How is one's hypoxia resistance affected by the time of day?
As noted by others here, PPL course questions might not be designed according to pure deductive or inductive reasoning. My approach would have been the following:

Medical-related aviation questions tend to base their background on "old" studies, so let's have a look at Van Liere, E. J. (1964). Resistance to Hypoxia. Archives of Internal Medicine, 113(3), 418.:


  As a corollary, it would be anticipated that if the metabolic rate of
  an animal were elevated, the ability to withstand hypoxia would be
  decreased. Zarrowetal in 1951 demonstrated that hyperthyroid states
  decrease tolerance to hypoxia. The thyroid-stimulating hormone (TSH),
  thyroxin, and dinitrophenol all decrease hypoxic resistance.


TSH has a circadian rhythm (24 hour cycle) and levels peak between midnight and 6am (refer to https://medicalsciences.stackexchange.com/a/4034/15791). Therefore, 3am and 12am are not an option, which leaves us with 5pm.

I'm aware that you stated that the correct answer is 3am, and I'll definitely check back with my medical colleagues on that, but the question in itself is clearly not well-defined within the visible context on this platform.

As others mentioned, one measure of gauging the depression of cellular oxidation is metabolic rate, for which in 2014 according to Examining Variations of Resting Metabolic Rate of Adults: A Public Health Perspective no single value for RMR is appropriate for all adults.

Last but not least, if we talk about hypobaric hypoxia, conclusions change again.