1. Risotto
2. Pizza
3. Pasta Carbonara
4. Moussaka

Moussaka is the only tipical Greek dish while the others are Italian dishes

### N°5: Complete the sequence 4-8-6-12-10….

1. 20
2. 12
3. 11
4. 5

X* 2 – 2

In this sequence you have to multiply the first number for 2 and subtract from the result 2 and it is until the end:

4 (x2) 8 (-2) 6 (x2) 12 (-2) 10 (x2) = 20

### N°6: Find the character who is out of the context:

1. Giuseppe Verdi
2. Aldo Moro
3. Gioachino Rossini
4. Giacomo Puccini

Aldo Moro was an Italian politician murdered, after many days of captivity, by the far-left terrorist group called Red Brigades; he was, with the Communist Leader Berlinguer, the father of the Historic Compromise that completely changed Italian politics. Verdi, Rossini and Puccini are famous and important composers and musicians of the Italian music history.

### N°7: complete the sequence 1-2-3-5-8-13….?

1. 22
2. 21
3. 11
4. 7

1+2=3+2=5+3=8…

In this sequence you have to add the number that follow one other:

1+2=3; 2+3=5; 3+5=8; 5+8=13;8 +13= 21

### N°8: Italians are skiers. Skiers can be tennis players. Find the following conclusions that can be completed the proposed syllogism:

1. Some tennis players are Italian
2. Italians are tennis players
3. Italians don’t know play tennis
4. Italians can be tennis players

A syllogism, in logic, is a valid deductive argument having two premises and a conclusion. In this case the two premises are “the Italians are skiers” and “the skiers can be tennis players”.  The conclusion can only be “Italians can be tennis players”

### It is inferred that surely:

1. Paula did not go to the beach to swim
2. Paula was not well
3. Mark did not feel like swimming
4. Mark was not feeling well

The correct answer is the third because the fact that Mark was at the playground does not give any information about the health of Paula, nor whether she went swimming or not. The only possibility that Mark did not go swimming is who was not feeling well, as from option C

### N°10: complete the sequence: 10-14-7-9-?-?-12

1. 3, 6
2. 20, 25
3. 13, 10
4. 7, 9

To resolve this sequence you have to add a first 4, from the result subtract 3 an the add again 2 and repeat this for two times.

10 (+4); 14 (-3); 7 (+2); 9 (+4); 13 (-3); 10 ( +2); 12

### Given the two premises, what is the conclusion of the following syllogism?

1. So no mammal is a snake
2. So no snake is a mammal
3. So no mammal breast-feeds its young
4. So some snakes feed their young

The two premises, as one universal affirmative and the other universal negative, exclude each other the possibility of intersection. So the two sets are totally separated and the only answer in that no snake is a mammal.

### N°12: The following sequence follows a certain logic. What is the value of X?2 – 5 – 10 – 17 – 26 – 37 – X – 65

1. 52
2. 46
3. 50
4. None of the above

The sequence is created by adding always odd numbers, starting in 3.
Thus, X is 50 because 2 + 3 = 5; 5 + 5 = 10; 10 + 7 = 17; 17 + 9 =26; 26 + 11 = 37; 37 + 13 = 50; 50 + 15 = 65

### N°13: Inside a plot, there is a tree. The shade of the tree doubles every day. On the 9th day the shadow of the tree covered the whole plot. Which day the shadow of the tree covered half of the plot?

1. 2
2. 4
3. 5

If the shadow doubles every day, it will cover the plot on the eve of the day that fills it completely. So it covers half of the plot on the 8th day.

### N°14: A brick weighs a kilo and a half brick. How many kilos do the two bricks weigh?

1. 2kg
2. 3kg
3. 4kg
4. 5kg

The two bricks weigh 4 kg. Because a brick weighs one kilo and a half brick, so if we remove half a brick from each side of the scale, we will find that half a brick weighs one kilo so the two bricks weigh 4 kilos.

