Inequalities — Direct & Coded — Practice

Question 1

Statement: A > B ≥ C = D < E. Conclusions: (I) A > C  (II) A > E. Which follow?
(a) Only I  (b) Only II  (c) Both  (d) Neither

Accepted Answer

(I) A > B ≥ C is unbroken with a strict link ⇒ A > C follows. (II) The chain to E reverses (D < E) ⇒ broken, no relation.

Answer: (a) Only I.

Question 2

Statement: P ≥ Q = R. Conclusions: (I) P > R  (II) P = R. Which follow?
(a) Only I  (b) Only II  (c) Either I or II  (d) Neither

Accepted Answer

P ≥ Q = R ⇒ P ≥ R, i.e. either P > R or P = R. Complementary and exhaustive.

Answer: (c) Either I or II.

Question 3

Statement: M < N > O ≥ P. Conclusion: M < P. Does it follow?
(a) Follows  (b) Does not follow  (c) Either/or  (d) M = P

Accepted Answer

M < N then N > O — signs oppose at N ⇒ no relation between M and P.

Answer: (b) Does not follow.

Question 4

Statement: A ≥ B ≥ C. Conclusion: A > C. Does it follow?
(a) Follows  (b) Does not follow  (c) Only if B > C  (d) A = C

Accepted Answer

No strict '>' link exists, so the result is only A ≥ C. A > C is not guaranteed (A could equal C).

Answer: (b) Does not follow.

Question 5

Code: X @ Y = X ≥ Y; X © Y = X < Y. Statement: A @ B @ C © D. Conclusion: A ≥ C. Does it follow?
(a) Follows  (b) Does not follow  (c) Either/or  (d) A < C

Accepted Answer

Decode: A ≥ B ≥ C < D. A ≥ B ≥ C ⇒ A ≥ C (no strict link).

Answer: (a) Follows.

Question 6

Statement: L ≤ M < N = O. Conclusions: (I) L < O  (II) N ≥ L. Which follow?
(a) Only I  (b) Only II  (c) Both  (d) Neither

Accepted Answer

L ≤ M < N = O: (I) L ≤ M < N ⇒ L < N = O ⇒ L < O follows (strict link present). (II) N = O and N > M ≥ L ⇒ N > L ⇒ N ≥ L follows. Answer: (c) Both.

Practice — Inequalities — Direct & Coded

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities