When you encounter ratio problems on the DAT, you're working with proportional relationships where quantities maintain a consistent relationship to each other.

Given that hygienists use gloves in a $$5:3$$ ratio compared to dentists, this means for every 5 pairs hygienists use, dentists use 3 pairs. Since you know hygienists ordered 640 pairs, you can set up a proportion: $$\frac{5}{3} = \frac{640}{x}$$, where $$x$$ represents dentist glove pairs.

Cross-multiplying: $$5x = 3 \times 640 = 1920$$, so $$x = \frac{1920}{5} = 384$$ pairs for dentists.

Looking at the wrong answers: Choice B (256) results from incorrectly calculating $$640 \times \frac{3}{5} = 384$$ but making an arithmetic error. Choice C (192) comes from mistakenly using $$640 \times \frac{3}{10}$$, suggesting confusion about whether to use parts of the ratio versus the total ratio. Choice D (128) appears to come from using $$640 \times \frac{1}{5}$$, which completely misapplies the ratio relationship.

The correct answer is A (384).

Strategy tip: In ratio problems, always identify what you know and what you're solving for, then set up your proportion carefully. Double-check by verifying the ratio: $$640:384$$ should simplify to $$5:3$$. Dividing both by 128 gives you exactly $$5:3$$, confirming your answer. This verification step catches most calculation errors.