Reasoning Inequalities Practice Questions

Mentor for Bank Exams
Here are the questions on Reasoning Mathematical Inequalities for upcoming Banking exams like SBI PO/Clerk and other Banking Exams. This quiz contains important questions which match the pattern of SBI and other Banking Exams, so make sure you practice today’s SBI PO/Clerk Reasoning Quiz to enhance your preparation level.
Directions (1 – 10): In the following question assuming the given statements to be true, find which of the conclusion among given three conclusions is /are definitely true and then give your answers accordingly.
1. Statements: P = S; S < T; T ≤ U; Q ≤ U; U = A; B ≤ A
Conclusions:
I. Q > B
II. S ≤ A
III. A ≥ Q
a) None is true
b) Only I is true
c) Only II is true
d) Only III is true
e) All are true
2. Statement: S ≥ P > L < U ≤ N; P ≥ Y > G; M ≥ J ≥ N
Conclusions:
I.  S ≥ L 
II. L > Y
III. P > G                                   
IV. U ≤ J
V. P > J
a) Both conclusions III and conclusion IV are true.
b) Conclusion I, conclusion III and conclusion IV are true.
c) Both conclusion II and conclusion IV are true.
d) Conclusion II and Either conclusion I or conclusions III are true.
e) Only conclusion II is true.
3. Statement: D ≠ M ≠ P ≠ L = R = Q = W > F > K
Conclusions:
I.  D > L                                    
II. D < L
III. L < F       
IV. D > Q
V. P < K
a) Either conclusion I or conclusion IV is true.
b) Only conclusion I is true.
c) Either conclusion I or conclusion III is true.
d) Either conclusion I or conclusion II is true.
e) None of the conclusion is true.
4. Statements: A ≤ B < C > D ≥ E; B ≤ F < H; I ≤ K ≤ E
Conclusions:
I.  A ≤ C 
II. C < F
III. B < H                                   
IV. D ≥ K
V. B < K                                 
a) Only conclusions III and IV are true.
b) Conclusion I, III and IV are true.
c) Only conclusion II and IV are true.
d) Conclusion II and either conclusion I or III are true.
e) Only conclusion II is true.
5. Statements: M ≥ L ≤ J ≥Y; L > U > V > S; N ≤ G ≤ V > A
Conclusions:
I.  S > M
II. N < G
III. Y ≥ V
IV. M ≥ J
a) Only conclusion I is true.
b) Only conclusion II is true.
c) Only conclusion III is true.
d) Only conclusion IV is true.
e) None of conclusions I, II, III and IV are true.
6. Statement: B < X < M; C > V ≥ Z; M < V > N; X = L
Conclusion:
I. X < C
II. M < C
III. N > L
IV. B ≤ L
a) Both I and II are true
b) Only III is true
c) Only II is true
d) II, III and IV are true
e) None is true
7. Statement: G > O = I ≥ P; Q > S ≥ I ≥ T ≥ P; D > R < P
Conclusions:
I. D > P
II. S > I
III. R ≤ I
IV. D ≤ P
a) All are true
b) None is true
c) Both I and III are true
d) Only III is true
e) Either of I or IV is true
8. Statement: B > K ≥ S < A; F < K < L < D; C ≤ S < A < B
Conclusions:
I. C < L
II. F ≤ D
III. K > D
IV. F = C
a) Only I is true
b) Only III is true
c) Only IV is true
d) Both II and IV are true
e) None is true
9. Statements: C > O ≥ Q ≤ T ≤ N ≥ Y = R; I ≥ V ≥ E ≤ S ≤ R; R > L > A; K < G ≤ M > Q ≥ D
Conclusions:
I. T ≥ G
II. N > A
III. N > E
IV. N = E
a) None is true
b) Only II and either III or IV are true
c) Only II and III are true
d) Only III is true
e) Only III and IV are true
10. Statements: C < P ≤ A = I ≥ T > N; O ≥ L = E > A < D; V < S > I > R
Conclusions:
I. C < L
II. S ≥ N
III. O > R
IV. V > N
a) None is true
b) Only I and III are true
c) Only III and IV are true
d) Only I, III and IV are true
e) All are true

Solutions:
1. D) Given statements: P = S; S < T; T ≤ U; Q ≤ U; U = A; B ≤ A
On combining: P = S < T ≤ U = A ≥ B; Q ≤ U
Conclusions:
I. Q > B → False (as U = A ≥ B and Q ≤ U → Q ≤ U ≥ B → thus clear relation between Q and B cannot be determined)
II. S ≤ A → False (as S < T ≤ U = A → S < A)
III. A ≥ Q→ True (as U = A and Q ≤ U → A ≥ Q)
Therefore, only conclusion III is true.
2. A) Given statement: S ≥ P > L < U ≤ N; P ≥ Y > G; M ≥ J ≥ N
On combining: S ≥ P > L < U ≤ N ≤ J ≤ M; P ≥ Y > G
Conclusion:
I. S ≥ L → Not true as it is given that S ≥ P > L therefore S cannot be equal to L.
II. L > Y → True as it is given that Y ≤ P > L therefore there is no definite relation between them.
III. P > G → True as it is given that P ≥ Y > G.
IV. U ≤ J → True as it is given that U ≤ N ≤ J.
V. P > J → Not true as it is given that P > L < U ≤ N ≤ J.
Hence only conclusion III and conclusion IV follows.