### N°15: John has 20 euros more than Georgia. If he adds 10 euros to half of his money, then he will have as much money as Georgia. How much money does Georgia have?

1. 60
2. 50
3. 30
4. 40

In half of John’s money we add 10 euros and we find the money of Georgia. Then, to the previous amount, we add 20 euros more and find the money that John has in total. So we find the total amount of John if we add 30 euros to half of his money. So, half of John’s money is 30 euros, therefore he has a total of 60 euros. So Georgia has 60-20 = 40 euros.

1. Iron
2. Cotton
3. Gold
4. The same

All weight 1kg.

### N°17: A skier wakes up at dawn and gets ready to go skiing. In a drawer he has 4 black and 8 blue gloves. Unfortunately, the room is too dark to distinguish their colours. How many gloves should he take with him to make sure he has two of the same colour?

1. 3
2. 4
3. 5
4. 6

He must get at least 3 gloves. He has two pairs of black gloves, so if he takes 3 left gloves, it is guaranteed that he will have both colours.

### N°18: We have 3 boxes, one of which contains chocolates, the other cookies and the third one contains candies. Each box has a label on which its contents are written. The labels, however, are wrong in all three boxes. What is the smallest number of boxes we need to open to see what each box contains?

1. 0
2. 1
3. 2
4. 3

We only need to open one box because if we know the contents of one box, then we can say with certainty what the other two boxes contain. Let’s say we open the box whose label says “chocolates” and we find the candies. From this we understand that the box with the label “Cookies” will contain the chocolates, since it can not contain either the cookies (due to its label) or the candies (since we found them in the previous box). Finally, the box labeled “candies” will contain the cookies.

### N°19: The whole of Cyprus is EU territory.

1. True
2. False

Despite joining the EU as a de facto divided island, the whole of Cyprus is EU territory. Turkish Cypriots who have, or are eligible for, EU travel documents are EU citizens. EU law is suspended in areas where the Cypriot government (Government of the Republic) does not exercise effective control.

### N°20: Either Cyprus is in Europe or Greece is in Asia.

1. True
2. False

This proposition is true because one of the part of the proposition is true. Cyprus is EU territory. Greece is, also, in Europe.

### N°21: It is false that, Cyprus has two official European languages: Greek and Turkish language

1. True
2. False

Only Greek is an official EU language.

### N°22: Cyprus is either located between Europe or Asia or Africa.

1. True
2. False

Cyprus is an island in the Eastern Mediterranean, situated at the crossroads of three continents and civilizations. The island is situated South-East of Europe, North of Africa and West of Asia.

### N°23: If Cyprus is located south of the coast of Turkey, then Cyprus is located east of Greece.

1. True
2. False

The island, geographically already part of Asia (Middle East), is located about 80 km (50 mi) south of the coast of Turkey, west of Syria and Lebanon, northwest of Israel, north of Egypt and east of Greece.

### N°24: Cyprus is larger than Malta, if Germany is larger than Italy?

1. True
2. False

Germany has the largest population (83.2 million residents) accounting for 18.6% of the total EU population at 1 January 2020 and Malta has the smallest population of the total EU population (515,000  residents).

### N°25:  In which tradition(s) did “logic” as an explicit analysis of reasoning originally occurred?

1. In China
2. In India
3. In Greece
4. In all the above

The history of logic documents the development of logic as it occurs in various cultures and traditions in history. While many cultures have employed intricate systems of reasoning, logic as an explicit analysis of the methods of reasoning received sustained development originally only in three traditions: China, India and Greece. Although exact dates are uncertain, especially in the case of India, it is possible that logic emerged in all three societies in the fourth century B.C.E. The notions of systems of reasoning and logic, however, are sufficiently imprecise that various answers to the questions of what they are and how they are to be understood have been given. The formally sophisticated treatment of modern logic descends from the Greek tradition, but comes not wholly through Europe, but instead comes from the transmission of Aristotelian logic and commentary upon it by Islamic philosophers to logicians in Medieval Europe

### N°26: How many logical traditions emerged in ancient Greece?

1. One
2. Two
3. Three
4. Four

In Greece, two main competing logical traditions emerged. Stoic logic traced its roots back to Euclid of Megara (c. 430 – c. 360 B.C.E.), a pupil of Socrates, and with its concentration on propositional logic was perhaps closer to modern logic. The Megarians were interested in puzzles, and studied modality and conditionals. The Stoics used numbers as variables for replacing whole propositions. The most important Stoic logician was Chrysippus (c. 279 – 206 B.C.E.), who discussed five basic or valid inference schemata, and from them derived or proved many other valid inference schemata.

