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Home / Reasoning Ability / Reasoning: Inequality Questions For Upcoming Exams # Reasoning: Inequality Questions For Upcoming Exams

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given five conclusions is/are definitely true and then give your answers accordingly.

Ques.1: Statements:

M ≥ O = N; I ≥ G > R; N > Z; Z ≥ I

Conclusions:

I. R < I
II. O < Z
III.  Z < M
IV. G ≤ Z
V. M = N

1.Both conclusions I and II are true.
2.Conclusion I, III and IV are true.
3.Both conclusion III and IV are true.
4.Either conclusion I or III is true.
5.Only conclusion V is true
Given statements: M ≥ O = N; I ≥ G > R; N > Z; Z ≥ I
On combining: M ≥ O = N > Z ≥ I ≥ G > R
Conclusion:
I. R < I → True as it is given that I ≥ G > R.
II. O < Z → Not true as it is given that O = N > Z
III. Z < M → True as it is given M ≥ O = N > Z.
IV. G ≤ Z → True as it is given that Z ≥ I ≥ G,
V. M = N → Not true as it is given that M ≥ O = N therefore N can be smaller than M as well.
Hence, conclusion I, III and IV are true.
Ques.2: Statements: T < S; S ≤ U; L > U; R ≥ U

Conclusions:

I. R ≥ S
II. L > S
III. T < U

1.Only III is true
2.Only I is true
3.Only I and III are true
4.Either II or III is true
5.All are true
Given statements: T < S; S ≤ U; L > U; R ≥ U
On combining: T < S ≤ U < L; T < S ≤ U ≤ R
Conclusions:
I. R ≥ S → True (as T < S ≤ U ≤ R → R ≥ S)
II. L > S → True (as S ≤ U < L → L > S)
III. T < U → True (as T < S ≤ U → T < U)
Therefore, all conclusions are true.
Ques.3: Statements: A ≤ K; K > P; P = O

Conclusions:

I. A ≥ P
II. K > O
III. O > A

1.Only III is true
2.Only I and II are true
3.Only II is true
4.None is true
5.All are true
Given statements: A ≤ K; K > P; P = O
On combining: A ≤ K > P = O
Conclusions:
I. A ≥ P → False (as A ≤ K > P → thus clear relation between A and P cannot be determined)
II. K > O → True (as K > P = O)
III. O > A → False (as A ≤ K > P = O → thus clear relation between A and O cannot be determined)
Therefore, only conclusion II is true.

Directions(Q4-Q8): In the following questions, the symbols \$, %, *, & and © are used with the following meaning as illustrated below:

‘A % B’ means ‘A is greater than B’.

‘A \$ B’ means ‘A is not greater than B’.

‘A * B’ means ‘A is neither greater than nor equal to B’.

‘A & B’ means ‘A is either greater than or equal to B’.

‘A © B’ means ‘A is neither smaller than nor greater than B’.

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

Ques.4: Statements:

R * A, A \$ M, P & M, M \$ C

Conclusions:

I. P % R
II. A \$ P
III. P % C

1.Only Conclusion I is true.
2.Both Conclusions I and II are true.
3.Either Conclusion I or III is true.
4.Neither Conclusion I nor III is true.
5.Either Conclusions I or II and III are true.
According to the given information,
R * A, A \$ M, P & M, M \$ C
→ R < A, A ≤ M, P ≥ M, M ≤ C
→ P ≥ M ≥ A > R and C ≥ M ≥ A > R
Conclusions:
I. P % R ⇒ P > R (True)
II. A \$ P ⇒ A ≤ P (True)
III. P % C ⇒ P > C (Can’t be determined since P ≥ M and C ≥ M)
Hence, both the conclusions I and II follow.

