Direction : Read the following information carefully and answer the questions…
2021
Direction : Read the following information carefully and answer the questions given below:
Twelve buildings are constructed in two parallel rows from top to bottom such that 6 buildings are there in each row. In row 1- A, B, C, D, E, and F are constructed and all face towards the east direction while in row 2-J, K, L, M, N and O are constructed and all face towards the west direction. All buildings in each row are facing each other. Each building has a different number of offices. None of the buildings has more than 28 offices and less than 5 offices.
M is constructed second to the right of the building which has 15 offices. The number of buildings towards the right of M is one less than the number of buildings towards the left of L. L has prime numbered offices. The building which faces M constructed second to the left of the building which is immediate right of D. F which has 22 offices is second from the either ends. The difference between the offices of F and L is 5. The number of buildings between D and F is same as between J and L. K which has 12 offices constructed second to the left of J. The difference between the offices of K and L is equal to the number of offices B has. C is constructed third to the right of B which doesn’t face M. C has 16 offices. O has two offices less than N. N has less offices than L. The number of offices in E has a multiple of 11. E is constructed right to the building which has 18 offices. The difference between the offices of O and A is equal to M. The number of offices in J has a perfect square value. J has more offices than D. M has 15offices less than J.
Which among the following statement is true?
- A.
M has the least number of offices
- B.
A is constructed fourth to the right of E
- C.
D faces the building constructed adjacent to L
- D.
N has more offices than B
- E.
J and K are constructed adjacent to each other
Show answer & explanation
Correct answer: D
Concept
A two-row linear-arrangement puzzle is solved in two interlocking layers: a POSITION layer (who sits where, fixed by directional clues like ‘second to the right of’, ‘faces’, ‘between’) and a VALUE layer (how many offices each building holds, fixed by arithmetic clues — fixed counts, primes, perfect squares, multiples and differences). The disciplined method is to first nail every value that is forced uniquely, because each fixed value unlocks the next clue, and only then read off the single statement the final table makes true.
Fixing the office values
Each clue below forces exactly one new value (all counts lie in 5–28 and are distinct):
Given directly: F = 22, K = 12, C = 16.
L is prime and |F − L| = 5, so L is 17 or 27; only 17 is prime → L = 17.
|K − L| equals the offices of B, so B = |12 − 17| = 5.
E is a multiple of 11 within range; 22 is already F, so E = 11.
J is a perfect square in range (9, 16, 25); 16 is taken by C and 9 would make M negative, so J = 25, and M = J − 15 = 10.
O = N − 2 with N < 17; the clue that some building has 15 forces N = 15, hence O = 13.
D is the 18-office building that E is placed to the right of, so D = 18.
|O − A| = M = 10 with O = 13 gives A = 23 (3 is below the range), which uses the last free value.
This yields one and only one consistent office table:
Building | Offices |
|---|---|
B | 5 |
M | 10 |
E | 11 |
K | 12 |
O | 13 |
N | 15 |
C | 16 |
L | 17 |
D | 18 |
F | 22 |
A | 23 |
J | 25 |
Fixing the row positions
With the counts known, the directional clues pin the two rows uniquely (one consistent reading shown; its mirror gives the same facing pairs):
F sits second from an end, C is three places along the row from B, and E sits to the right of the 18-office building (D); this orders one row as B, D, E with C and A at the outer parts and F second from an end.
In the other row, K is two places from J on one side, M is two places from the 15-office building, and the ‘second-to-the-right of the 15-office building’ and ‘faces M’ clues fix M, J, N, K, L, O across the columns.
The two rows align column-by-column, giving the facing pairs A–M, D–J, B–N, E–K, F–L, C–O (or the identical set read from the mirror).
Reading the true statement
Now test each claim against the table and the fixed positions:
A claim that the 10-office building holds the fewest offices fails — the genuine minimum in the table is the 5-office building.
A claim placing the 23-office building four steps along its row from the 11-office building fails the position layer — the 23-office building sits at an end of its row while the 11-office building is interior, so they are not four apart.
A claim that the 18-office building faces a neighbour of the prime-numbered (17-office) building fails — it faces the 25-office building, whereas that prime building’s two neighbours are the 12- and 13-office buildings.
The claim comparing the 15-office and 5-office buildings: the first count exceeds the second, so this is the one TRUE statement.
A claim that the 25-office and 12-office buildings are next to each other fails — a single building separates them in the second row.
Cross-check
Exactly one statement survives, the hallmark of a correctly solved single-answer puzzle: ‘N has more offices than B’ (15 versus 5). Re-substituting every value into the original clues — the prime L, the perfect-square J, the multiple-of-11 E, and each difference relation — confirms the table is fully self-consistent.