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Question:

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?

Explanation:

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).

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