In the context of MS-EXCEL spreadsheet software, consider a case where there…

Concept

A counting function returns the number of records that satisfy its condition set. A count is nonnegative, and when every candidate record contributes at most once, it cannot exceed the number of candidate records.

COUNTIFS applies all supplied criteria to corresponding rows and counts each qualifying row once. Adding criteria can reduce or preserve the qualifying set, but it does not change these numerical bounds.

Application

1. The range A1:A10000 contains 10,000 candidate cells, so any COUNTIFS result based on this range is a count of qualifying rows.

2. The smallest possible count is 0, whether the formula has one criterion or two; therefore statements A and B hold.

3. The largest possible count is 10,000 because no row can contribute more than one to the result; therefore statements C and D hold.

4. Thus all four statements A-D are true.

Cross-check

An impossible criterion gives 0, while a criterion satisfied by every cell gives 10,000. A second criterion only filters the same 10,000 rows, so it cannot produce a negative result or a count above 10,000.

Contrast

• The value 4 counts both lower-bound statements and both upper-bound statements.

• The value 3 would omit one valid bound even though the criteria count does not alter the range size.

• The value 2 would apply the bounds to only one of the two COUNTIFS cases.

• The value 1 would retain only one bound from one formula case.

Result

Therefore, the number of true statements is 4.