# Logical Reasoning – Set – Fuel contamination levels at each of 20

## DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.

1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

1) Which of the following MUST be true?

a) The contamination level at P20 was recorded as medium.

b) The contamination level at P10 was recorded as high.

c) The contamination level at P12 was recorded as high.

d) The contamination level at P13 was recorded as low.

2) What best can be said about the number of pumps at which the contamination levels were recorded as medium?

a) At least 8

b) More than 4

c) Exactly 8

d) At most 9

3) If the contamination level at P11 was recorded as low, then which of the following MUST be true?

a) The contamination level at P14 was recorded as medium.

b) The contamination level at P18 was recorded as low.

c) The contamination level at P15 was recorded as medium.

d) The contamination level at P12 was recorded as high.

4) If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?

a) Contamination level at P14 was recorded to be higher than that at P15.

b) Contamination levels at P13 and P17 were recorded as the same.

c) Contamination levels at P11 and P16 were recorded as the same.

d) Contamination levels at P10 and P14 were recorded as the same.

Solution:

From point 2) we can say that P6 was the only pump among P1 – P10 where the contamination level was recorded as low and in other pipe it can be either medium or high .

From point 3) only P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded

And From point 1) Contamination levels at three pumps among P1 – P5 were recorded as high it means P1 , P3 and P5 have high Contamination level and P2 and P4 will have medium Contamination level. Thus we get two possible cases for P1 to P10 .

Case a )

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 H M H M H L H H M H

Case b)

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 H M H M H L M M H M

From point 5)

H = 2L

Thus H + L = 3L must be multiple of 3.

Case 1) From point 4)  High contamination levels were not recorded at any of the pumps P16 – P20.

So maximum possible number of pipe with High contamination levels = 8 (P1,P3,P5,P7,P8 ,P10 , P12 and P14)

In this case number of pipes with Low contamination levels = 8/2 = 4

So medium (M) = 8

The possible arrangement will be

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 H M H M H L H H M H M H M H M/L L/M M/L L/M M/L L/M

Or

 P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 H M H M H L H H M H L M H M H M L M L M

Case 2) if Low contamination levels pipes were minimum , which can be 3,then number of pipes with high contamination level = 6

Number of pipes with medium contamination level = 11 which is not possible .

So only case 1) is possible

Now all the questions can be answered.

1) b) The contamination level at P10 was recorded as high

2) c) Exactly 8

3) a) The contamination level at P14 was recorded as medium

4) c) Contamination levels at P11 and P16 were recorded as the same.

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