- A pharmaceutical company mixes three compounds in a ratio such that compound A comprises 25% of the mixture, the ratio of compound B to compound C is 5:7, and the absolute difference between the actual percentage of compound C and 43.75% is minimized. If the total mixture is 800 mL, what is the volume of compound B in mL?
Answer: 250 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.
- A laboratory needs to prepare a buffer solution where the ratio of acid to base to salt is 1:3:2. If the final solution must contain exactly 240 mL of base, and the absolute deviation of the acid concentration from 16.67% must not exceed 0.83%, what is the range of possible total volumes for the solution?
Answer: 480 mL only
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.
- In a dental clinic, the ratio of disposable gloves used by the hygienists to those used by the dentists is 5:3. If the clinic ordered 640 pairs of gloves for hygienists this month, how many pairs were ordered for dentists, assuming the same ratio is maintained?
Answer: 384
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: 35=x640, where x represents dentist glove pairs.
Cross-multiplying: 5x=3×640=1920, so x=51920=384 pairs for dentists.
Looking at the wrong answers: Choice B (256) results from incorrectly calculating 640×53=384 but making an arithmetic error. Choice C (192) comes from mistakenly using 640×103, suggesting confusion about whether to use parts of the ratio versus the total ratio. Choice D (128) appears to come from using 640×51, 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. - In a dental practice, the ratio of pediatric to adult to geriatric patients is 3:7:2. After a community outreach program, the ratio changes to 5:6:4. If the absolute value of the change in the number of adult patients is 45, and the total number of patients increases, what was the original total number of patients?
Answer: 180
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 ✓.