Ques.5: Statements:

A \$ S © D, Z & X © A, C % S

Conclusions:

I. S % Z
II. D * C
III. X * C

1.Only Conclusion I is true.
2.Both Conclusions II and III are true.
3.Either Conclusion II or III is true.
4.Neither Conclusion I nor III is true.
5.Either Conclusions I or II and III are true.
A \$ S © D, Z & X © A, C % S
→ A ≤ S = D, Z ≥ X = A, C > S
→ Z ≥ X = A ≤ S = D < C
Conclusions:
I. S % Z ⇒ S > Z → false (as Z ≥ X = A ≤ S → relation between S and Z cannot be established)
II. D * C ⇒ D < C → true
III. X * C ⇒ X < C → true
Hence both the conclusion II and III follows.

Ques.6: Statements:

F © G, F % H & V, B \$ H

Conclusions:

I. F % V
II. G © H
III. V % B

1.Only Conclusion I is true.
2.Both Conclusions I and II are true.
3.Either Conclusion I or III is true.
4.Neither Conclusion I nor III is true.
5.Either Conclusions I or II and III are true.
Statement:
F © G, F % H & V, B \$ H
→ F = H, F > H ≥ V, B ≤ H
→ G = F > H ≥ V, B ≤ H
Conclusions:
I. F % V ⇒ F > V → true
II. G © H ⇒ G = H → false (as G = F > H → G > H)
III. V % B ⇒ V > B → false (as H ≥ V and B ≤ H → B ≤ H ≥ V → relation between V and B cannot be established)
Hence only conclusion I follows.
Ques. 7: Statements:

E % J; J & H; H © D; D \$ C; D % F

Conclusions:

I. E % C
II. F * E
III. J % F

1.Only Conclusion I is true.
2.Both Conclusions I and II are true.
3.Both Conclusions II and III are true.
4.Neither Conclusion I nor III is true.
5.Either Conclusions I or II and III are true.
Statements:
E % J; H © D; D \$ C; D % F; J & H
→ E > J; H = D; D ≤ C; D > F; J ≥ H
→ E > J ≥ H = D > F ≤ C
Conclusions:
I. E % C ⇒ E > C → False (as E > J ≥ H → E > H and H = D → E > D and D ≤ C → thus clear relation between E and C cannot be determined)
II. F * E ⇒ F < E → True
III. J % F ⇒ J > F → True
Therefore, only conclusions II and III are true.

Ques. 8: Statements:

Z © Y; Y & V; W % V; W \$ R

Conclusions:

I. W & Y
II. R % V
III. V \$ Z

1.Only Conclusion I is true.
2.Both Conclusions I and II are true.
3.Both Conclusions II and III are true.
4.Neither Conclusion I nor III is true.
5.Either Conclusions I or II and III are true.
Statements:
Z © Y; Y & V; W % V; W \$ R
→ Z = Y; Y ≥ V; W > V; W ≤ R
→ Z = Y ≥ V < W ≤ R
Conclusions:
I. W & Y ⇒ W ≥ Y → False (as Y ≥ V < W → thus clear relation between W and Y cannot be determined)
II. R % V ⇒ R > V → True
III. V \$ Z ⇒ V ≤ Z → True
Therefore, only conclusions II and III are true.

Ques.9: Statements: 6 < 2; 5> 2; 7 = 6; 8 > 6

Conclusions:

I. 8 > 7
II. 8 > 5
III. 6 > 2

1.None is true
2.Only I is true
3.Only II is true
4.Only III is true
5.All are true
Given statements: 6 < 2; 5 > 2; 7 = 6; 8 > 6
On combining: 5 > 2 > 6 = 7 < 8
Conclusions:
I. 8 > 7→ True (as 8 > 7)
II. 8 > 5→ False (as 8 > 7 < 5 → No direct relationship between 5 & 8 can be obtained)
III. 6 > 2→ False (as 2 > 6)
Therefore, only conclusion 1 is true.

Ques.10: Statements: \$ < @; @ > %; % = &; &< 4

Conclusions:

I. \$ ≥ 4
II. @ >&
III. 4 > %

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