### N°27: Which of the following slogans explained Parmenide’s philosophy about logic?

1. “whatever is is, and what is not cannot be”
2. a & b
3. none

Parmenides of Elea was a pre-Socratic Greek philosopher who has been considered the founder of metaphysics or ontology and has influenced the whole history of Western philosophy. He was the founder of the Eleatic school of philosophy, which also included Zeno of Elea and Melissus of Samos. His philosophy denied motion and multiplicity and has been explained with the slogan “whatever is is, and what is not cannot be”. He is also credited with the phrase “out of nothing nothing comes”.

### N°28: Which of the following words is a necessary part of “language”

1. words
2. tongue
3. writing
4. dialect

Words are a necessary part of language. Dialect is not necessary to language (choice d). Not all languages are written (choice c). Not all languages are spoken (choice b).

### N°29: The dialectical logic of Thucydides is widely known as the….? (dialectical logic in politics)

1. Thucydides’ dialogue
2. the historian dialogue
3. the Melian dialogue
4. none of the above

Thucydides in his classic study of the Peloponnesian war describes the Siege of Melos, which occurred in 416 BC, during the fight between Athens and Sparta, when the Melians (Melos is a small island in the Aegean Sea) refused to surrender to Athens that in turn sieged the island. This siege is best remembered for the Melian Dialogue, which refers to Thucydides’ description of the negotiations between the Athenians and the Melians before the siege, providing a dramatized version of the dialectical logic behind political  motivation to enter into war. The Melian Dialogue is “at the same time … the result of art … [and] the reflection of reality”

### N°30: This method of proving something by assuming its alternative and showing that this assumption leads to absurdity is known as?

1. induction and abduction
2. deduction
3. hypothesis
4. all of the above

This method of proving something by assuming its alternative and showing that this assumption leads to absurdity is known as reduction ad absurdum, which means reduction and abduction. Inductive reasoning, or induction, is making an inference based on an observation, often of a sample. You can induce that the soup is tasty if you observe all of your friends consuming it. Abductive reasoning, or abduction, is making a probable conclusion from what you know.

### N°31: What is the name of the standard collection of Aristotle’s six works on Logic?

1. Organon
2. Metaphysics
3. Politics
4. Nicomachean Ethics

Organon is the name given by the Peripatetics to the standard collection of Aristotle’s six works on Logic, namely: The Categories, On Interpretation, Prior Analytics, Posterior Analytics, Topics and Sophistical Refutations. Logic comes from the Greek word logos, originally meaning “the word” or “what is spoken”, but coming to mean “thought” or “reason”. In the Western World, logic was first developed by Aristotle.

### N°32: Logic circuits are formed by Gate combinations:

1. Formed by combinations of gates only AND
2. Formed by combinations of gates only OR
3. Formed by combinations of gates only NOT
4. Formed with combinations of gates (AND, OR, NOT)

Logic circuits are formed by combinations of gates (AND, OR, NOT). Each circuit can be characterized by a proposition of Propositional Calculus.

