Directions : Each of the questions below, consist of a question and three…
2024
Directions : Each of the questions below, consist of a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read the three statements and Give answer
Six persons i.e. A, B, C, D, E and F sit around an equilateral triangle table such that three persons sit at the corners and face inside while three persons sit in the middle of each of the side and face outside but not necessarily in the same order. Who among the following sits immediate right of D?
Statement I: Two persons sit between B and A who sits immediate left of E. F and D sits immediate left of each other. Statement II: One person sits between E and D. A does not sit at the corner.
Statement III: C sits immediate left of B and second to the left of A. D and E does not sit adjacent to each other.
- A.
Both statements I and II together are necessary to answer the question whereas statement III alone is not sufficient to answer the question
- B.
Only statement III alone is sufficient to answer the question whereas both statements I and II are not sufficient to answer the question
- C.
All the three statements together are not sufficient to answer the question
- D.
Any two of the given statements are necessary to answer the question
- E.
Only statement II alone is sufficient to answer the question whereas both statements I and III are not sufficient to answer the question
Show answer & explanation
Correct answer: A
Concept
In a data-sufficiency item you do not pick the seating answer itself; you judge which statement, or which combination of statements, pins down a single answer to 'who sits to the immediate right of D'. An information set is SUFFICIENT only if it forces exactly one value for the asked relationship. If it leaves two or more possibilities it is insufficient, and if its conditions admit no consistent seating at all then it determines nothing and is likewise insufficient. The aim is to find the SMALLEST set of statements that fixes the answer.
Table reading: six seats alternate around the triangle - three corner seats face inside, three mid-side seats face outside - so a corner person and a mid-side person read 'left' and 'right' from opposite facings.
Application - each statement on its own
Statement I (two persons between B and A; A immediate left of E; F and D immediate-left of each other) is consistent with two distinct seatings for the asked relationship - in one the immediate-right neighbour of D works out to A, in the other to B. Two possible answers means Statement I on its own is insufficient.
Statement II (one person between E and D; A not at a corner) leaves the remaining persons free across many seatings, so the immediate-right neighbour of D is not fixed - insufficient on its own.
Statement III (C immediate left of B; C second to the left of A; D and E not adjacent) cannot be satisfied by any seating on the fixed corner/mid-side facing pattern, so it yields no determinate seating and is insufficient on its own.
Cross-check - the minimal sufficient set
Intersect the conditions of Statement I and Statement II. The 'two between B and A' chain with 'A immediate left of E' and the 'F-D immediate-left pair', combined with 'one person between E and D' and 'A not at a corner', survive in only one consistent seating (up to rotation): going round the table D (corner), F (mid), B (corner), C (mid), E (corner), A (mid). Reading from D's own facing, the immediate-right neighbour of D is A - a single, fixed answer.
So Statements I and II are needed TOGETHER and are then sufficient, while Statement III on its own fixes nothing. Note the question asks for the smallest sufficient set: because the pair I and II already settles the answer, the correct characterisation is 'I and II together are necessary, III alone is not sufficient' - not that the statements jointly fail.