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 above is/are correct?

1. A. I only
2. B. II only
3. C. Both I and II
4. D. Neither I nor II

Answer: D

Explanation

Let’s analyze each statement:

Statement I: If A ≤ B > C E > F ≥ G = H; then B is always greater than E.
To determine the relationship between B and E, we look at the chain B > C E. The inequality signs change direction (from ‘>’ to ”). When the signs change direction like this, a definite relationship between the two variables (B and E) cannot be established. B could be greater than E, less than E, or equal to E, depending on the specific values. For example:
– If B=10, C=5, D=12, E=6: B > E (10 > 6)
– If B=10, C=5, D=12, E=11: B < E (10 Q = R ≥ S = T ≤ U = V > W; then S is always less than V.
To determine the relationship between S and V, we look at the chain S = T ≤ U = V. This simplifies to S ≤ V. This means S can be either less than V (S < V) or equal to V (S = V). The statement claims that S is *always* less than V. This is not true because the possibility of S = V exists. For example, if S=5, T=5, U=5, V=5, then S=V, not S<V.
Since S is not *always* less than V, Statement II is incorrect.

As both statements I and II are incorrect, the correct answer is (d). This question tests logical deduction and understanding of inequality symbols, particularly in "coded inequality" problems, which are common in UPSC CSAT's logical reasoning section.