ISAT Quantitative Reasoning 3 — Questions and Answers
Question 1: A company's profit increased by 20% in the first year and decreased by 15% in the second year. If the initial profit was $200,000, what was the profit at the end of the second year?
- $210,000
- $204,000 (Correct answer)
- $198,000
- $195,000
Correct answer: $204,000
After year 1: $200,000 x 1.20 = $240,000. After year 2: $240,000 x 0.85 = $204,000.
Sequential percentage changes compound. Year 1: $200,000 x 1.20 = $240,000. Year 2: $240,000 x 0.85 = $204,000. The overall change is +2%, not +5%.
Question 2: Three pipes can fill a swimming pool. Pipe A fills it in 6 hours, Pipe B in 8 hours, and Pipe C in 12 hours. If all three pipes work together, how long will it take to fill the pool?
- 2 hours 40 minutes
- 3 hours
- 2 hours
- 8/3 hours (Correct answer)
Correct answer: 8/3 hours
Combined rate: 1/6 + 1/8 + 1/12 = 9/24 = 3/8 pools per hour. Time = 8/3 hours.
Pipe rates: 1/6 + 1/8 + 1/12 = 4/24 + 3/24 + 2/24 = 9/24 = 3/8 pool per hour. Time = 8/3 hours = 2 hours 40 minutes.
Question 3: A train 150 meters long passes a platform 250 meters long in 20 seconds. What is the speed of the train in km/h?
- 72 km/h (Correct answer)
- 54 km/h
- 80 km/h
- 60 km/h
Correct answer: 72 km/h
Total distance = 150 + 250 = 400 meters. Speed = 400/20 = 20 m/s = 72 km/h.
Total distance = train + platform = 400 meters. Speed = 400/20 = 20 m/s. Converting: 20 x 3.6 = 72 km/h.
Question 4: If the ratio of boys to girls in a school is 3:5 and there are 240 students in total, how many more girls are there than boys?
- 60 (Correct answer)
- 30
- 90
- 45
Correct answer: 60
Total parts = 8. Each part = 30. Boys = 90, Girls = 150. Difference = 60.
Ratio 3:5 means 8 total parts. Each part = 240/8 = 30. Boys = 90, Girls = 150. Difference = 60.
Question 5: A shopkeeper buys an article for $400 and marks it up by 50%. He then offers a 20% discount on the marked price. What is his profit percentage?
- 30%
- 20% (Correct answer)
- 25%
- 15%
Correct answer: 20%
Marked price = $600. Selling price = $600 x 0.80 = $480. Profit = $80. Profit % = 20%.
Cost = $400. Marked price = $400 x 1.50 = $600. After 20% discount: $600 x 0.80 = $480. Profit = $80. Profit % = 80/400 x 100 = 20%.
Question 6: The average of five numbers is 42. If one number is removed, the average of the remaining four numbers becomes 38. What number was removed?
- 58 (Correct answer)
- 50
- 54
- 62
Correct answer: 58
Sum of five = 210. Sum of four = 152. Removed = 210 - 152 = 58.
Sum = average x count. Original: 42 x 5 = 210. Remaining: 38 x 4 = 152. Removed = 210 - 152 = 58.
ISAT Quantitative Reasoning 3
A company's profit increased by 20% in the first year and decreased by 15% in the second year.
If the initial profit was $200,000, what was the profit at the end of the second year?