### S1: All humans are mortal./S2: X/Conclusion: Socrates is mortal.

1. Socrates is immortal
2. Socrates is human
3. Humans have two legs
4. Gods are immortal

All humans (A) = mortal (B)

X

So: Socrates (C) = mortal (B)

According to the mathematical logic, the sentence C=A is missing, namely: Socrates is a human.
In Europe, Aristotle (ancient Greek philosopher and scientist, 384–322 BC) first developed the science of logic. Aristotelian logic was widely accepted in science and mathematics, while it remained in widespread use in the Western World until the early 19th century. The Aristotelian system of logic was what introduced hypothetical syllogism, temporal modal logic and inductive logic, as well as important terms such as predicables, syllogisms and propositions

### N°34: Which is the Greek word used in logic to indicate that a statement is true in all circumstances?

1. Cycle
2. Tautology
3. Metaphor
4. Tactic

The four words are all of greek origin, but “tautology” (tautos=the same + logos) is the term first introduced by the great Austrian-born philosopher Ludwig Wittgenstein in 1921 in his Tractatus Logico-Philosophical. Tautologies are also sometimes called logical truths or truths of logic, because they can be recognized as true solely in virtue of the principles of propositional logic and without recourse to any additional information. A very well-known wittgensteinian tautology is the following: “Whereof one cannot speak, thereof one must be silent”. Wittgenstein argued that in fact all necessary propositions are tautologies and that there is, therefore, a sense in which all necessary propositions say the same thing, namely: nothing at all.

### Which of the following prophecies predicts that a male child will be born?

1. boy not girl
2. boy not, girl
3. boy, not girl
4. boy, not, girl

When a wealthy father asked Pythia what child he would have, he received the ambiguous answer: “male no female”. Depending on where a comma would be placed, the interpretation of the prophecy changes and thus, it can be considered true by the father independent of the true outcome: “Male, not female” and “Male not, female”.

Delphi, in ancient times was a sacred precinct that served as the seat of Pythia, the major oracle who was consulted about important decisions throughout the ancient classical world. The ancient Greeks considered the centre of the world to be in Delphi, marked by the stone monument known as the omphalos (navel). During the 7th and 6th centuries BC, the Oracle of Delphi experienced its greatest prosperity.

### N°36: Which creature has one voice and yet becomes four-footed and two-footed and three-footed according to the Greek Sphinx?

1. Man
2. Insect with 2, 3 and 4 legs during its lifecycle
3. A mythical creature of Sphinx imagination
4. A special reptile living in Ancient Egypt

In Greek tradition, the sphinx has the head of a woman, the haunches of a lion, and the wings of a bird. She is mythicized as treacherous and merciless, and will kill and eat those who cannot answer her riddle unlike the Egyptian Sphinx which is typically shown as a man. The Sphinx is said to have guarded the entrance to the Greek city of Thebes, asking a riddle to travellers to allow them passage. She asked all passersby the most famous riddle in history: “Which creature has one voice and yet becomes four-footed and two-footed and three-footed?” She strangled and devoured anyone who could not answer. Oedipus solved the riddle by answering: “Man—who crawls on all fours as a baby, then walks on two feet as an adult, and then uses a walking stick in old age”. By some accounts (but much more rarely), there was a second riddle: “There are two sisters: one gives birth to the other and she, in turn, gives birth to the first. Who are the two sisters?” The answer is “day and night” (both words—ημέρα and νυξ, respectively—are feminine in Ancient Greek). This second riddle is also found in a Gascon version of the myth and could be very ancient.

### N°37: Who was the author of the Tractatus Logico Philosophicus (1921) and the Philosophical Investigations (1953)?

1. John Locke
2. John Stuart Mil
3. Ludwig Wittgenstein
4. Ludwig Klages

Ludwig Wittgenstein (1889 – 1951) was one of the most important philosophers of the twentieth century. Wittgenstein made a major contribution to conversations on language, logic and metaphysics, but also ethics. He shifted the idea of seeing language as a fixed structure imposed upon the world to seeing it as a fluid structure that is intimately tied and influenced by our everyday practices and forms of life.

### N°38:  When was the first Vienna Circle of Logical Empiricism that was a group of philosophers meeting regularly?

1. 1904-1910
2. 1902-1906
3. 1907-1912
4. 1889-1905

The first circle of Vienna was carried out between 1907-1912. It entailed meetings of the physicist Philip Frank, the mathematician Hans Hahn and Otto Neurath during which they discussed the philosophy of science.

