Reasoning Ability: Concepts of Inequality with Examples: Part 2

Read Type 1 and Type 2 in Concepts of Inequality Part 1

TYPE-3

Let’s first see the basic structure of these types of questions.

In the following questions, the symbols @, #, $, * and % are used as illustrated below:
‘P @ Q’ means ‘P is not smaller than Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P $ Q’ means ‘P is neither smaller than nor greater than Q’
‘P * Q’ means ‘P is not greater than Q’‘P % Q’ means ‘P is neither smaller than nor equal to Q’

Give answer

(1) if only Conclusion I is true.
(2) if only Conclusion II is true.
(3) if either Conclusion I or II is true.
(4) if neither Conclusion I nor II is true.
(5) if both Conclusions I and II is true.

Statements: N % A, A # L, F $ N
Conclusions: 

 I. L % F 

II. F % A

HOW TO SOLVE THESE TYPES OF QUESTIONS?

First of all on a separate place write down the meaning of the symbols. For e.g. in the above question:

@→ ≥

# → <

$ → =

* → ≤

% → >

Similarly write down the equation as per the meaning of the symbols. For e.g.
Statement: F = N > A < L
Conclusions: 

 I. L > F 

 II. F > A

Now follow the basic rules that we follow in the simple questions. So in accordance with the rules we get Answer (2) i.e. only Conclusion II is true.
I hope u have so far understood the concept and now let’s practice together.

Exercise with Answers

Ques 1

Statements: B * D, D $ M, F % M
Conclusions: 

 I. B # M 

 II. F % B
Answer (2): only Conclusion II is true

Ques 2

Statements: M $ K, D * K, R # K
Conclusions: 

 I. D $ M 

 II. M % D
Answer (3): either Conclusion I or II is true

Ques 3

Statements: E $ A # D @ B % F $ C
Conclusions: 

 I. E # B 

 II. C # D
Answer (2): only Conclusion II is true

Ques 4

Statements: P % T $ U * W; Q @ R @ W
Conclusions: 

I. T $ R 

II. U # R
Answer (4): neither Conclusion I nor II is true

Ques 5

Statements: R @ S % W $ X; Y * R $ P
Conclusions: 

I. P % X 

II. Y * X
Answer (1): only Conclusion I is true

Directions: In the following questions, the symbols @, #, % $ and © are used with the following meaning as illustrated below:
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P © Q’ means ‘P is neither equal to nor smaller than Q’
‘P % Q’ means ‘P is neither smaller than nor greater than Q’
‘P $ Q’ means ‘P is not smaller than Q’
‘P @ Q’ means ‘P is not greater than Q’

Ques 1. 

Statements: R @ D, D © W, B $ W
Conclusions: 

I. W # R 

II. B © D 

III. W $ R

Options

1. None is true 
2. Only I is true
3. Only III is true
4. Only either I or III is true
5. All are true

Ques 2.

Statements: H $ V, V % M, K © M

Conclusions: 

I. K © V 

II. M @ H 

III. H © M
Options

1. Only I and III are true
2. Only II and III are true 
3. Only I and II are true
4. All are true
5. None of these

Ques 3

Statements: K # T, T $ B, B @ F
Conclusions: 

I. F $ T 

II. K # B 

III. T $ F
Options

1. None is true
2. Only I is true 
3. Only I and II are true
4. Only II and III are true
5. All are true

Answers

1. (4) only either I or III is true

2. (3) only I and II are true
3. (1) None is true

In the following questions, the symbols ©, #, @, £, and $ are used with the following meaning as illustrated below:
‘P © Q’ means ‘P is not greater than Q’
‘P # Q’ means ‘P is neither greater than nor equal to Q’
‘P @ Q’ means ‘P is neither greater than nor smaller than Q’
‘P £ Q’ means ‘P is neither smaller than or equal to Q’
‘P $ Q’ means ‘P is not smaller than Q’

Now in each of the following questions assuming the given statements to be true, find which of the conclusions given below them are definitely true?

Ques 1

Statements: A £ N, S $ N, S £ W, W © R
Conclusions: I. R $ A II. S £ R III. S £ A IV. W © A
Options

1. Only I and II are true
2. Only II, III and IV are true
3. None is true
4. All I, II, III and IV are true
5. None of these

Ques 2

Statements: D # E, E © T, T @ C, C # A
Conclusions: I. D # A II. C © D III. A £ E IV. T # A
Options

1. Only I, III and IV are true
2. Only I, II and IV are true
3. Only I, II and III are true
4. Only I and III are true
5. All I, II , III and IV are true

Ques 3

Statements: O $ B, B @ S, S # E, E © R
Conclusions: I. S © O II. R £ S III. B # R IV. B # E
Options

1. Only I and II are true
2. Only III is true
3. Only I, III and IV are true
4. All I, II, III, IV are true
5. Only III and IV are true

Ques 4

Statements: D © S, S £ P, P $ I, P @ T
Conclusions: I. P # D II. P $ T III. T # S IV. I © D
Options

1. Only I and III are true 
2. Only III is true
3. Only III and IV are true 
4. Only II, III and IV are true 
5. Only I, III and IV are true

Answers

1. (3) None is true
2. (1) Only I, III and IV are true
3. (4) All I,II, III and IV are true
4. (2) Only III are true