1. Which of the following expressions is true, if the given expression is true? P > A ≤ S < U = M ≥ B
A) A = B B) P > U C) M > A D) S < B E) None of these]
2. Statements: A ≤ M ≤ B = Q > E > S; M > U
Conclusions: I. Q ≥ A II. B > S
A) Only conclusion I is true B) Either conclusion I or II is true C) Only conclusion II is true D) Both conclusions I and II are true E) Neither conclusion I nor II are true
Explanation:
Statements: A ≤ M ≤ B = Q > E > S ...(i) M > U ...(ii)
From (i), we get
A ≤ Q or Q ≥ A.
Thus, conclusion I is true.
Again, B > S is true.
Hence both conclusions I and II are true.
Ans: D
3. Statements: I > S ≥ G = A ≤ U ≤ W; E ≤ A ≤ K
Conclusions: I. U ≥ E II. S > W
A) Only conclusion I is true B) Either conclusion I or II is true C) Only conclusion II is true D) Both conclusions I and II are true E) Neither conclusion I nor II are true
Explanation:
Statements: I > S ≥ G = A ≤ U ≤ W ...(i)
E ≤ A ≤ K ...(ii)
Combinng (i) and (ii), we get
E ≤ A ≤ U
Thus, E ≤ U or U ≥ E. Hence I is true.
Again we can't compare S and W.
Hence II (S > W) is not true.
Ans: A
4. Statements: C ≥ D > E ≤ F ≤ G < H
Conclusions: I. C ≥ G II. E < H
A) Only conclusion I is true B) Either conclusion I or II is true C) Only conclusion II is true D) Both conclusions I and II are true E) Neither conclusion I nor II are true
Explanation:
Statement: C ≥ D > E ≤ F ≤ G < H
Thus, we can't compare C and G. Hence I (C ≥ G) is not true.
Again, E < H is true.
Hence II is true.
Ans: C
5. Statements: i) I = J < K ii) J = L > M ≥ N iii) M > G ≤ T < U
Conclusions: I. I > N II. L > T
A) Only conclusion I follows. B) Only conclusion II follows. C) Both conclusions I and II follow. D) Either conclusion I or conclusion II follows. E) Neither of the conclusions follows.
Explanation:
For conclusion I: I > N
Combining statements i and ii: I = J = L > M ≥ N
As, “>”, is the highest priority sign in the combination so, “I > N”, is the true relation between I and N.
Hence, conclusion I follows.
For conclusion II: L > T
Combining statements II and III:
L > M > G ≤ T
As, sign between “L” and “T” are in different direction so, this conclusion does not follow.
Ans: A
6. Statements: i) B > C ≥ D = E ii) D < F = G > H ≥ I iii) G < L ≤ M
Conclusions: I. D ≤ M II. E < F
A) Only conclusion I follows. B) Only conclusion II follows. C) Both conclusions I an II follow. D) Either conclusion I or conclusion II follows. E) Neither of the conclusions follows.
Explanation: For conclusion I: D ≤ M
Combining statements ii and iii:
D < F = G < L ≤ M
As, “<”, is having highest priority, therefore, this conclusion does not follow.
For conclusion II: D < E
Combining statements i and ii E > C = D
As, “<”, is having highest priority, so the conclusion follows.
Ans: B
7. Statements: i) B = C ≤ Y ≤ Z ii) Q ≥ Y = A
iii) Y ≤ O < P > Q
Conclusions: I. Q > C II. Q = C
A) Only conclusion I follows. B) Only conclusion II follows. C) Both conclusions I and II follow. D) Either conclusion I or conclusion II follows. E) Neither of the conclusions follows.
Explanation: For conclusion I: Q > C
Combining statements i and ii: C ≤ Y ≤ Q
So, Q > C, does not follow.
For conclusion II: Q = C
Combining statements I and II: C ≤ Y ≤ Q
So, Q = C, does not follow.
Now, we can see that:
Both the objects of conclusions I and II are same i.e. ‘Q’ and ‘C’.
Both the conclusions I and II are wrong. On combining both the relations we get the actual relation i.e. Q ≥ C
So, Either conclusion I or conclusion II follows.
Ans: D
8. Statements: M = Q ≤ N ≤ W ≤ B, R ≥ S = O > Q
Conclusions: I. R > M II. O ≤ B
A) None follows. B) Only conclusion II follows. C) Either conclusion I or conclusion II follows. D) Only conclusion I follows. E) Both conclusion I and conclusion II follow.
Explanation: Given Statements: M = Q ≤ N ≤ W ≤ B, R ≥ S = O > Q
Conclusions: I. R > M II. O ≤ B
For Conclusion I, combining both the equations, we get
R ≥ S = O > Q = M ≤ N ≤ W ≤ B ........... (i)
We can observe that between R and M, the common sign of inequality is of '>' which confirms R > M which is given as conclusion I. For Conclusion II,
We can observe that between O and B the signs are getting reversed and hence we can't derive a definite conclusion between these two elements
. Conclusion II, hence, doesn't follow.
Ans: D
9. Statements: T ≤ E > R > W; N ≤ O < R = X
Conclusions: I. E ≥ N II. O < E
A) Only conclusion I follows B) Neither conclusion I nor conclusion II follows C) Only conclusion II follows
D) Either conclusion I nor conclusion II follows E) Both conclusions I and conclusion II follow
Explanation: Statements: T ≤ E > R > W; N ≤ O < R = X
Conclusions: I. E ≥ N II. O < E
Combining eq (i) and (ii) for the relation between E and N & O and E, we get E > R > O ≥ N and O < R < E
Common sign between E and N is of '>'. Thus, the given conclusion E ≥ N is not valid. Now, common sign between O and E (moving from O to E) is '<' and the given conclusion is O < E.
Ans: C