Question

Directions: Each of the following questions is followed by two statements, labelled (A) and (B). Decide whether the statements are sufficient to conclusively answer the question, and choose:
(A) if Statement (A) alone is sufficient but Statement (B) alone is not.
(B) if Statement (B) alone is sufficient but Statement (A) alone is not.
(C) if Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
(D) if either Statement (A) alone or Statement (B) alone is sufficient.
(E) if both statements together are still not sufficient.

Five integers A, B, C, D and E are arranged in such a way that there are two integers between B and C, and B is not the greatest. There exists one integer between D and E, and D is smaller than E. A is not the smallest integer. Which one is the smallest?
(A) E is the greatest.
(B) There exists no integer between B and E.

• (A) Statement (A) alone is sufficient, but Statement (B) alone is not sufficient.
• (B) Statement (B) alone is sufficient, but Statement (A) alone is not sufficient.
• (C) Statement (A) and Statement (B) together are sufficient, but neither alone is sufficient.
• (E) Both Statement (A) and Statement (B) together are not sufficient to answer the question.

Hint:

The clues describe how A to E are spaced out in an arrangement, not their numeric order; check whether either statement actually links a seat/position to a value.

Answer 1

The Correct Option is D

Step 1: Understand what the clues actually describe.
The clues describe how A, B, C, D, E are laid out relative to each other ("two integers between B and C", "one integer between D and E") in an arrangement. They do not say this arrangement is in increasing or decreasing order of value. The question, however, asks for the smallest value among the five integers. Positional information only tells us about value if we also know how position and value are related, or unless we're explicitly told the arrangement is sorted by value.

Step 2: Test Statement A alone.
"E is the greatest" tells us about the value of E only. It says nothing about how B, C, D compare with A, or with each other, since the original clues never fixed value order for the whole group, only relative spacing in the arrangement. So we still cannot identify the smallest value. Not sufficient.

Step 3: Test Statement B alone.
"No integer between B and E" is again a statement about their positions in the arrangement (they sit next to each other), not about which of the two, or which of the other three, holds the smallest value. Not sufficient.

Step 4: Test both statements together.
Even combined, Statement A fixes only that E is the largest by value, and Statement B fixes only a positional adjacency between B and E. Neither statement, alone or together, ties the original spacing clues (which are about position in the arrangement) to the actual numeric order of A, B, C, D, E. Since we are never told the arrangement itself is in ascending or descending order of value, we cannot work out which of A, B, C, D is the smallest.

Final Answer:
Both statements together are still not enough to identify the smallest integer.
\[ \boxed{\text{Both statements together are not sufficient}} \]