CAT 2018 Slot 1 — DILR Question 29
Answer the following question based on the information given below.
Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
- Contamination levels at three pumps among P1 – P5 were recorded as high.
- P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
- P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
- High contamination levels were not recorded at any of the pumps P16 – P20.
- The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
Which of the following MUST be true?
Answer & solution
The contamination level at P10 was recorded as high.
- B
The contamination level at P12 was recorded as high.
- C
The contamination level at P13 was recorded as low.
- D
The contamination level at P20 was recorded as medium.
From (5), the number of pumps where high contamination levels were recorded is even.
From (1) and (2), high contamination levels recorded at 3 petrol pumps among P1 - P6 i.e., P1, P3 and P5 recorded high levels of contamination.
Therefore, using (4) it can be concluded that high contamination levels could have been recorded at pumps P7 – P15. From (3), the maximum number of pumps where the high contamination levels were recorded must be 5. So this number could be 1, 3 or 5 among P7 – P15.
So, we have the following cases.
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From (3), the number of pumps with the same levels of contamination cannot be more than 11.
For 11 pumps with same levels of contamination, P1 and P20 should have the same level of contamination, which is not the case as P1 recorded high levels of contamination while P20 recorded either low or medium levels of contamination. Thus, cases (i) and (ii) are not valid.
Considering case iii we have the following cases:
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Refer case1 given in the last table.
Statements [1] and [3] are false.
Refer case 6 given in the last table.
Statement [4] is false.
It can be seen that the contamination level at P10 was recorded as high in each case.
Hence, option (a).