Consider the following statements : I. If A ≤ B > C < D > E > F ≥ G = H; then B is always greater than E. II. If P > Q = R ≥ S = T ≤ U = V > W; then S is always less than V. Which of the statements given above is/are correct ?

(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II ✓ UPSC's answer

Why the answer is (d)

• In Statement I, the chain is A ≤ B > C < D > E > F ≥ G = H. The relationship between B and E cannot be definitively established because the inequality signs between them (B > C < D > E) do not form a continuous path of the same direction; B could be greater than, less than, or equal to E depending on the specific values. Therefore, B is not always greater than E, making Statement I incorrect. In Statement II, the chain is P > Q = R ≥ S = T ≤ U = V > W. The relationship between S and V is S = T ≤ U = V, which implies S ≤ V. This means S can be less than or equal to V, not strictly always less than V. Therefore, Statement II is also incorrect. Since both statements are incorrect, the correct option is (d).

Why the other options are wrong

(a) I only: Statement I is incorrect because the relationship between B and E is indeterminate due to the mixed inequality signs (B > C < D > E).
(b) II only: Statement II is incorrect because S can be equal to V (since S = T ≤ U = V), so it is not always strictly less than V.
(c) Both I and II: Both statements are incorrect, so the option claiming both are correct is invalid.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.