Read the following scenario and answer the THREE questions that follow.
A T20 cricket match consists of two teams playing twenty overs each, numbered 1 to 20. The runs scored in any over is a non-negative integer. The run rate at the end of any over is the average runs scored up to and including that over, i.e., the run rate at the end of the k-th over is the average number of runs scored in overs numbered 1, 2, …, k, where 1 ≤ k ≤ 20, k a positive integer.
The following table indicates the run rate of a team at the end of some of the overs during a T20 cricket match (correct up to 2 decimal places), where 1 ≤ N - 2 < N + 6 ≤ 20, N a positive integer. It is also known that the team did not score less than 6 runs and more than 15 runs in any over.
In which of these pairs of over numbers, the team could have scored 22 runs in total?
It is given that the runs in any over is an integer. So, the run rate multiplied by overs should give us an integer.
1 ≤ N - 2 < N + 6 ≤ 20
The range of N is [3, 14].
After N overs, the run rate is given as 7.43. So, 7.43*N has to be an integer. Let's try putting all the possible values N and see where we get an integer.
3*7.43=22.29
4*7.43=29.72
5*7.43=36.15
6*7.43=44.58
7*7.43=52.01
Here, we got an integer; since the run rate is reduced to 2 decimal points, We can not get an exact integer.
So, N can be 7. Let's also check the remaining possible values of N.
8*7.43=59.44
9*7.43=66.87
10*7.43=74.3
11*7.43=81.73
12*7.43= 89.16
13*7.43=96.59
14*7.43=102.02
N can also be 14.
If N=14, the (N+2)*8.11=16*8.11 should also be an integer. But it is 129.76. So, N is not 14. The only possible value is 7.
N-2 --- 8.0 = 5*8=40
N --- 7.43 = 52.01
N+2 --- 8.11 = 9*8.11=72.99
N+4--- 8.45 = 11*8.45 = 92.95
N+6 --- 8.08 = 13*8.08= 105.04
Every number is almost an integer, so N will be 7.
Now, let's calculate the runs scored in each of these overs.
After five overs, the score is 40
After seven overs, the score is 52
So, the sum of scores in 6 and 7 overs is 12. They have to score a minimum of 6 in an over. So, 6 is the sixth over, and 6 in the seventh over.
After the 9th over, the score was 73. They scored 21 in the 8th and 9th over.
After the 11th over, the score was 93, they scored 20 in the 10th and 11th.
After the 13th over, the score was 105, they scored 12 in the 12th and 13th over.
We know the runs scored in every pair of options except Option D. So, only option D could be the answer.
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