Multiple choice

In the first four papers of $100$ marks each, Rishi got $95, 72, 73, 83$ marks respectively. If he wants an average of greater than or equal to $75$ marks and less than $80$ marks, find the range of marks he should score in the fifth paper.

  1. $52 \le x < 77$
  2. $25 < x < 75$
  3. $75 < x < 80$
  4. $73 < x < 100$
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A Correct answer
Explanation

Sum of 4 papers = 95+72+73+83 = 323. Let x be the 5th mark. Average = (323+x)/5. 75 <= (323+x)/5 < 80. 375 <= 323+x < 400. 52 <= x < 77.

AI explanation

The sum of the first four papers is 95 + 72 + 73 + 83 = 323 marks. To get an average of at least 75 marks across five papers, he needs a total of 5 times 75, which is 375 marks, so the fifth paper score x must be at least 375 minus 323, giving x is greater than or equal to 52. To keep the average under 80, the total must be under 5 times 80, which is 400, making the upper limit 400 minus 323, which is 77. Therefore, the range is 52 is less than or equal to x which is less than 77.

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