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Solve this DILR Question on Dorms from CAT 2017. You are required to understand the underlying classifications of repairs and use all the information that is provided in the constraints. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

CAT DILR : 2017 slot 2 questions


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.

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Question 4: Suppose further that:
1. 4 of the 10 dorms needing repair are women's dorms and need a total of Rs. 20 Crores for repair.
2. Only one of Dorms 1 to 5 is a women's dorm.
Which of the following is a women's dorm?

  1. Dorm 2
  2. Dorm 5
  3. Dorm 8
  4. Dorm 10

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Explanatory Answer

Method of solving this Question on CAT DILR

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.

CAT DI LR 2017 Slot 2

CAT DI LR 2017 Slot 2

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.

CAT DI LR 2017 Slot 2

CAT DI LR 2017 Slot 2

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?

CAT DI LR 2017 Slot 2

CAT DI LR 2017 Slot 2

So, dorm 6 should cost Rs. 2C and dorm 4 should cost Rs. 5C.
What can we say about dorms 1 and 3?

CAT DI LR 2017 Slot 2

CAT DI LR 2017 Slot 2

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
If dorm 9 were to cost Rs. 4C, then the one of dorms 1 to 5 should also cost Rs. 4C – this is impossible. So, dorm 9 should cost Rs. 3C. The Women’s dorms should be 7, 9, 10 and 4.

The question is "Which of the following is a women's dorm?"

Hence, the answer is "Dorm 10".

Choice D is the correct answer.

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