CAT Logical Reasoning (LR) 2019 Questions and Answers

Result Date: 4th Jan 2020

Logical Reasoning for CAT Exam, CAT LR Logical Reasoning Questions

The Logical Reasoning section in the MBA entrance examination tests your problem solving skills, as you tackle problems in the form of images, figures or diagrams and puzzling questions that require some level of abstract thinking.

To help you prepare better, it is important to familiarise yourself with the type of questions you can expect in this section. Some of them include:

1. Statement and Assumption

2. Number Series

3. Venn Diagrams

4. Syllogism

5. Direction Sense

1. Statement and Assumption

Understanding the Terms

  • Statement A statement is either a meaningful declarative sentence that is either true or false, or that which a true or false declarative sentence asserts. It is an assertion that something is or is not the case. For instance, ‘It is desirable to put a child in school around 3 or so.’
  • Assumption An assumption is an unstated premise that we take for valid or granted or that supports the conclusion. The assumption is stated implicitly and needs to be identified. For example, in the above statement, that ‘ it is desirable to put a child in school around 3 or so’, the assumption is that ‘At that age, the child reaches appropriate level of growth and development and is ready to learn.’

 

Type of Questions

Usually, these questions ask you to test whether the statements are implied in the given statement or not. For instance,

Statement- "If you trouble me, I will slap you." - A father warns his child.

Assumptions- i. With the warning, the child may stop troubling him.

                         ii. All children are basically mischievous.

A. Only assumption i is implicit

B. Only assumption ii is implicit

C. Either i or ii is implicit

D. Neither i nor ii is implicit

E. Both i and ii are implicit

 

The father warns her child with the expectation that he would stop troubling him. So, I is implicit. The general nature of children cannot be derived from the statement. So, II is not implicit.

For such questions, you must be able to identify the assumptions of the author. Do not make your own assumptions while attempting questions in logical reasoning. Strictly go by what is given to you.

 

Ways to ascertain Assumption

The best way to identify if a given statement is an assumption is to ask the question ‘why’.  It is an assumption if it answers the question, otherwise it is not. For example, in the statement, ‘if you are a teacher, we have a job for you’, ask yourself why is the advertisement done- the answer is because a teacher is needed. Assumptions cannot be exclusive in nature, which means, words like most, best, always, all and the like cannot be a part of assumptions. The statement and assumption have to be related to each other to be valid.

2. Number Series

This is one of the most common types of questions to figure in competitive exams. In such questions, a number series is given with a missing link and you have to find the missing link. For instance, 1,3,5,7,___,11. For such questions, you should try and find a pattern in the number series, a link between every number and its predecessor.

 

Types of Number Series

 

Number series can be based on various combinations, such as

i. Constant difference- In this type of series, any two consecutive numbers in the series will have the same difference between them. For example- 1,3,5,7,9,11

 

ii. Increasing difference- In this type of series, the difference between two consecutive numbers in the series keeps on increasing. For example- 2,4,7,11,16

 

iii. Decreasing difference- In this type of series, the difference between two consecutive numbers in the series keeps on decreasing. For example, 16,11,7,4,2

 

iv. Squares/Cubes- In this type of series, the terms in the series are related to the squares or cubes  of numbers. For example, 1,4,9,16,25,36

 

v. Mix of various operations- In this type of series, more than one arithmetic operations need to be applied or two different series can be combined to form one series. For example- 2,10,3,11,4,12,5,13

3. Venn Diagrams 

A Venn diagram uses overlapping curves, usually circles to organize things and highlight how the things are similar or different. Venn diagrams help to visualise the given data clearly and derive the right conclusions from it. For example,

All humans are dogs

Socrates is a human

Lgogical reasoning

The conclusion derived from looking at the Venn diagram is that since all humans are dogs and Socrates is a human, therefore, Socrates is a dog. The Venn diagram depict each item in the statement and highlight the relationship between them, thus, making the job of decoding the conclusion simpler.

 

How to solve Venn Diagram?

The whole point of drawing up Venn diagrams is to simplify the given information and make sense out of it.  To depict this information, circles are used. The larger item in the information is depicted by a circle first, followed by circles depicting other items in the information. Finally, the relation between the larger item and other items is depicted by aligning these circles appropriately. For instance, to draw a Venn diagram that best depicts the relation between Sports, Cricket and Football, we would first identify the larger item in this statement, that is, Sports followed by Cricket and Football. Hence, the Venn diagram shall be:

LR

What the above Venn diagram tells us is that Football and Cricket are sports. As Cricket and Football have no relation to each other and are two different types of sports, there will be no overlapping between the circle denoting football and the circle denoting cricket.

