# Inequalities Set 14

Directions (1-5): In each of these questions the symbols @, #, \$, % and * are used with different meanings as follows.
I. ‘P @ Q’ means ‘P is not smaller than Q’.
II. ‘P # Q’ means ‘P is not greater than Q’.
III. ‘P \$ Q’ means ‘P is neither smaller than nor greater than Q’.
IV. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
V. ‘P * Q’ means ‘P is neither greater than nor equal to Q’.
In each question, four statements showing relationships have been given, which are followed by four conclusions I, II, III and IV. Assuming that the given statements are true, find out which conclusion(s) is/are definitely true.
Q1. Statements: M # N, N * O, O @ P, P \$ Q
Conclusions:
I. Q * O
II. Q # O
III. M * O
IV. Q \$ M
(a) I and III are true
(b) II and III are true
(c) III and IV are true
(d) I and II are true
(e) None of the above

1. Ans.(b)
Sol. M ≤ N < O ≥ P = Q

Q2. Statements: A \$ B, B @ C, C % D, E * D
Conclusions:
I. A @ C
II. E * B
III. B % D
IV. A % D
(a) None is true
(b) I and II are true
(c) II and III are true
(d) I, II and III are true
(e) All are true

2. Ans.(e)
Sol. A = B ≥ C > D > E

Q3. Statements: A @ B, B * C, C # D, D % E
Conclusions:
I. B % E
II. A @ D
III. B # E
IV. A * D
(a) Either I or III is true
(b) Either II or IV is true
(c) II and III are true
(d) Either I or III and either II or IV are true
(e) None is true

3. Ans.(d)
Sol. A ≥ B < C ≤ D > E

Q4. Statements: A % B, B # C, C @ D, D \$ E
Conclusions:
I. C % E
II. A @ C
III. A * C
IV. B \$ D
(a) Either II or III is true
(b) Only I is true
(c) Only IV is true
(d) I and II are true
(e) None of the above

4. Ans.(a)
Sol. A > B ≤ C ≥ D = E

Q5. Statements: T % U, U @ V, V * Z, Z # X
Conclusions:
I. T @ V
II. T % V
III. X @ V
IV. X % V
(a) I and III are true
(b) II and III are true
(c) II and IV are true
(d) All are true
(e) None of these

5. Ans.(c)
Sol. T > U ≥ V< Z ≤ X

Q11.Which of the following expressions will be true if the expression Z> O = Y> S
(a) O >C
(b) Z>S
(c) C>Y
(d) S = O
(e)C

6. Ans.(b)
Sol. Z>S

Q12.Which of the following symbols should replace the question mark (?) in the given expression in order to make the expressions B>A as well as U≤V definitely true?
B>V? A ≥ N = U
(a) ≤
(b) >
(c) <
(d)≥
(e)Either ≤ or <

7. Ans.(d)

Q13.Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that makes the expression Y>Z as well as X≤W definitely true?
Y _ W _ O _ Z _ X
(a) =, =, ≥, ≥
(b) >, ≥, =, >
(c) >, <, =, ≤
(d)>, =, =, ≥
(e)>, =, ≥, >

8. Ans.(d)

Q14.Which of the following should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that makes the expression Z
_ ≤ _ < _ > _
(a) L, N, X, Z
(b) L, Z, X, N
(c) Z, L, X, N
(d) N, Z, X, L
(e)X, N, Z, L

9. Ans.(e)

Q15.Which of the following symbols should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that makes the expression A>B and C>E definitely false?
A _ O _ C _ B _ E
(a) <, <, >, =
(b) <, =, =, >
(c) <, =, =, <
(d) ≥, =, =, ≥
(e)>, >, =, <