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 building has the maximum offices?
Correct Answer :
J
Solution :
To determine which building has the maximum number of offices, let's analyze the given information step-by-step to deduce the positions and number of offices for each building.
1. Understanding the Layout:
• Row 1 (Facing East): A, B, C, D, E, F
• Row 2 (Facing West): J, K, L, M, N, O
2. Calculating the Number of Offices:
• F: Given directly as 22 offices.
• L: The difference between the offices of F and L is 5, and L has a prime number of offices.
(since 17 is prime).
• K: Given directly as 12 offices.
• B: The difference between K and L equals B's offices.
offices.
• C: Given directly as 16 offices.
• J & M: The number of offices in J is a perfect square, J has more offices than D, and no building has more than 28 offices or less than 5 offices. Since M has 15 offices less than J (), and , we have .
The only perfect square between 20 and 28 is 25.
Therefore, J = 25 offices and M = 10 offices.
Summary of Office Counts:
• J = 25
• F = 22
• L = 17
• C = 16
• K = 12
• M = 10
• B = 5
Comparing all calculated building values, J has the highest number of offices (25 offices).
The correct option is J.
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