# Inequalities 9

Directions (1-5): In the given questions, assuming the given statements to be true. Find which of the given four conclusions numbered I, II, III and IV is/are definitely true and give your answer accordingly.
Q1. Statement: S > M ≥ D > H ≤ R ≤ T < W
Conclusions:
I. S > H
II. W > H
III. R < W
IV. M > T
(a) Only I, II and III are true.
(b) Only II is true.
(c) Only I and II are true.
(d) Only I and either II or IV are true.
(e) All I, II, III and IV are true.

1. Ans.(a)
Sol. Conclusions:
I. S > H (  True)
II. W > H(  True)
III. R < W(  True)
IV. M > T( Not True)

Q2. Statement: M > U > L ≤ N; L ≥ Y > A
Conclusions:
I. Y < N
II. M>N
III. N = Y
IV. M > A
(a) Only either II or III is true.
(b) Only IV and either I or III are true.
(c) Only IV is true.
(d) Only II is true.
(e) Only III is true.

2. Ans.(b)
Sol. Conclusions:
I. Y < N ( Not True)
II. M>N( Not True)
III. N = Y( Not True)
IV. M > A(  True)

Q3. Statement: J ≥ A > D = E; L < A < M
Conclusions:
I. M < J
II. J > L
III. D > L
IV. E < M
(a) Only II is true.
(b) Only I and III are true.
(c) None is true.
(d) Only II and IV are true.
(e) Only I and II are true.

3. Ans.(d)
Sol Conclusions:
I. M < J ( Not True)
II. J > L(  True)
III. D > L( Not True)
IV. E < M(  True)

Q4. Statement: Y > F ≤ O ≤ P; F ≥ U < T
Conclusions:
I. Y > P
II. T < F
III. O > T
IV. P < U
(a) Only I is true.
(b) Only II is true.
(c) Only III is true.
(d) None is true.
(e) Only I and IV are true.

4. Ans.(d)
Sol. Conclusions:
I. Y > P( Not True)
II. T < F( Not True)
III. O > T( Not True)
IV. P < U( Not True)

Q5. Statement: K ≤ O < M D = T;
Conclusions:
I. T < E
II. K > J
III. T > O
IV. E < M
(a) Only I is true.
(b) Only I and III are true.
(c) None is true.
(d) Only II and IV are true.
(e) Only I and II are true.

5. Ans.(a)
Sol Conclusions:
I. T < E (True)
II. K > J (Not True)
III. T > O (Not True)
IV. E < M (Not True)

Directions (6-7): Study the information carefully and answer the questions given below.
Six persons A, B, C, D, E and F are comparing their weights and each of them is having a different weight. D is heavier than only two persons. E is the only person heavier than F and lighter than D. C’s weight is less than only B’s weight. The third heaviest weight is 150kgs and the fifth heaviest weight is 110kgs.
Q6. What is the possible weight of D?
(a) 110kgs
(b) 100kgs
(c) 105kgs
(d) 125kgs