### N°39: When was the Institute Vienna Circle (IVC) established?

1. 1991
2. 1985
3. 1973
4. 1968

In 1991 the Institute Vienna Circle (IVC) was established as a society in Vienna. It is dedicated to studying the work and influence of the Vienna Circle. In 2011 it was integrated in the University of Vienna as a subunit of the Faculty of Philosophy and Education..

### N°40: Four people are crossing a bridge at night, so they all need a torch—but they just have one that only lasts 15 minutes. Alice can cross in one minute, Ben in two minutes, Cindy in five minutes and Don in eight minutes. No more than two people can cross at a time; and when two cross, they have to go at the slower person’s pace. Who crosses first so that get across in 15 minutes?

1. Alice and Ben
2. Cindy
3. Don
4. Cindy and Don

Alice and Ben cross first in two minutes, and Alice crosses back alone with the torch in one minute. Then the two slowest people, Cindy and Don, cross in eight minutes. Ben returns in two minutes, and Alice and Ben return in two minutes. They just made it in 15 minutes exactly.

### N°41:  What is the name of the philosophical movement that arose in Vienna in the 1920s and was characterized by the view that scientific knowledge is the only kind of meaninful knowledge?

1. Empiricism
2. German idealism
3. Modernism
4. Logical positivism

Logical positivism was a movement in that arose in Vienna and whose central thesis was the verification principle. According to this principle, only statements verifiable through direct observation or logical proof are meaningful. Starting in the late 1920s, groups of philosophers, scientists, and mathematicians formed the Berlin Circle and the Vienna Circle, which, would further develop the ideas of logical positivism.

### N°42: A girl meets a lion and unicorn in the forest. The lion lies every Monday, Tuesday and Wednesday and the other days he speaks the truth. The unicorn lies on Thursdays, Fridays and Saturdays, and the other days of the week he speaks the truth. “Yesterday I was lying,” the lion told the girl. “So was I,” said the unicorn. What day is it?

1. Monday
2. Thursday
3. Saturday
4. Wednseday

Thursday. The only day they both tell the truth is Sunday; but today can’t be Sunday because the lion also tells the truth on Saturday (yesterday). Going day by day, the only day one of them is lying and one of them is telling the truth with those two statements is Thursday.

### N°43: You are on your way to visit your Grandma, who lives at the end of the valley. It’s her anniversary, and you want to give her the cakes you’ve made. Between your house and her house, you have to cross 5 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake. How many cakes do you have to leave home with to make sure that you arrive at Grandma’s with exactly 2 cakes?

1. 10
2.  5
3.  2
4. 15

2 Cakes. How? At each bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

### N°44: A man, his wife, and their son are in a car accident. They are all rushed to the hospital and the doctor says, “I can’t operate on him, he’s my son.” Who is the doctor?

1. The woman´s father
2. The boy´s brother
3. The man´s father and the boy´s grandfather
4. The woman´s sister

The doctor is the man’s father and the boy’s grandfather.

### N°45: Which one of the following information on Ernst Waldfried Josef Wenzel Mach is not true?

1. He was an Austrian physicist
2. He made contribution to physics such as the study of shock waves
3. As a philosopher of science, he was a major influence on logical positivism and American pragmatism.
4. He completely agreed with Newton’s theories

He criticized Newton’s theories of space and time

### N°46: How many flies are flying if there are 3 half flies plus a fly and a half?

1. 3
2. 2 and a half
3. 1
4. 4

Just 1 fly. Half flies neither exist, nor can they fly.

### N°47:  You’re rummaging around your great grandmother’s attic when you find five short chains each made of four gold links. It occurs to you that if you combined them all into one big loop of 20 links, you’d have an incredible necklace. So you bring it into a jeweler, who tells you the cost of making the necklace will be \$10 for each gold link that she has to break and then reseal. How much will it cost?

