Directions: The questions below, consist of a question and three statements…
2023
Directions: The questions below, consist of a question and three statements numbered as I, II and III given below it. You have to decide whether the data given in the statements are sufficient to answer the question or not. Read all statements and choose the most appropriate option.
Q. Twelve persons sit in two parallel rows such that six persons sit in each row. In row 1- O, K, L, M, N and Q sit and face the south direction while in row 2 – A, B, C, D, E and F sit and face the north direction but not necessarily in the same order. The persons sit in row 1 face the persons sit in row 2 and vice versa. Which person faces Q?
I. One person sits between D and the person who faces K. Two persons sit between N and L. One person sits between B and A. F sits to the left of E. M neither faces E nor sits to the left of O.
II. N neither faces D nor sits adjacent to the person who faces D. More than two persons sit to the right of F. K and B don’t sit at the end. O doesn’t sit adjacent to N and L.
III. L and K do not sit adjacent to each other. B neither faces N nor sits adjacent to the person who faces N. More than one person sits to the right of D who does not sit adjacent to E. E and F don’t sit at the end.
- A.
If data in statement I alone is sufficient
- B.
If data in statement II alone is sufficient
- C.
If data either in statement I alone or in statement III alone is sufficient
- D.
If data in all statements i.e., I, II and III even together is not sufficient
- E.
If data in all statements i.e., I, II and III together is sufficient
Show answer & explanation
Correct answer: E
Concept
A data-sufficiency question does not ask you to find the answer; it asks whether the supplied data is ENOUGH to pin the answer down to a single value. A statement (or a set of statements) is SUFFICIENT only if it forces exactly ONE possible arrangement for the quantity asked about. If two or more arrangements survive the constraints, the data is insufficient. The correct procedure is: take each statement (and each combination) on its own, apply ALL its clues, and check whether the person facing Q is forced to be unique.
Setup
Twelve people sit in two facing rows of six. Row 1 (O, K, L, M, N, Q) faces south; Row 2 (A, B, C, D, E, F) faces north, so each Row-1 seat sits directly opposite one Row-2 seat. Because the rows face opposite ways, "left/right" reverses between them. We must determine who is seated opposite Q.
Testing each statement alone
Statement I alone (gap clues for D-vs-K-facer, N-L, B-A; F left of E; M restrictions): these clues fix some relative gaps but leave the row order only partly determined, so many full arrangements survive and Q's opposite is not unique. Insufficient.
Statement II alone (N not facing/adjacent to D's facer; F has more than two to its right; K and B not at ends; O not adjacent to N or L): this constrains positions but never locks the whole layout; multiple seatings remain. Insufficient.
Statement III alone (L-K not adjacent; B not facing/adjacent to N's facer; D's right-count and E-adjacency; E and F not at ends): again only partial restrictions, leaving several valid layouts. Insufficient.
Testing the pairs
Combining any two of the statements still leaves more than one arrangement consistent with the clues, so no pair fixes Q's opposite uniquely. Each pair is therefore insufficient on its own.
Combining all the data
The three statements are mutually consistent and each removes a different family of possibilities. Applied together, the gap and facing constraints from I, the end/adjacency limits from II, and the non-adjacency and right-count limits from III intersect to a SINGLE seating that satisfies every clue:
Column | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
Row 1 (faces south) | L | M | K | N | Q | O |
Row 2 (faces north) | D | B | F | A | E | C |
In this unique layout Q (column 5, Row 1) sits opposite E (column 5, Row 2), so Q faces E. Because the answer becomes unique only after all the data is used, the full set of statements together is what makes the question answerable.
Cross-check
Exhaustively scanning every seating of both rows, each single statement and each pair admit several arrangements (the facing person is not pinned), whereas the intersection of all the constraints admits exactly one. This confirms that nothing smaller than the complete data resolves the question, and that the complete data resolves it cleanly.