3. D) Given statements: D ≠ M ≠ P ≠ L = R = Q = W > F > K
On combining: D >< M >< P >< L = R = Q = W > F > K
Conclusion:
 I. D > L → It may be possible as it is given that D >< M >< P >< L but D can be less than L as well.
II. D < L → It may be possible as it is given that D >< M >< P >< L but D can be greater than L as well.
III. L < F → Not true as it is given that L = R = Q = W > F.
IV. D > Q → Not true as it is given that D >< M >< P >< L = R = Q therefore there is not a definite relation between them
V. P < K → Not true as it is given that P >< L = R = Q = W > F > K therefore there is not a definite relation between them.
Conclusion I and conclusion II are complimentary to each other.
Hence either conclusion I or conclusion II is true.
4. A) Given statement:A ≤ B < C > D ≥ E; B ≤ F < H; I ≤ K ≤ E
On combining: A ≤ B < C > D ≥ E ≥ K ≥ I; B ≤ F < H
Conclusion:
I. A ≤ C → Falseas A ≤ B < C, thus A < C.
II. C < F → Falseas F ≥ B < C, therefore there is no definite relation between them.
III. B < H → True as B ≤ F < H, thus B < H.
IV. D ≥ K → True as D ≥ E ≥ K, thus D ≥ K.
V. B < K → False as B < C > D ≥ E ≥ K,there is no definite relation between them.
Hence only conclusion III and IV follows.
5. E) Given statements: M ≥ L ≤ J ≥ Y; L > U > V > S; N ≤ G ≤ V > A
On combining: M ≥ ≤ J ≥ Y, M ≥ > U > V > S, Y ≤ J ≤ > U > V ≥ G ≥ N
* Connector alphabets are shown by bold letter.
Conclusion: I. S > M → Not true as it is given that M ≥ L> U > V > S therefore M can be equal to S as well.
II. N < G → Not true as it is given that N ≤ G therefore they can be equal as well.
III. Y ≥ V → Not true because no clear relationship can be established between Y and V as Y ≤ J ≤ L > U > V.
IV. M ≥ J → not true because no clear relationship can be established between M and J as    M ≥ L ≤ J.
None of conclusions I, II, III and IV are true.
6. A) Given statement: B < X < M; C > V ≥ Z; M < V > N; X = L
On combination: B < X = L < M < V < C; V ≥ Z; V > N
Conclusion:
I. X < C → True (X = L < M < V < C, → X < C)
II. M < C → True (M < V < C, → M < C)
III. N > L → False (V > N; L < M < V, → relation between N and L cannot be determined)
IV. B ≤ L → False (B < X = L, → B < L, Strict inequality)
Conclusion I and II are true
7. E) Given statement: G > O = I ≥ P; Q > S ≥ I ≥ T ≥ P; D > R < P
On combining: R < P ≤ T ≤ I = O ≤ S < Q; I = O < G; R < D
Conclusions:
I. D > P → False (R < D; R < P, → relation between D and P cannot be determined)
II. S > I → False (I = O ≤ S, → I ≤ S, there is no strict relation between I and S) 
III. R ≤ I → False (R < P ≤ T ≤ I, → R < I, there is a strict relation between R and I)
IV. D ≤ P → False (R < D; R < P, → relation between D and P cannot be determined)
Conclusion I and IV form complementary pair.
8. A) Given statement:  B > K ≥ S < A; F < K < L < D; C ≤ S < A < B
On combining: B > K ≥ S; C ≤ S < A < B; F < K < L < D
Conclusions:
I. C < L → True (K ≥ S; C ≤ S, → K ≥ C & K < L → L > C)
II. F ≤ D → False (F < K < L < D, → F < D, there is strict relation between F and D)
III. K > D → False (K < L < D, → K < D)
IV. F = C → False (F < K; C ≤ K → No relation between F and C)
Conclusion I is true.
9. B) Given statements: C > O ≥ Q ≤ T ≤ N ≥ Y = R; I ≥ V ≥ E ≤ S ≤ R; R > L > A; K < G ≤ M > Q ≥ D
On combining: N ≥ Y = R > L > A; N ≥ Y = R ≥ S ≥ E
Conclusions:
I. T ≥ G → False (as Q ≤ T and G ≤ M > Q → G ≤ M > Q ≤ T thus clear relation between T and G cannot be determined)
II. N > A → True (as R > L > A and N ≥ Y = R → N ≥ Y = R > L > A → N > A)
III. N > E → True (as N ≥ Y = R and E ≤ S ≤ R → N ≥ Y = R ≥ S ≥ E → N ≥ E → thus either N > E or N = E is true)
IV. N = E → True (as N ≥ Y = R and E ≤ S ≤ R → N ≥ Y = R ≥ S ≥ E → N ≥ E → thus either N > E or N = E is true)
Therefore, only conclusions II and either conclusion III or IV are true.
10. B) Given statements: C < P ≤ A = I ≥ T > N; O ≥ L = E > A < D; V < S > I > R
On combining: C < P ≤ A < E = L; S > I ≥ T > N; O ≥ L = E > A = I > R; L = E > A ≥ P > C
Conclusions:
I. C < L → True (as C < P ≤ A and L = E > A → C < P ≤ A < E = L → C < L)
II. S ≥ N → False (as I ≥ T > N and S > I → S > I ≥ T > N → S > N)
III. O > R → True (as I > R, A = I and O ≥ L = E > A → O ≥ L = E > A = I > R → O > R)
IV. V > N → False (as V < S > I and I ≥ T > N → V < S > I ≥ T > N → thus clear relation between V and N cannot be determined)
Therefore, only conclusion I and conclusion III are true.