﻿ Verbal Reasoning Based on Binary Logic - Binary Logic - Verbal Reasoning - How to Prepare for Verbal Ability and Reading Comprehension for the CAT ﻿

## How to Prepare for Verbal Ability and Reading Comprehension for the CAT (2014)

### Chapter 4. Verbal Reasoning Based on Binary Logic

These question types are called binary logic questions simply because each question contains two logic streams that have to be matched, in order to get to the correct answer. Mainly, there are two types of questions as below:

BINARY LOGIC QUESTION — PATTERNS

Type 1

In this question type, three people speak two statements each—one of which is true, the other is false.

The two logic streams to be considered are:

1.The logic of the Statements, i.e., the logic of what is said within the statements.

2.The logic of the Basic Conditions, i.e., the logic of the fact that if one sentence is taken as true, the other will be false automatically.

The process of solving these questions is best illustrated through an example.

Gauri Islands is the name of an island. The inhabitants of this island always answer any question with two sentences. One of which is always true and the other always false.

Milly, Silly and Dilly are the three daughters of the chief whip of this island. Out of them, two are minor and one is of a marriageable age. You have been caught as an intruder on the island and you have two options given by the chief whip: identify his daughter who is of marriageable age. If you do so, you can have the privilege of marrying her and becoming the new chief whip in the future. On the other hand, if you cannot, you will be executed. Only Silly has dentures in her teeth. On questioning the three daughters, these are the answers you get:

Milly: “I am shorter than Silly. The girl of marriageable age has dentures in her teeth “

Silly: “I am shorter than Milly. Dilly is the one who is of a marriageable age.”

Dilly: The girl of marriageable age is amongst the three of us. I am of a marriageable age”.

Who is the girl of marriageable age?

 (a) Milly (b) Dolly (c) Silly (d) Can’t say

In the above question, you should see that, the first statement of Dilly has to be correct (By Logic of the statement—If you evaluate what the statement is saying, it is clear that it has to be true. It can be easily understood that the girl of marriageable age is amongst the three of the girls.)

In this case, if this statement is true, then Dilly’s second statement is automatically false. Further, since Dilly’s second statement is false, Silly’s second statement will also be false. (By evaluating the sentence logic—as both these statements are saying the same thing.) Hence, Silly’s first statement will be true (Basic Condition logic) and hence further, Milly’s first statement will be false ( It is saying the opposite of Silly’s true first statement—Statement Logic). Hence, Milly’s second statement has to be true. Hence, Silly has to be the one of marriageable age.

Practice Exercises

Type 1

Type 2

In this type of questions, we have two types of people: those who always speak the truth, and those who always lie. These questions are also classified as Binary Logic questions since they are solved on the basis of two logical streams that run parallel to each other, viz: Basic Condition Logic (BCL) and Logic of the Statements(LoS).

The Basic Condition Logic flows from the fact that if a person always speaks the truth, then whatever statement he says must be true. However, in some cases, a clash might arise between the Basic Condition Logic and the Statement Logic, if it can be seen that the statement is obviously false.

The best way to understand this question type is by looking at an example:

You meet three inhabitants—Rohit, Mohit and Sohit—standing together. You ask Rohit “Are you a type X or type Y?” He mumbles something, which you cannot catch, so you ask Mohit, “What did Rohit say?” Mohit replies “Rohit said that he is type Y.” You look at Sohit and he says, “Do not believe Mohit, he is lying.”

Which of the following is true?

1.Rohit is a type X.

2.Mohit is a type Y.

3.Sohit is a type Y.

4.All of these.

By BCL, Sohit could be Type X or Type Y:

If Sohit is Type Y, his statement must be false. That means Mohit is not lying. Hence, Mohit should be Type X and hence his statement must be true, i.e., Rohit must have said that he is Type Y.

However, if you look at Rohit, he could not have made this statement in either case.

If we assume that Rohit is Type X, he would only speak the truth and he would then say that he is Type X, not that he is Type Y.

On the other hand, if we were to assume that Rohit is a Type Y, he would only speak false. But then he could not have said that he is Type Y, since that statement would be true.

Direction for Questions 1 to 4: The following questions are based on an island called Gutar Goo on which there are only two kinds of inhabitants:

Type X: people who always speak the truth; and

Type Y: people who always lie.