At a management school, the oldest 10 dorms, numbered 1 to 10, need to be repaired urgently, The 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.

Further, the following are known:

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

**General Solution**

Let us go step-by-step. We have 10 dorms, each with some repairs needing to be done. Repair costs would be Rs. 1 crore, Rs. 2 crores, Rs. 3 crores, 4, 5 or 6 crores.

From the irritating and unnecessary chart, we can infer that 2 dorms have repair costs of Rs. 1 crore each, 1 has a cost of Rs. 2c, 3 cost Rs. 3C, one each costs Rs. 4C and Rs, 5 C, and finally two dorms take up Rs. 6 crores each. Total cost should be Rs. 34 crores.

Now, let us try to do this more visually. Even-numbered ones do not need moderate repairs – or all 4 moderate-repair dorms are odd-numbered. Likewise, all 3 light-repair ones are even-numbered.

So, odd numbered dorms - 4 moderate and one extensive

Even-numbered dorms - 3 light-repair ones and two extensive.

Dorms 4 to 9 should have all costs from Rs. 1 crore to Rs. 6 crores. Dorm 7 should see Rs. 6 crores and dorm 8 should see Rs. 1 crore.

Dorms 1, 3, 5, 9 should all have moderate numbers. So, three of them should cost RS. 3C and one should cost Rs. 4C. Dorms 4, 5, 6 and 9 should have costs 2, 3, 4, 5.

Put these two together!

Dorms 5 and 9 - Rs. 3C and Rs. 4C

Dorms 4 and 6 - Rs. 2C and Rs. 5C. Dorms that are multiples of 3 do not need extensive repair.

What does this tell us?

So, dorm 6 should cost Rs. 2C and dorm 4 should cost Rs. 5C.

What can we say about dorms 1 and 3?

Both 1 and 3 should have seen moderate costs and since one of 5 or 9 costs Rs. 4C.

Both 1 and 3 should cost Rs. 3C.

What else do we have?

Dorms 5 and 9 - Costs Rs. 3C and Rs. 4C in some order

Dorms 2 and 10 - Costs Rs. 1C and Rs. 6C in some order.

Now, let us go to the questions

1. Which of the following is NOT necessarily true?

A) Dorm 1 needs a moderate repair

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

C) Dorm 7 needs an extensive repair

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

Ans. Statement A has to be true. Statement B also has to be true as dorm 5 will see a cost of Rs. 3C or Rs. 4C. Statement 7 has to bne true as it sees a cost of Rs. 6C. Statement D need not be true. Dorm 10 could see a cost of Rs. 1C or Rs. 6C. Choice D is our answer.

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