A, B, C, D, E and F compared their marks in an examination and found that A obtained the highest marks, B obtained more marks than D, C obtained more than at least two others and E had not obtained the lowest marks.
Consider the following statements :
- Statement 1 : At least two members obtained less marks than C
- Statement 2 : E and F obtained the same marks
Which of the above statement(s) is/are sufficient to identify the one with the lowest marks ?
1. A is 1st.
2. B > D.
3. C > at least two others (C is among ranks 2, 3, 4).
4. E is not 6th (E is among ranks 1, 2, 3, 4, 5). Since A is 1st, E is among 2, 3, 4, 5.
From these facts, the person with the lowest marks (rank 6) can be B, D, or F.
Statement 1: At least two members obtained less marks than C. This is already stated in the problem (C > at least two others). This provides no new information to distinguish between D and F as the lowest. So, Statement 1 alone is insufficient.
Statement 2: E and F obtained the same marks. Also, E is not 6th (from initial facts). If E and F are tied and E is not the lowest, then F also cannot be the lowest. Since the lowest person must be from {B, D, F} (after eliminating A, C, E as candidates for lowest), and F is eliminated by Statement 2, the lowest person must be from {B, D}. Given B > D, D must have the lowest marks among B and D. Therefore, D has the lowest marks. Statement 2 alone is sufficient.