On five of the six working days last week a small unit turned out 96, 104, 88, 112 and 97 items. On the sixth day it turned out n items, where n is more than 90 and less than 96. If the average daily output over the six days is a whole number, how many items were turned out on the sixth day?

The five known days total 96 + 104 + 88 + 112 + 97 = 497. For the six-day average to be a whole number, 497 + n must be a multiple of 6. Since 497 leaves a remainder of 5 on division by 6, n must leave a remainder of 1, and the only such value strictly between 90 and 96 is 91. Then the total is 588 and the average is 588/6 = 98. The other options fail the divisibility test: 497 + 92 = 589, 497 + 94 = 591 and 497 + 95 = 592 all leave a remainder, so none of them gives a whole-number average.