1. 50\$
2. 30\$
3. 40\$
4. None of the above

The most straightforward approach would be to break a link on the end of each of the five chains, and then reattach the link to the back of the next chain in the loop. This would cost you \$50 for the five links that were broken and resealed.

But you can actually do it for \$40! Instead of breaking a link in each chain, break all four links in one of the chains and then use those four links to attach the remaining four chains together. Now you’ve saved \$10.

### N°48: Amanda lives with her teenage son, Matt, in the countryside—a car ride away from Matt’s school. Every afternoon, Amanda leaves the house at the same time, drives to the school at a constant speed, picks Matt up exactly when his chess club ends at 5 p.m., and then they immediately return home together at the same constant speed. But one day, Matt isn’t feeling well, so he leaves chess practice early and starts to head home on his portable scooter. After Matt has been scooting for an hour, Amanda comes across him in her car (on her usual route to pick him up), and they return together, arriving home 40 minutes earlier than they usually do. How much chess practice did Matt miss?

1. 30 min
2. 1hr
3. 1hr and 20 min
4. 50 min

Let’s call the spot at which Amanda and Matt meet on the road, point M. In this problem, Amanda drives from their home to point M, where she picks up Matt, and then drives back to their home. Let’s call the time it takes her to do this “T”.  We don’t know T, but we do know the time it took Amanda to do this is 40 minutes less than the time it usually takes her to drive back and forth from school. From this, we can infer the back-and-forth trip she did not drive (from M to school and back to M) must take 40 minutes. Since she drives at a constant speed, the one-way trip from M to school must therefore take 20 minutes. Since we know Amanda times her day to arrive at school for pickup at exactly 5 p.m., she must have reached M at 20 minutes before pickup, or at 4:40 pm.

Now, we know from the problem that Matt left chess club one hour before he met Amanda at point M. Thus, he must have left at 3:40 pm. Since chess typically ends at 5 pm, we have our answer: Matt missed 1 hour and 20 minutes of chess practice

### N°49: At the end of a race, four bikes crossed the finish line, one after the other. The four bikes were colored: yellow, red, brown and orange. Consider the following statements:

1. John arrived right behind Peter
2. The red bike arrived before the orange bike
3. Charles was not on the brown bike
4. Peter was on the red bike
5. Paul, who was on the yellow bike, arrived after João

### Based on the above information, which statement is true?

1. The brown bike ended the race before the orange bike
2. Charles reached the third position
3. John was on the orange bike
4. Paul came in third place
5. The orange bike arrived in third position

First place: Peter (red motorcycle); Second place: John (brown motorcycle);

We know that Paul (yellow bike) arrived after John, but we cannot say in which position. We cannot say what is Charles’ position (orange bike).

### N°50: Select the correct option that fills the series gap: MCD – NEF – OGH – … – QKL

1. CMN
2. UJI
3. PIJ
4. IJT

There are two alphabetical series. The first series is based on the first letter: MNOPQ. The second series involves the following two letters: CD, EF, GH, IJ, KL

### N°51: Consider the series of numbers: 7, 5, 7, 19, 73,… What is the next number?

1. 198
2. 314
3. 546
4. 361

The logic of this series works according to the following formula:

7 X 1 – 2 = 5; 5 X 2 – 3 = 7; 7 X 3 – 2 = 19; 19 X 4 – 3 = 73; 73 X 5 – 4 = 361

### N°52: Indicate the cause and effect relationship between the sentences, if any: All schools in the neighborhood were closed during the week. Many parents have canceled their children’s enrollment at neighborhood schools.

1. Sentence 1 is the cause and sentence 2 is its effect
2. Sentence 2 is the cause and sentence 1 is its effect
3. Sentences 1 and 2 are independent causes
4. Sentences 1 and 2 are effects of independent causes

The closing of schools in the neighborhood during the week and the decision to cancel enrollment for children are independent events that had different causes.

