There are certainly many ways in one can attack this problem. But one of the easiest approach is to simply calculate the lower bound and the upper bound based on the 5% discrepancy limit. By knowing the lower bound and upper bound we can then easily deduce which numbers in the list provided in your question that fulfills the criteria as trusted.

The computer reported the number 10500, this means that the upper bound must be deducible by taking 1.05 multiplied by it while the lower bound must be deducible by taking 0.95 multiplied by it, therefore the numbers, x, that lie within the 5% discrepancy limit must be:

0.95 * 10500 < x < 1.05 * 10500

9975 < x < 11025

As we see from your list of numbers,

10,127

10,589

10,926

11,027

All the numbers except 11,027 fit within the range.

All the numbers listed are within 5% of 10,500 except 11,027 which is outside the (arbitrary) limit given in this inventory theorem. The idea is that either the store-wide counting method or the computer records themselves are not perfectly accurate, and that a 5% discrepancy is reasonable.

...The figure that differs by 5%, over or under the 10,500 will be the one that indicates a problem. The one that has a 5% difference, in this case over 10,500, is 11,027.

...The figure that differs by 5%, over or under the 10,500 will be the one that indicates a problem. The one that has a 5% difference, in this case over 10,500, is 11,027.

...You are welcome. If your question is answered well, you should pick it as the best answer.

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