Study the following graph carefully and answer the question below-
The table given below gives the percentage of total runs scored by a particular player in the match. The table also provides the boundary count of the players in the match.
(boundaries represent 4 runs, and there are no 6's in the match)
N is the minimum possible number of runs scored by the whole team. What is the number of factors of N?
Solution
Runs scored by the players through boundaries are,
KL - 23 * 4 = 92
YASH - 6 * 4 = 24
GILL - 1 * 4 = 4
VIRAT - 2 * 4 = 8
PANT - 0 * 4 = 0
ROHIT - 0 * 4 = 0
WASHI - 5 * 4 = 20
NITISH - 5 * 4 = 20
We know that for a particular player, the runs scored must be greater than or equal to the runs he scored through boundaries. We also know that the combined runs of all the players together must be a multiple of 100 for individual player runs to be integers.
The minimum score cannot be 100 or 200 because, in the case of 100, runs scored by KL becomes $$\dfrac{53}{100}\ \times\ 100\ =\ 53$$, but we already know that KL scored 92 runs through boundaries. So, 100 does not satisfy the given conditions.
In the case of 200, the runs scored by WASHI can be calculated as $$\dfrac{9}{100}\ \times\ 200\ =\ 18$$, but we already know that he scored 20 runs through boundaries. So, 200 does not satisfy the given conditions.
So, the minimum score possible is 300 to satisfy all the given conditions.
The number of factors of 300 can be calculated as,
$$300\ =\ 2^2\ \times\ 3\ \times\ 5^2$$
Number of factors = (2 + 1) * (1 + 1) * (2 + 1) = 3 * 2 * 3 = 18
The correct answer is option D.
