DAT Quantitative Reasoning Quiz: Ratios Proportions And Absolute Value

What this quiz covers

This quiz focuses on Ratios Proportions And Absolute Value, giving you a quick way to practice the rules, question types, and explanations that matter most for DAT Quantitative Reasoning.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. 384 (correct answer)
2. 256
3. 192
4. 128

Explanation: 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.

Question 2

1. 480 mL only (correct answer)
2. 460 mL to 500 mL
3. 470 mL to 490 mL
4. 465 mL to 495 mL
5. 475 mL to 485 mL

Explanation: 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.

Question 3

1. 250 mL (correct answer)
2. 225 mL
3. 275 mL
4. 200 mL
5. 300 mL

Explanation: 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.

Question 4

1. 180 (correct answer)
2. 240
3. 300
4. 360
5. 420

Explanation: 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 ✓.