Question

If a group comprises of five persons A, B, C, D and E, then how many persons are taller than E?
Statement (I): A is taller than B and B is shorter than A and E only.
Statement (II): C is shorter than A and A is shorter than E.

• A. Only statement I is sufficient to answer the question.
• B. Only statement II is sufficient to answer the question.
• C. Both statement I and II if sufficient to answer the question.
• D. Both statement I and statement II together are required to answer the question.

Hint:

In data sufficiency, "sufficient" means the statement provides enough information to arrive at one, and only one, unique answer. If a statement leads to multiple possible answers or no answer at all, it is not sufficient.

Answer 1

The Correct Option is A

Step 1: Analyze Statement (I) alone.

- "A is taller than B" gives us \(A > B\). 
- "B is shorter than A and E only" is the key. This means B is shorter than exactly two people: A and E. And B is taller than everyone else. 
- The other people are C and D. So, \(B > C\) and \(B > D\). 
- Combining this, we have the order for four people: A, E \textgreater B \textgreater C, D. The relative order of A and E, and C and D is not known. 
- However, we know that the only people taller than B are A and E. This means A and E are the two tallest people in the group. 
- 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. So, either 0 or 1 person is taller than E. This is not sufficient to give a unique answer.

Let's re-read "B is shorter than A and E only". This means that for any person X in the group, if \(B < X\), then X must be either A or E. This implies that A and E are the only two people taller than B. Thus A and E are the two tallest people. The question is "how many are taller than E?". We don't know if \(A > E\) or \(E > A\). So we can't answer.

Let's try another interpretation of "B is shorter than A and E only". Maybe it implies the complete order? \(E > A > B > C, D\). If this is the case, then 0 people are taller than E. This gives a unique answer. Or \(A > E > B > C, D\). Then 1 person is taller than E. The wording is ambiguous. Let's assume the first interpretation: A and E are the top two. Let's re-evaluate. Statement I is not sufficient.

Step 2: Analyze Statement (II) alone.

- "C is shorter than A" gives \(A > C\). 
- "A is shorter than E" gives \(E > A\). 
- Combining these gives \(E > A > C\). This gives the relative order of three people. It 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), we know A and E are the two tallest people. 
- From (II), we know \(E > A\). 
- Combining these, E must be the single tallest person in the group. 
- Therefore, exactly zero people are taller than E. 
- This gives a definite answer. So both statements together are required. This contradicts the provided answer key.

Let's reconsider the wording of Statement I. "B is shorter than A and E only". This is a very strong statement. It means there is no one else taller than B. It defines the set of people taller than B as \{A, E\}. It does not say anything about people shorter than B. 
The question is "how many are taller than E?". We still cannot tell if \(A > E\) or \(E > A\). Statement I alone is NOT sufficient.

There seems to be a fundamental error in the question or the provided answer key. My analysis suggests both statements are needed. Let's assume there is a common interpretation I am missing. Perhaps "B is shorter than A and E only" implies a rank order, with A and E being just above B. Even so, their internal rank isn't specified.