A cell that is entering the M phase of the cell cycle is:

A. always diploid, either with duplicated or unduplicated chromosomes
B. always haploid, always with duplicated chromosomes
C. either haploid or diploid, always with duplicated chromosomes
D. either haploid or diploid, either with duplicated or unduplicated chromosomes
E. none of the above

To determine the correct answer, we need to understand the characteristics of the M phase of the cell cycle. The M phase, also known as mitosis, is the stage during which the cell divides its genetic material and separates into two daughter cells. During mitosis, the duplicated chromosomes are divided equally between the two daughter cells.

Now let's analyze the options:

A. The statement says that a cell entering the M phase is always diploid, either with duplicated or unduplicated chromosomes. This is incorrect because a cell entering the M phase must have already duplicated its chromosomes in the S phase of the cell cycle. So, this option is not correct.

B. This option states that a cell entering the M phase is always haploid and always with duplicated chromosomes. This is incorrect because in most organisms, including humans, the cells entering the M phase are diploid, not haploid. Therefore, this option is not correct.

C. This option suggests that a cell entering the M phase can be either haploid or diploid, but always with duplicated chromosomes. This option is incorrect because in most organisms, the cells entering the M phase are diploid, not haploid. Therefore, this option is not correct.

D. The statement claims that a cell entering the M phase can be either haploid or diploid, and it can have either duplicated or unduplicated chromosomes. This option is not entirely accurate because in most organisms, the cells entering the M phase are diploid, and their chromosomes are already duplicated. However, there may be exceptional cases where certain organisms or specific cell types enter the M phase with unduplicated chromosomes. Nevertheless, this option is the closest to the correct answer since it accounts for the possibility of both haploid and diploid cells.

E. This option suggests that none of the above options are correct. Although it is possible that none of the above options are entirely correct, it is evident that option D, despite its potential inaccuracies, is the closest to the correct answer.

Therefore, the most accurate answer is D. A cell entering the M phase of the cell cycle can be either haploid or diploid, and it can have either duplicated or unduplicated chromosomes.