ISAT Quantitative Reasoning 2 — Questions and Answers
Question 1: A water tank is being filled at a rate of 3.5 liters per minute and simultaneously drained at 1.2 liters per minute. If the tank has a capacity of 460 liters and starts empty, how many minutes will it take to fill completely?
- 131 minutes
- 200 minutes (Correct answer)
- 384 minutes
- 160 minutes
Correct answer: 200 minutes
Net fill rate = 3.5 - 1.2 = 2.3 liters per minute. Time = 460 / 2.3 = 200 minutes.
When water flows in and out simultaneously, only the net flow rate matters. Inflow is 3.5 L/min and outflow is 1.2 L/min, giving a net rate of 2.3 L/min. Time = volume / rate = 460 / 2.3 = 200 minutes.
Question 2: A store offers a 20% discount on all items, and members receive an additional 15% off the discounted price. If an item originally costs $85, what does a member pay?
- $55.25
- $57.80 (Correct answer)
- $52.70
- $54.40
Correct answer: $57.80
After 20% discount: $85 x 0.80 = $68. After additional 15%: $68 x 0.85 = $57.80.
Sequential percentage discounts must be applied one at a time, not added together. First: $85 x 0.80 = $68.00. Second: $68 x 0.85 = $57.80. A combined 35% discount would give $55.25, which is incorrect.
Question 3: A car travels the first half of a journey at 60 km/h and the second half at 40 km/h. What is the average speed for the entire journey?
- 50 km/h
- 48 km/h (Correct answer)
- 45 km/h
- 52 km/h
Correct answer: 48 km/h
For equal distances, average speed is the harmonic mean: 2/(1/60 + 1/40) = 240/5 = 48 km/h.
Average speed = total distance / total time. Let each half be d km. Time for first half: d/60. Time for second half: d/40. Total time: 5d/120. Average speed = 2d / (5d/120) = 240/5 = 48 km/h. The arithmetic mean of 50 is wrong because more time is spent at the slower speed.
Question 4: If 8 machines can complete a job in 6 days working 5 hours per day, how many machines are needed to complete the same job in 4 days working 6 hours per day?
- 12 machines
- 10 machines (Correct answer)
- 8 machines
- 15 machines
Correct answer: 10 machines
Total work = 8 x 6 x 5 = 240 machine-hours. Required machines = 240 / (4 x 6) = 10.
Total work is constant at 240 machine-hours. New setup: unknown machines x 4 days x 6 hours = 24 x machines. Setting equal: 24 x machines = 240, so machines = 10.
Question 5: A rectangular garden has a perimeter of 56 meters. If the length is 4 meters more than twice the width, what is the area of the garden?
- 160 sq meters (Correct answer)
- 180 sq meters
- 192 sq meters
- 168 sq meters
Correct answer: 160 sq meters
Let width = w. Length = 2w + 4. Perimeter: 2(w + 2w + 4) = 56, so w = 8. Length = 20. Area = 160 sq meters.
Width = w, Length = 2w + 4. Perimeter: 2(3w + 4) = 56, so 6w + 8 = 56, w = 8. Length = 20. Area = 20 x 8 = 160 square meters.
Question 6: In a class of 40 students, 28 study French, 22 study Spanish, and 6 study neither language. How many students study both French and Spanish?
- 10
- 12
- 16 (Correct answer)
- 14
Correct answer: 16
Students studying at least one: 40 - 6 = 34. By inclusion-exclusion: 28 + 22 - Both = 34, so Both = 16.
Total minus neither = at least one: 40 - 6 = 34. Inclusion-exclusion: 28 + 22 - Both = 34. Both = 16. Verify: French only 12, Spanish only 6, Both 16, Neither 6. Total: 40.
ISAT Quantitative Reasoning 2
A water tank is being filled at a rate of 3.5 liters per minute and simultaneously drained at 1.2 liters per minute.
If the tank has a capacity of 460 liters and starts empty, how many minutes will it take to fill completely?