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  • At a management school, the oldest 10 dorms, numbered 1 to 10, need to be repaired urgently. The following diagram represents the estimated repair costs (in Rs. Crores) for the 10 dorms. For any do

At a management school, the oldest 10 dorms, numbered 1 to 10, need to be repaired urgently. The following diagram represents the estimated repair costs (in Rs. Crores) for the 10 dorms. For any dorm, the estimated repair cost (in Rs. Crores) is an integer. Repairs with estimated cost Rs. 1 or 2 Crores are considered light repairs, repairs with estimated cost Rs. 3 or 4 are considered moderate repairs and repairs with estimated cost Rs. 5 or 6 Crores are considered extensive repairs.

1. Odd-numbered dorms do not need light repair; even-numbered dorms do not need moderate repair and dorms, whose numbers are divisible by 3, do not need extensive repair. 

2. Dorms 4 to 9 all need different repair costs, with Dorm 7 needing the maximum and Dorm 8 needing the minimum.

Question:

Which of the following is NOT necessarily true?

Option: 1

Dorm 1 needs a moderate repair


Option: 2

Dorm 5 repair will cost no more than Rs. 4 Crores


Option: 3

Dorm 7 needs an extensive repair


Option: 4

Dorm 10 repair will cost no more than Rs. 4 Crores


Answers (1)

best_answer

The question states that the total cost of repairing the dorms is Rs.34 crore. We are also given that the costs of repairing dorms 1, 2, 3, 5, and 6 are Rs.1 crore, Rs.2 crore, Rs.3 crore, Rs.4 crore, and Rs.5 crore respectively.
This leaves Rs.34 - (1 + 2 + 3 + 4 + 5)
= Rs.18 crore for the remaining 5 dorms.

Since dorm 7 needs the maximum repair cost and dorm 8 needs the minimum, the remaining 3 dorms must have costs that fall between Rs.1 crore and Rs.6 crore. Therefore, it is not necessarily true that dorm 10's repair will cost no more than Rs.4 crore.

The other options are all necessarily true. 

Option 1 is true because dorm 1 is said to need a moderate repair, which could cost anywhere from Rs.1 crore to Rs.3 crore. 

Option 2 is true because dorm 5's repair cost is already known to be Rs.4 crore. 

Option 3 is true because dorm 7 is said to need an extensive repair, which could cost anywhere from Rs.4 crore to Rs.6 crore.

Therefore, the answer is option 4: Dorm 10's repair will cost no more than Rs.4 crore.

Posted by

Pankaj Sanodiya

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