# Inequalities Set 15

Directions (1-5): In the following questions, the symbols \$, @, %, & and # are used with the following meanings as illustrated below:
‘A \$ B’ means A is neither greater nor smaller than B
‘A @ B’ means A is neither greater than nor equal to B
`A % B’ means A is neither smaller than nor equal to B
‘A& B’ means A is not smaller than B
‘A # B’ means A is not greater than B
In each of the following questions, assuming the given statements to be true, find out which of the two conclusions I and II given below them is/are definitely true. Give answer
a) if only conclusion I is true.
b) if only conclusion II is true.
c) if either conclusion I or II is true.
d) if neither conclusion I nor II is true.
e) if both conclusions I and II are true.
Q1.Statements: W&P, P %G, G @ I, I # N
Conclusions: I. N%W II. N # W
Q2.Statements: U @ D, D \$ E, E % Y, Y& W
Conclusions: I. U @ Y II. W %D
Q3.Statements: Z % N, N # K, K \$ M, M @ R
Conclusions: I. M \$ N II. M% N
Q4.Statements: V&D, D %T, K \$ T, K # F
Conclusions: I. V% F II. V% K

Q5.Statements: S \$ Q, Q @ B, B &K, K # W
Conclusions: I. W%K II. S @ B

1. Ans.(c)
Sol. Conclusions: I. N%W( Not True)  II. N # W (Not true)
2. Ans.(d)
Sol. Conclusions: I. U @ Y( Not true)  II. W %D ( Not true)
3. Ans.(c)
Sol.Conclusions: I. M \$ N ( Not true) II. M%  N (Not true)

4. Ans.(b)
Sol.  I. V% F( Not true) II. V% K ( true)
5. Ans.(b)
Sol. Conclusions: I. W%K ( Not true) II. S @ B (True)

Directions (6-10): In these questions, relationship between different elements is shown in thestatements. These statements are followed by two conclusions:
(a) If only conclusion I follows.
(b) If only conclusion II follows.
(c) If either conclusion I or II follows.
(d) If neither conclusion I nor II follows.
(e) If both conclusion I and II follow.

Q6. Statements: A ≤ D < C ≥ B < E
Conclusion:
I. C > A
II. A ≥ C
Q7. Statements: P > L ≤ M < N > Q
Conclusion:
I. P > Q
II. Q > M
Q8. Statement: S ≥ T = U < V ≥ X
Conclusions:
I. V > S
II. V > T
Q9. Statement: M ≤ N > O ≥ P = Q
Conclusions:
I. M ≥ Q
II. Q < M

Q10. Statement: U ≤ V < W =X < Y
Conclusions:
I. Y > V
II. W > U

6. Ans.(a)
Sol. Conclusion:
I. C > A (  True )
II. A ≥ C( Not True )
7. Ans.(d)
Sol. Conclusion:
I. P > Q( Not True )
II. Q > M( Not True )
8. Ans.(b )
Sol. Conclusions:
I. V > S( Not True )
II. V > T( True )
9. Ans.(d)
Sol.Conclusions:
I. M ≥ Q( Not True )
II. Q < M( Not True )
10. Ans.(e)
Sol. Conclusions:
I. Y > V(  True )
II. W > U( True )

Q11. In which of the following expressions will the expression ‘H < J’ be definitely true?
(a) G < H ≥ I = J
(b) H > G ≥ I = J
(c) J = I ≥ G > H
(d) H ≥ G > I < J
(e) None of these
Q12. Which of the following expressions will be true if the expression ‘K ≥ L > M ≥ N’ is definitely true?
(a) N ≤ K
(b) K = M
(c) K < N
(d) L ≥ N
(e) None is true
Q13. Which of the following expressions will be true if the expression ‘M ≥ K < T = Q’ is definitely true?
(a) Q < K
(b) M ≥ T
(c) K < Q
(d) T = M
(e) None is true

11. Ans.(c)
Sol.  J = I ≥ G > H
12. Ans.(e)
Sol. None is true
13. Ans.(c)
Sol. K < Q

Directions (14-15): In each question, four statements showing relationship have been given, which are followed by three conclusions I, II and III. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true.
Q14. Statements: F ≥  M, M> A, R< A, E > R
Conclusions: I. M>  E
II. F ≥ E
III. F<  E
(a) Only I follows
(b) Only I & II follow
(c) Only II and III follow
(d) either II or III follows
(e) All follow
Q15. Statements: A ≥ B, M >B, D<  M, F =D
Conclusions: I. B > D
II. B < A
III. M> F
(a) All follow
(b) Only I & II follow
(c) Only II and III follow
(d) Only either II or III follows
(e) Only III follows