XAT 2017 — QA & DI Question 18
Answer the next 2 questions based on the following information:
In an innings of a T20 cricket match (a team can bowl for 20 overs) 6 bowlers bowled from the fielding side, with a bowler allowed maximum of 4 overs. Only the three specialist bowlers bowled their full quota of 4 overs each, and the remaining 8 overs were shared among three non-specialist bowlers. The economy rates of four bowlers were 6, 6, 7 and 9 respectively. (Economy rate is the total number of runs conceded by a bowler divided by the number of overs bowled by that bowler). This however, does not include the data of the best bowler (lowest economy rate) and the worst bowler (highest economy rate). The number of overs bowled and the economy rate of any bowler are in integers.
Read the two statements below:
S1: The economy rates of the specialist bowlers are lower than that of the non-specialist bowlers.
S2: The cumulative runs conceded by the three non-specialist bowlers were 1 more than those conceded by the three specialist bowlers.
Which of the above statements or their combinations can help arrive at the economy rate of the worst bowler?
Answer & solution
- A
S1 only
- B
S2 only
- C
Either S1 or S2
S1 and S2 in combination
- E
The economy rate can be calculated without using S1 or S2.
S1: The given economy rates of 4 bowlers are 6, 6, 7 and 9. So, the non-specialist bowlers would have 7, 9, x as their economy rates and specialist bowlers would have y, 6, 6 as their economy rates.
S2: The overs bowled by specialist bowlers would be 4, 4 and 4 each. The number of overs bowled by non-specialist bowlers would in any combination of 3, 3 and 2 each.
The runs given by specialist bowlers would be 6 × 4 + 6 × 4 + 4y = 48 + 4y …(1)
Case 1: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is 7, 9 and x respectively.
∴ The runs given by non-specialist bowlers = (7 × 3 + 9 × 3 + x × 2) = 48 + 2x ...(2)
According to the question: (2) – (1) = 1
∴ 2x – 4y = 1
Now, 2x – 4y cannot give an odd value.
Case 2: For non-specialist bowlers, overs bowled are 3, 3, 2 and economy rate is x, 7 and 9 respectively.
The runs given by non-specialist bowlers would be (9 × 2 + 7 × 3 + 3x) = 39 + 3x
According to the question: (2) – (1) = 1
∴ 39 + 3x = 48 + 4y + 1
This is satisfied for x =10 and y = 5
Thus, we need both the statements to get to worst economy rate of the bowler.
Hence, option (d).