Inequalities Set 16

Q1. 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
Q2. 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
Q3. 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) M < Q
(d) T = M
(e) None is true
Directions (4-7): In the following questions, the symbols @, ©, # $ and % are used with the following meanings.
‘P @ Q’ means ‘P is neither smaller than nor equal to Q’.
‘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 not smaller than Q’.
Now, in each of the following questions assuming the given statements to be true, find which of the three conclusions I, II and III given below them is/are definitely true and mark your answer accordingly.
Q4. Statements: L @ W, M # W, M % J
Conclusions: 
I. M © L
II. W % J
III. L @ J
(a) None follows
(b) Only I follows
(c) II and III follow
(d) Only III follows
(e) None of these
Q5. Statements: N © B, B $ T, T # S
Conclusions: 
I. N # S
II. S @ B
III. T % N
(a) None follows
(b) I and II follow
(c) I and III follow
(d) II and III follow
(e) All follow
Q6. Statements: G @ H, H % K, K # D
Conclusions: 
I. D $ H
II. D # H
III. D % H
(a) Only I follows
(b) Only II follows
(c) Either II and III follows
(d) Only III follows
(e) None of these
Q7. Statements: F # D, D © K, R @ K
Conclusions: 
I. F # K
II. R % D
III. R @ F
(a) I and II follow
(b) I and either II or III follow
(c) Either II and III follows
(d) I and III follow
(e) All of these
Directions (8-10): 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.
Q8. Statements: F ≥ M > A > R > E
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) Only either II or III follows
(e) All follow
Q9. Statements: A ≥ B> M > D=F
Conclusions: I. B > D
II. B < A
III. M > F
(a) All follow
(b) Only I & III follow
(c) Only II and III follow
(d) Only either II or III follows
(e) Only III follows
Q10. Statements: P ≤ Q =R < S≤T
Conclusions: I. Q ≤ T
 II. T > Q
III. P > S
(a) All follow
(b) Only I & II follow
(c) Only II and III follow
(d) Only either I or II follows
(e) Only II follows
Directions (11-15): In these questions, the symbols @, #, $, * and © are used with different meanings as follows.
‘A @ B’ means ‘A is smaller than B.’
‘A # B’ means ‘A is either smaller than or equal to B’.
‘A $ B’ means ‘A is greater than B.’
‘A * B’ means ‘A is either greater than or equal to B.’
A © B’ means ‘A is neither greater than nor smaller than B.’
In each question, three statements showing relationships have been given, which are followed by two Conclusions I and II. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true.
(a) If only Conclusion I is true
(b) If only Conclusion II is true
(c) If either Conclusion I or Conclusion II is true
(d) If neither Conclusion I nor Conclusion II is true
(e) If both Conclusion I and II are true
Q11. Statements: H # Q, Q @ F, L $ F
Conclusions:
I. L $ H
II. H # F
Q12. Statements: J $ T, T @ V, V # M
Conclusions:
I. T # M
II. J © M
Q13. Statements: U # D, D @ R, R © T
Conclusions:
I. U @ R
II. T $ D
Q14. Statements: M * L, L $ K, K @ R
Conclusions:
I. M * R
II. M @ R
Q15. Statements: J @ N, N © W, W $ V
Conclusions:
I. J © V
II. J @ W

Answers

1. Ans. (c)
2. Ans. (e)
3. Ans. (e)

Solutions (4-7):
4. Ans.(d)
Sol.
I. M © L ( Not True)
II. W % J( Not True)
III. L @ J(  True)

5. Ans.(e)
Sol.
I. N # S(  True)
II. S @ B(  True)
III. T % N( True)

6. Ans.(c)
Sol.
I. D $ H( Not True)
II. D # H( Not True)
III. D % H( Not True)

7. Ans.(d)
Sol.
I. F # K( True)
II. R % D( Not True)
III. R @ F( True)

Solutions (8-10):8. Ans.(b)
Sol.
I. M > E (true)
II. F > E   (true)
III. F < E (false)

9. Ans.(b)
Sol.    
I. B > D (true)
II. B < A (false)
III. M > F   (True)

10.Ans.( e)
Sol. 
I. Q ≤ T (False)
II. T > Q ( True)
III. P > S ( False)

Solutions (11-15):

> = $
<[email protected]
≤=#
≥= *
==©
11. Ans.(a)
Sol. H ≤Q
12. Ans.(d)
Sol. J>T
13. Ans.(e)
Sol. U≤D
14. Ans.(c)
Sol. M≥L>K
15. Ans.(b)
Sol. JV

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