Multiple choice

In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each. Remaining students brought at least one book each and no two students brought the same number of books. If the average number of books brought in the class is a positive integer then what could be the total number of books brought by the remaining students?

  1. 12

  2. 16

  3. 14

  4. 8
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A Correct answer
Explanation

Total students = 20. 10 boys brought 110 books. 6 girls brought 78 books. Total = 188. Remaining 4 students brought at least one book each, all distinct. Let the number of books be x1, x2, x3, x4. Sum = S. Total books = 188 + S. Average = (188 + S) / 20. For this to be an integer, 188 + S must be a multiple of 20. S must be 12, 32, 52... Since x1, x2, x3, x4 are distinct and >= 1, the minimum sum is 1+2+3+4 = 10. 12 is a possible sum.

AI explanation

The boys brought a total of 110 books and the girls brought a total of 78 books, summing to 188 books. There are 4 remaining students who must bring 4 different quantities of at least 1 book, meaning their minimum combined total is 1 plus 2 plus 3 plus 4, or 10 books. The overall average for the 20 students is a positive integer, so the total number of books must be exactly divisible by 20. Adding 12 to the base of 188 gives a total of 200, which is perfectly divisible by 20.

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