Whenever you're asked to STRENGTHEN or WEAKEN an argument, it's implied that there is a logical flaw - a missing piece - in the argument. Break down the argument carefully and identify what's missing before diving into the answer choices.

Premises:
- deer ticks pick up Lyme bacterium while in larval stage, feeding on white-footed mice
- larvae also feed on other species that do not carry the bacterium

Conclusion:
If the non-bacterium-carrying species were increased, the NUMBER of ticks carrying the bacterium would decline, and the NUMBER of people with the disease would decline

Logical Flaws:
Pay particular attention to the word "number" in CR. Can we justify that fewer ticks would get the disease if we increased other food supplies? Imagine that there was some contaminated yogurt in your fridge. If I said, "just add other food to the fridge, and you won't get sick." Is that logical? You could still get sick if you also ate the yogurt, in addition to the non-contaminated food.

The flaw in this argument: the author is assuming that if there are more non-infected food sources, then there will be ticks who do not feed on ANY infected sources (the white-footed mice). The argument would be invalid if we found out that ticks fed a little bit on white-footed mice in addition to the other new sources.

Strengthen:
In order to strengthen the argument, we need to make it MORE LIKELY that the ticks (at least some of them) were avoiding white-footed mice altogether.

A. Ticks do not suffer any adverse consequences from carrying the bacterium that causes Lyme disease in humans.
Irrelevant. We only care whether they acquire it.

B. There are no known cases of a human's contracting Lyme disease through contact with white-footed mice.
Irrelevant. The chain of transmission is white-footed mice --> ticks --> humans.

C. A deer tick feeds only once while in the larval stage.
If this were true, then it reduces the possibility that the ticks are feeding on white-footed mice AND these non-infected species. This makes it MORE LIKELY that the ticks (at least some of them) were avoiding white-footed mice altogether. Correct!

D. A single host animal can be the source of bacteria for many tick larvae.
Yes, but that animal could be a white-footed mouse (leading to more carriers) or some other species (fewer carriers). Unclear whether this helps or hurts.

E. None of the other species on which deer tick larvae feed harbor other bacteria that ticks transmit to humans
Other bacteria are irrelevant to our argument, which only deals with Lyme disease.

The answer is C.