Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
Q.1: Which of the following MUST be true?
Q.2: What best can be said about the number of pumps at which the contamination levels were recorded as medium?
Q.3: If the contamination level at P11 was recorded as low, then which of the following MUST be true?
Q.4: If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?
There can be two cases for petrol pumps from P1 to P10.
Petrol Pumps |
Possibility 1 n(H) = 8 |
Possibility 2 n(H) = 8 |
Possibility 3 n(H) = 6 |
P1 | H | H | H |
P2 | M | M | M |
P3 | H | H | H |
P4 | M | M | M |
P5 | H | H | H |
P6 | L | L | L |
P7 | H | H | M |
P8 | H | H | M |
P9 | M | M | H |
P10 | H | H | M |
P11 | L | M | |
P12 | M | H | |
P13 | H | M | |
P14 | M | H | |
P15 | H | M | |
P16 | M | L | |
P17 | L | M | |
P18 | M | L | |
P19 | L | M | |
P20 | M | L |
Possible number of H petrol pumps from P1 to P10 = 6 or 4
Possible number of H petrol pumps from P11 to P15 = 0, 1, 2 or 3
Given that, n(H) = 2 × n(L)
So, n(H) has to be even.
So, n(H) from P11 to P15 can be 0 or 2.
So, possible n(H) = 4, 6, 8
Accordingly, n(L) = 2, 3, 4
But, minimum n(L) = 3. So, n(L) can be 3 or 4.
So, n(M) can be 8 or 11.
Accordingly, n(H) can be 6 or 8. There has to be 2 H from P11 to P15. Out of three remaining, either all 3 can be M or two M and one L if number of L from P16 to P20 is 2.