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.

Given the ratio acid:base:salt = 1:3:2, total parts = 6. If base = 240 mL represents 3 parts, then each part = 80 mL. Therefore: acid = 80 mL, base = 240 mL, salt = 160 mL. Total volume = 480 mL. Acid concentration = 80/480 = 16.67% exactly. Since the concentration is exactly 16.67%, the absolute deviation is 0%, which satisfies the ≤0.83% requirement. The fixed ratio and exact base volume uniquely determine the total volume as 480 mL.

Compound A = 25% × 800 = 200 mL. Remaining volume for B and C = 600 mL. With B:C = 5:7, total parts = 12. Therefore B = (5/12) × 600 = 250 mL and C = (7/12) × 600 = 350 mL. Verification: C percentage = 350/800 = 43.75% exactly, so the absolute difference from 43.75% is 0%, which is minimized.

Let the original total be T patients. Originally: pediatric = 3T/12 = T/4, adult = 7T/12, geriatric = 2T/12 = T/6. Let the new total be S patients. After program: pediatric = S/3, adult = 2S/5, geriatric = 4S/15. Since the total increases and adults decreased from 58.33% to 40% of total, we test if adults decreased by 45. If T = 180: Original adults = 7(180)/12 = 105. If adults increased by 45: new adults = 150. Then 2S/5 = 150, so S = 375. Original ratios: 45:105:30 = 3:7:2 ✓. New ratios: 125:150:100 = 5:6:4 ✓. Change in adults = |150 - 105| = 45 ✓.