Bluebook SAT Test Percentages Ratios and Proportions 2 — Questions and Answers
Question 1: On a map, 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance?
- 125 miles
- 150 miles
- 175 miles (Correct answer)
- 200 miles
Correct answer: 175 miles
Distance = 3.5 × 50 = 175 miles.
Using the map scale: 1 inch = 50 miles. For 3.5 inches: 3.5 × 50 = 175 miles. You can also use the proportion: 1/50 = 3.5/x, giving x = 175 miles.
Question 2: A student scored 45 out of 60 on a test. What percentage did the student score?
- 65%
- 70%
- 75% (Correct answer)
- 80%
Correct answer: 75%
Percentage = (45/60) × 100 = 0.75 × 100 = 75%.
Percent = (part/whole) × 100 = (45/60) × 100 = 0.75 × 100 = 75%. The student scored 75%.
Question 3: The ratio of red to blue marbles is 4:7. There are 77 marbles total. How many are red?
- 22
- 28 (Correct answer)
- 33
- 44
Correct answer: 28
Total parts = 4+7 = 11. Red = (4/11) × 77 = 28.
The ratio 4:7 means 4 + 7 = 11 total parts. Each part = 77/11 = 7 marbles. Red marbles = 4 × 7 = 28. Check: blue = 7 × 7 = 49; 28 + 49 = 77. ✓
Question 4: After a 20% increase, a salary becomes $48,000. What was the original salary?
- $36,000
- $38,400
- $40,000 (Correct answer)
- $42,000
Correct answer: $40,000
Original × 1.20 = 48,000 → Original = 48,000/1.20 = $40,000.
A 20% increase means the new salary = 120% of the original. So original × 1.20 = $48,000. Dividing: original = $48,000 ÷ 1.20 = $40,000.
Question 5: If x:y = 5:8 and y = 40, what is x?
- 20
- 25 (Correct answer)
- 30
- 32
Correct answer: 25
5/8 = x/40 → x = 5 × 40/8 = 25.
Given the ratio x:y = 5:8 and y = 40: x/40 = 5/8. Cross-multiplying: 8x = 200, so x = 25. Verify: 25:40 = 5:8 (both divide by 5). ✓
Question 6: A store charges a 8% sales tax. If an item costs $25, what is the total price with tax?
- $25.80
- $26.00
- $27.00 (Correct answer)
- $28.00
Correct answer: $27.00
Tax = 8% × $25 = $2.00. Total = $25 + $2.00 = $27.00.
Sales tax = 8% × $25 = 0.08 × $25 = $2.00. Total price = $25 + $2.00 = $27.00. Alternatively: $25 × 1.08 = $27.00.
Question 7: A machine produces 120 items in 4 hours. At this rate, how many items does it produce in 9 hours?
- 240
- 270 (Correct answer)
- 300
- 360
Correct answer: 270
Rate = 120/4 = 30 items/hour. In 9 hours: 30 × 9 = 270 items.
The rate is 120 items ÷ 4 hours = 30 items per hour. In 9 hours: 30 × 9 = 270 items. Using a proportion: 120/4 = x/9, cross-multiplying: 4x = 1080, x = 270.
Question 8: What number is 60% of 150?
- 80
- 85
- 90 (Correct answer)
- 95
Correct answer: 90
60% × 150 = 0.60 × 150 = 90.
To find 60% of 150: 0.60 × 150 = 90. You can also compute: 10% of 150 = 15, so 60% = 6 × 15 = 90.
Bluebook SAT Test Percentages Ratios and Proportions 2
On a map, 1 inch represents 50 miles.
If two cities are 3.5 inches apart on the map, what is the actual distance?