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  • 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

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.

Question:

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

 

Option: 1

Exactly 8 

 

 


Option: 2

More than 4 
 


Option: 3

At least 8 

 


Option: 4

At most 9 


Answers (1)

best_answer

Based on the given conditions 1 and 2, we can derive the following results:

P1 P2 P3 P4 P5 P6
H M H M H L

Additionally, from condition 4, we encounter two possible cases:

P16 P17 P18 P19 P20
L M L M L
M L M L M

According to condition 5, we have two scenarios:

If the total number of low (L) pipes is 3:

  • Number of high (H) pipes: 6
  • Number of medium (M) pipes: 11

If the number of low (L) pipes is 4:

  • Number of high (H) pipes: 8
  • Number of medium (M) pipes: 8

For P7 and P8, they can either be HH or MM, resulting in two distinct cases for P1 to P10.

1 2 3 4 5 6 7 8 9 10
H M H M H L M M H M
H M H M H L H H M H

Combining conditions 1 and 2, we find the following potential cases for P1 to P20:

Case 1: H M H M H L H H M H M H M H M L M L M L

  • Number of (L) pipes: 4
  • Number of (H) pipes: 8
  • Number of (M) pipes: 8

Case 2: H M H M H L H H M H L M H M H M L M L M

  • Number of (L) pipes: 4
  • Number of (H) pipes: 8
  • Number of (M) pipes: 8

Case 3: H M H M H L H H M H M L H M H M L M L M

  • Number of (L) pipes: 4
  • Number of (H) pipes: 8
  • Number of (M) pipes: 8

First, we create a table and fill in the information provided with absolute certainty.

Pumps Contamination Level
P1  
P2  
P3  
P4  
P5  
P6 Low
P7  
P8  
P9  
P10  
P11  
P12  
P13  
P14  
P15  
P16  
P17  
P18  
P19  
P20  

According to statement 3, pumps P7 and P8 are the only consecutive pumps with the same contamination level recorded.

Statement 1 indicates that three pumps among P1 - P5 have high contamination levels. Therefore, pumps 1, 3, and 5 must have a high level of contamination. Additionally, P6 is the only pump among P1 - P10 with a recorded low contamination level. Hence, pumps 2 and 4 have a medium level of contamination.

Pumps Contamination Level
P1 High
P2     Medium
P3 High
P4 Medium
P5 HIgh
P6 Low
P7  
P8  
P9  
P10  
P11  
P12  
P13  
P14  
P15  
P16  
P17  
P18  
P19  
P20  

It is stated that high contamination levels were not recorded at any of the pumps P16 - P20. Thus, we can conclude that high contamination is limited to the first 15 pumps. The maximum number of pumps with high contamination can be '8' (considering consecutive pumps have different contamination levels, except for one case). Additionally, the number of pumps with high contamination is twice the number of pumps with low contamination. Therefore, the number of pumps with high contamination is an even number less than or equal to '8'.

Suppose there are '6' pumps with high contamination. In that case, there would be only '3' pumps with low contamination, leaving 11 pumps with a medium contamination level. However, the number of pumps of a single type cannot exceed 10 (due to consecutive pumps having different contamination levels, except for one case).

Hence, we can conclude that the number of pumps with high contamination is 8, the number of pumps with low contamination is 4, and the number of pumps with medium contamination is 12.

Since P7 and P8 are the only consecutive pumps with the same contamination level, if they both recorded a medium contamination level, there can be a maximum of 7 pumps (P1, P3, P5, P9, P11, P13, P15) with high contamination. Therefore, we can determine that pumps P7 and P8 recorded a high contamination level, allowing us to uniquely determine the contamination levels up to P10.

Pumps Contamination Level
P1 High
P2 Medium
P3 High
P4 Medium
P5 High
P6 Low
P7 High
P8 High
P9 Medium
P10 High
P11  
P12  
P13  
P14  
P15  
P16  
P17  
P18  
P19  
P20  

Furthermore, as high contamination levels were not recorded at any of the pumps P16 - P20, we can infer that these 5 pumps recorded low and medium contamination levels. There are two possible cases:

Case 1: When there were 3 pumps with low contamination and 2 pumps with medium contamination recorded in pumps P16 - P20. In this scenario, P16, P18, and P20 would have low contamination levels.

Pumps Contamination Level
P1 High
P2 Medium
P3 High
P4 Medium
P5 High
P6 Low
P7 High
P8 High
P9 Medium
P10 High
P11 Medium
P12 High
P13 Medium
P14 High
P15 Medium
P16 Low
P17 Medium
P18 Low
P19 Medium
P20 Low

Case 2: When there were 2 pumps with low contamination and 3 pumps with medium contamination recorded in pumps P16 - P20. In this situation, P16, P18, and P20 would have medium contamination levels.

We know that exactly 8 pumps have recorded medium contamination levels.

Hence, option 1 is the correct answer.

 

Posted by

Rakesh

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