In case of particular statements that do not include the entire set, there will always be overlapping between the circles. For instance, Some taxis are cabbies. Some cabbies are Mercedes. Some taxis are Mercedes.

The Venn diagram for this will be overlapping circles,

Venn diagram

4. Syllogism

Syllogism is a form of reasoning in which the conclusion is drawn from two or three given propositions or statements. This implies that a conclusion is drawn from what is stated in the Major Premise and the Minor Premise. Generally, the sequence follows deductive reasoning, that is, the Major Premise comprises a general statement, moving to the particular in the Minor Premise, from which a conclusion is then drawn. For a syllogism to be valid, the conclusion must necessarily follow from the premises. For a syllogism to be true, it must make accurate claims and be consistent with facts. For a syllogism to be sound, it must be both true and valid.

 

How to tackle Syllogisms?

To tackle questions based on syllogism, the following points must be kept in mind:

1. Prepositions are of four types, namely:

  • Universal

       - Universal Affirmative [the symbol to denote Universal Affirmative is (A)]

       - Universal Negative [the symbol to denote Universal Negative is (E)]

 

  • Particular

- Particular Affirmative (the symbol to denote Particular Affirmative is (I)]

- Particular Negative [the symbol to denote Particular Negative is (O)]

 

Conclusions can be derived by applying the following rules:

a. It is not possible to get universal conclusion with two particular statements.

b. It is not possible to get negative conclusion with two affirmative sentences.

c. It is not possible to get positive conclusion with two negative statements.

d. It is not possible to get a conclusion with two particular statements. The exception to this rule is when a Particular Affirmative type of statement is given and by reversing it, a Particular Affirmative type of conclusion is given.

 

Also,

a. A Universal Negative statement when reversed, gives Universal Negative and Particular Negative as conclusion.

b. A Universal Affirmative statement when reversed, gives Particular Affirmative as conclusion.

c. A Particular Affirmative statement when reversed, gives Particular Affirmative as conclusion.

d. A Particular Negative statement when reversed, does not give a conclusion of any type.

 

Venn Diagrams and Syllogism

Venn Diagrams can be used to tackle Syllogism based questions.

Let’s consider some possibilities.

1. Some A's are B

Syllogism

Definite Conclusions

  • Some A is B
  • Some B is A

  Possible Conclusions

  • All A’s are B
  • All B’s are A
  • Some A are not B
  • Some B are not A

2. All A's are B

LR - Syllogism

Definite Conclusion

  • All A is B
  • Some A is B
  • Some B is A

Possible Conclusions

  • All B’s are A
  • Some B’s are not A

3. No A is B

LR Syllogism

Definite Conclusion

  • No A is B
  • No B is A
  • Some A is not B
  • Some B is not A

4. Some A's are not B

Syllogism questions

Definite Conclusion

  • Some A’s are not B

Possible Conclusion

  • Except All A’s are B, all other possibilities follow

Rules to keep in mind while using Venn Diagrams

  • Draw the Venn diagram based on the statement given and the terms in the statement
  • If the definite conclusion doesn’t satisfy the Venn diagram, then there is no need to check the possible conclusions
  • If the definite conclusion does satisfy the Venn diagram, then it must satisfy all possible conclusions

5. Direction Sense

Various tricky combinations can be framed using the four directions we have, namely, North, South, East and West. Such questions are a part of the logical reasoning section. The first step to tackle such questions is to brush up on the different possible directions that exist. The following diagram depicts all the eight possible directions:
Direction Sense
 

Points to keep in mind

  • Always consider yourself as facing North. The left side will be West, right side will be East.
  • Each direction change between the four main directions is equal to 900 in direction, whereas between the other four directions is 450.
  • A person facing north, on taking left will face towards west and on taking the right turn towards east.
  • A person facing west, on taking left will face towards south and on taking right turn towards north.
  • A person facing east, on taking left will face towards north and on taking the right turn towards south.
  • A person facing south, on taking left will face towards east and on taking the right turn towards west.

Clearly,

  • Whenever a person moves to his left side, he will move towards anti- clockwise direction.
  • Whenever a person moves to his right side, he will move towards clockwise direction.

Distance Questions

You should be able to do most questions that require you to find the distance, using the Pythagoras theorem, which states that in a right- angled triangle, Hypotenuse2 = Perpendicular2 + Base.

For instance, A man goes 3 kms East from point A and then takes a right turn from point B to move 4 kms to point C. What is the minimum distance between point A and point C?

The figure drawn for this question will be,

Direction Sense Questions

 

Mock Questions on Logical Reasoning

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