XAT 2024 — QA & DI Question 24
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.
| Over Number | Run Rate |
| N - 2 | 8.00 |
| N | 7.43 |
| N + 2 | 8.11 |
| N + 4 | 8.45 |
| N + 6 | 8.08 |
In which of these pairs of over numbers, the team could have scored 22 runs in total?
Answer & solution
- A
6 and 7
- B
7 and 8
- C
8 and 9
9 and 10
- E
10 and 11
Consider the solution for first question of this set.
Runs scored after:
5th over: 5 × 8 = 40
7th over: 7 × 7.43 = 52
9th over: 9 × 8.11 = 73
11th over: 11 × 8.45 = 93
13th over: 13 × 8.08 = 105
Option (a): In 6th and 7th overs total 52 - 40 = 12 runs are scored. Hence, option (a) is rejected.
Option (b): Minimum runs scored till 6th over 40 + 6 = 46
Maximum runs scored before 9th over 73 - 6 = 67
∴âââââââ Maximum runs scored in 7th and 8th over = 67 - 46 = 21
Hence, option (b) is rejected.
Option (c): In 8th and 9th overs total 73 - 52 = 21 runs are scored. Hence, option (c) is rejected.
Option (d): Minimum runs scored till 8th over 52 + 6 = 58
Maximum runs scored before 11th over 93 - 6 = 87
∴âââââââ Maximum runs scored in 9th and 10th over = 87 - 58 = 29
Hence, option (d) is the right answer.
Option (e): In 10th and 11th overs total 93 - 73 = 20 runs are scored. Hence, option (e) is rejected.
Hence, option (d).