CAT 2017 Slot 2 — DILR Question 15
Answer the following question based on the information given below.
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) in 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 of 6 Crores are considered extensive repairs.
Further, the following are known:
- 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.
- Dorms 4 to 9 all need different repair costs, with Dorm 7 needing the maximum and Dorm 8 needing the minimum.
Suppose further that:
- 4 of the 10 dorms needing repair are women’s dorms and need a total of Rs. 20 Crores for repair.
- Only one of Dorms 1 to 5 is a women’s dorm.
What is the cost for repairing Dorm 9 (in Rs. Crores)?
Answer & solution
Answer: 3
Let us tabulate the information given in the bar chart. As per condition (i) we get the following information
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From this we can conclude that Dorm 6 would require light repairs and that Dorm 3 and 9 would require moderate repairs. Now following condition (2), we get to know that Dorm 7 would require 6 cr for repair. and Dorm 8 would required 1 cr. This means that in light repairs, Dorm 8 requires 1 crore for repair and Dorm 2 requires 6 crores for repair. Now as each of Dorms to 9 requires a different amount for repairs, and no even numbered dorm requires ,moderate repair, it would imply that Dorm no 4 requires heavy repairs. Already Dorm 7 needs the maximum amount for repairs, (i.e, 6 crores) which means that Dorm4 would require 5 crores for repair. Now Dorm 9 would require 3 or 4 cr for repair. This leads us to 2 possible cases.
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In case 1, as 4 cr is required for Dorm no 9, 3 cr will be required for Dorm no. 5. Also, as no even numbered dorm can have a moderate expenditure, out of the remaining 4 dorms, 1 and 3 (which are also the only odd numbered dorms out of the remaining 4 dorms) will have an expenditure of 3 crores (also since there is only 1 dorm which has a expense of 4 cr which in this case is the expense for Dorm 9). This leaves out only Dorm 2 and Dorm 10, one of these 2 dorms will have an expense of 1 cr and the other an expense of 6 crores.
In case 2, 3 cr is the expense for Dorm No. 9 and 4 cr will be the expense for Dorm no 5. Like in case 1, Dorm no 1 and 3 will have an expense of 1 crore and the other an expense of 6 crores. So our final table for both cases will be as below
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Now the only way the cost of repairing 4 dorms adds upto 20 crores is when the repair cost of 2 of the dorms is 6 crores each, the repair cost of the 3rd dorm is 5 crores and the repair cost of the 4th dorm is 3 crores.
This means that dorms 7 and 4 are definitely women’s dorms. Now if we follow condition. Now if we follow condition (2), we get to know that from Dorm 1 to 5 only Dorm 4 is a women’s dorm. So, the remaining 3 women’s dorms have to be from Dorm 6 to 10. Now from Dorm 6 to Dorm 10, we already know that Dorm 7 is a women’s dorm. Now the Dorm for which the cost of repair is 3 crore has to be a dorm where number is between 6 to 10. This only happens in case 2, where Dorm 9 is one of the 3 dorm that costs Rs. 3 crore to repair. Also in case 2, the second dorm that cost Rs.6 crores to repair has to be Dorm No. 10 to satisfy condition (2).
Hence the 4 women’s dorms that Rs.20 crores to repair are Dorms 7, 10, 4 and 9. So the cost of repairing Dorm 9 is Rs. 3 crores.
Answer: 3