CAT 2017 Slot 2 — DILR Question 13
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.
Which of the following is NOT necessarily true?
Answer & solution
- 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
Dorm 10 repair will cost no more than Rs. 4 Crores
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 using these tables let us answer each of the questions.
Let us examine each of the statements individually
1] Statement 1 is true as Dorm no 1 needs a moderate repair of 3 crores
2] Statement 2 is also true as Dorm no 5 needs a repair of 3 or 4 crores
3] Statement 3 is also true as Dorm 7 requires a extensive repair of 6 crores
4] Statement 4 may or may not be true as Dorm 10 has a repair cost of 1 crore or 6 crores
Hence, option (d).