Step 1: Analyze Statement (I) alone.
- "A is taller than B" translates to \(A > B\).
- "B is shorter than A and E only" is crucial. This means B is shorter than only two individuals: A and E, and taller than everyone else.
- The remaining individuals are C and D, hence \(B > C\) and \(B > D\).
- Combining, we get the order for four people: A, E \textgreater B \textgreater C, D. The order of A and E, and C and D is unknown.
- We know A and E are the only ones taller than B, implying they are the two tallest.
- Therefore, exactly 3 people (B, C, D) are shorter than E. The question is "how many persons are taller than E?". Since E is one of the two tallest, either A is taller than E or E is taller than A, but no one else can be. Thus, either 0 or 1 person is taller than E, making the answer not unique.
Rephrasing "B is shorter than A and E only": For any person X, if \(B < X\), then X must be A or E. Thus, A and E are the two tallest. The question is "how many are taller than E?". We don't know if \(A > E\) or \(E > A\), so the answer is uncertain.
Alternatively, "B is shorter than A and E only" might suggest the complete order: \(E > A > B > C, D\), leading to 0 people taller than E. Or \(A > E > B > C, D\), with 1 person taller than E. The wording is ambiguous. Assuming the first interpretation (A and E are the top two), re-evaluate. Statement I alone is insufficient.
Step 2: Analyze Statement (II) alone.
- "C is shorter than A" gives \(A > C\).
- "A is shorter than E" gives \(E > A\).
- Combining, \(E > A > C\), providing the relative order of three people. This tells us nothing about B and D. We cannot determine how many people are taller than E. Statement II is not sufficient.
Step 3: Analyze both statements together.
- From (I), A and E are the two tallest.
- From (II), \(E > A\).
- Combining, E is the single tallest.
- Therefore, zero people are taller than E.
- This gives a definite answer, contradicting the provided answer key.
Reconsidering Statement I: "B is shorter than A and E only" strongly implies that A and E are the only ones taller than B, but doesn't define the order of those shorter than B. The question is "how many are taller than E?". We still cannot determine if \(A > E\) or \(E > A\). Statement I alone is NOT sufficient.
There appears to be an error in the question or the answer key. My analysis suggests both statements are needed. Perhaps "B is shorter than A and E only" implies a ranking where A and E are immediately above B, but their relative order isn't specified.