Question:hard

A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is

Updated On: Jan 15, 2026
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The Correct Option is A

Solution and Explanation

To determine the minimum possible value for \(x\), representing the lowest score across the initial \(n\) innings, adhere to the following procedure:

  1. Calculate total runs across \(n+2\) innings: With an average score of 29, the aggregate runs are \((n+2) \times 29 = 29n + 58\).
  2. Determine total runs in the final 2 innings: The scores were 38 and 15, totaling 38 + 15 = 53.
  3. Find runs scored in the first \(n\) innings: Subtract the last 2 innings' runs from the overall total: \(29n + 58 - 53 = 29n + 5\).
  4. Establish the average score for the first \(n\) innings: This is given as 30, implying a total of \(30n\) runs.
  5. Equate the run totals for the first \(n\) innings: Setting \(29n + 5 = 30n\) yields \(30n - 29n = 5\), thus \(n = 5\).
  6. Let the scores in the first \(n\) innings be \(a_1, a_2, ..., a_n\). With \(n = 5\) and an average of 30, the sum is \(a_1 + a_2 + ... + a_5 = 150\).
  7. Given that all scores are below 38 and \(\min(a_1, a_2, ..., a_5) = x\), to minimize \(x\), assign scores as close to 38 as possible. Consider the set: 37, 37, 37, 37, and \(x\). The sum becomes: \(4 \times 37 + x = 150\).
  8. Solve for \(x\): \(148 + x = 150\) results in \(x = 2\).

Consequently, the smallest achievable value for \(x\) is 2.

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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
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