Bluebook SAT Test Ratios, Rates, Proportional Relationships, and Units 8 — Questions and Answers
Question 1: A painting crew can paint a house in 6 days working 8 hours a day. How many days would it take if they worked 12 hours a day instead?
- 3
- 4 (Correct answer)
- 5
- 6
Correct answer: 4
Total hours = 6 × 8 = 48; at 12 hr/day: 48 ÷ 12 = 4 days.
Question 2: Oil and vinegar are mixed in a ratio of 2:5 in a salad dressing. If the total volume is 280 mL, how many mL of oil are in the dressing?
- 60 mL
- 70 mL
- 80 mL (Correct answer)
- 90 mL
Correct answer: 80 mL
Oil fraction = 2/7; oil = (2/7) × 280 = 80 mL.
Question 3: A car's fuel efficiency is 32 miles per gallon. If gas costs $3.60 per gallon, what is the fuel cost for a 400-mile trip?
- $40.00
- $42.50
- $44.50
- $45.00 (Correct answer)
Correct answer: $45.00
Gallons needed = 400 ÷ 32 = 12.5; cost = 12.5 × $3.60 = $45.00.
Question 4: The ratio of red marbles to blue marbles is 3:2. If 5 red marbles are added, the ratio becomes 2:1. How many blue marbles are there?
- 8
- 10 (Correct answer)
- 12
- 15
Correct answer: 10
Let red = 3x and blue = 2x; (3x+5)/(2x) = 2 → 3x+5 = 4x → x = 5; blue = 2×5 = 10.
Question 5: If 1 foot = 30.48 cm, what is 5 yards in centimeters? (1 yard = 3 feet)
- 396.24 cm
- 427.36 cm
- 457.2 cm (Correct answer)
- 487.68 cm
Correct answer: 457.2 cm
5 yards = 15 feet = 15 × 30.48 = 457.2 cm.
Question 6: A 500 mL bottle of juice is 30% real juice. A 1,000 mL bottle is 45% real juice. What percent of the combined mixture is real juice?
- 38%
- 40% (Correct answer)
- 41%
- 42%
Correct answer: 40%
Real juice = 0.30×500 + 0.45×1,000 = 150 + 450 = 600 mL in 1,500 mL total; 600/1,500 = 40%.
Question 7: A 60-liter solution is 35% alcohol. How many liters of pure alcohol must be added to make a 50% alcohol solution?
- 14 L
- 16 L
- 18 L (Correct answer)
- 20 L
Correct answer: 18 L
Current alcohol = 0.35 × 60 = 21 L; let x = liters added: (21+x)/(60+x) = 0.50 → 21+x = 30+0.5x → 0.5x = 9 → x = 18.
Bluebook SAT Test Ratios, Rates, Proportional Relationships, and Units 8
A painting crew can paint a house in 6 days working 8 hours a day.
How many days would it take if they worked 12 hours a day instead?