### N°53: Five fruits are arranged on a table and numbered from the bottom up. Consider the following statements:

1. One of the fruits is an apple
2. The fourth fruit is a banana
3. There are 3 fruits between the pear and the watermelon
4. There are 2 fruits below the peach, one of them is the pear

### In what position is the apple?

1. second position
2. third position
3. fourth position
4. fifth position

5 – watermelon, 4 – banana, 3 – peach, 2 – apple, 1- pear

### N°54: Each person who is a member of the Alpha club is also a member of the Beta club. Some members of the Gama club are also members of the Beta club. John is a member of two of these clubs. Indicate the true option, according to the previous information.

1. If John is a member of the Beta club, he is not a member of the Gama club.
2. If John is a member of the Beta club, he belongs to the Alpha club.
3. If John is a member of the Alfa club, he is not part of the Gama club.
4. All members of the Beta club are members of at least two clubs.

If John is a member of two clubs and knowing that whoever is a member of the Alpha club is also a member of the Beta club, then he cannot be a member of the Gama club.

Being a member of the Beta club, nothing prevents John from being a member of the Gama club.

It is possible to belong to the Beta club and not to belong to Alpha. The contrary is that it is not possible.

There may be members who belong only to the Beta club.

There may also be members who belong only to the Gama club.

### N°55: My cat meows when he is hungry. My cat also meows when he sees a mouse. Based on this information alone, indicate the true option.

1. If my cat meows, he saw a mouse and is hungry.
2. If my cat meows, he saw a mouse.
3. If my cat does not meow, he has not seen a mouse and is not hungry.
4. If the food bowl is full, my cat will not meow.

Based only on what has been reported, the only true statement is that if the cat does not meow, he has not seen a mouse and is not hungry.

### N°56: There are five boxes in the supermarket. The stack of boxes contains boxes of detergent, yogurt, pasta, milk and grape juice. Consider the following statements:

1. The detergent box is lower in the stack than the grape juice box
2. There are two boxes between the grape juice box and the pasta box
3. The yogurt box is the third from the top

### If the top box is the grape juice box, which box is at the bottom of the pile?

1. milk
2. detergent
3. detergent or milk, it is not possible to determine which of the two
4. detergent or pasta, it is not possible to determine which of the two

In the top position we have the grape juice box.

In the third position we have the yogurt box.

In the fourth position is the pasta box.

Therefore, the detergent box and the milk box can occupy both the second and fifth positions.

### N°57: Consider the series of numbers: 72, 14, 66, 22, 60,… What is the next number?

1. 68
2. 54
3. 30
4. 96

This is a series that alternates subtraction and addition. The first pattern is to subtract 6 from each number to calculate the next. The second 8 is added to each number to calculate the next one.

### N°58: A woman is going to have a baby. If he is a boy, only one son will be missing so that the number of boys is equal to that of daughters. However, if the baby is a girl, the woman’s number of daughters will be twice the number of boys. How many children does she have and what is their gender?

1. 3 children, 2 girls and 1 boy
2. 4 children, 3 girls and 1 boy
3. 6 children, 4 girls and 2 boys
4. 8 children, 5 girls and 3 boys

If the woman has 1 more boy, there will be only 1 more to have the same number of sons and daughters, for a total of 10. If the woman has 1 more girl, there will be 6 daughters in all, which is double the 3 children she already has.

### N°59: If five machines take five minutes to produce five pieces, how long would it take for 100 machines to produce 100 pieces?

1. 20 minutes
2. 15 minutes
3. 10 minutes
4. 5 minutes

It takes 5 minutes. If 5 machines take 5 minutes to produce 5 parts, it means that each machine takes 5 minutes to make a part. In this case, 100 machines would jointly produce 100 parts in the same 5 minutes.

### N°60: A bat and a baseball cost 1.10 euros in total. The putter costs one euro more than the ball. How much does the ball cost?

1. 10 cents
2. 5 cents
3. 1 cent
4. None of the options above is correct

The ball costs 5 cents. As the taco costs 1 euro more, we know that the taco costs 1 euro and five cents, which gives a total of 1.10 euros.