ISAT - International Student Admissions Mathematical Problem-Solving 2 — Questions and Answers
Question 1: A cylindrical tank: radius 3m, height 5m. Pump rate: 2 cubic meters/min. Time to fill to 80%? (pi=3.14)
- 56.5 minutes (Correct answer)
- 45.2 minutes
- 70.7 minutes
- 35.3 minutes
Correct answer: 56.5 minutes
Volume = 3.14 x 9 x 5 = 141.3. 80% = 113.04. Time = 113.04/2 = 56.5 minutes.
V = pi*r^2*h = 141.3 m^3. 80% = 113.04 m^3. Time = 113.04/2 = 56.52 minutes.
Question 2: Blend A: $12/kg. Blend B: $8/kg. Want 5kg at $9.60/kg. How much of each?
- 2 kg A, 3 kg B (Correct answer)
- 3 kg A, 2 kg B
- 2.5 kg each
- 1.5 kg A, 3.5 kg B
Correct answer: 2 kg A, 3 kg B
12x + 8(5-x) = 48. 4x = 8. x = 2kg A, 3kg B.
Let x = kg of A. 12x + 8(5-x) = 9.60 x 5 = 48. Solving: 4x = 8, x = 2. Blend A: 2kg, Blend B: 3kg.
Question 3: Revenue function R(x) = -2x^2 + 120x - 400. How many units (thousands) maximize revenue?
- 30,000 units; $1,400 (Correct answer)
- 40,000 units; $1,200
- 25,000 units; $1,350
- 35,000 units; $1,050
Correct answer: 30,000 units; $1,400
Vertex at x = -120/(2*-2) = 30. R(30) = -1800+3600-400 = 1400.
Maximum at x = -b/(2a) = -120/-4 = 30 thousand units. R(30) = -2(900)+120(30)-400 = $1,400.
Question 4: Anna pays 1/3 of a dinner bill, Ben pays 1/4. Carla pays the remaining $25. What was the total?
- $60 (Correct answer)
- $50
- $75
- $45
Correct answer: $60
Anna+Ben = 1/3+1/4 = 7/12. Remaining: 5/12 = $25. Total = 25 x 12/5 = $60.
Combined fraction: 7/12. Remaining: 5/12 = $25. Total = $60. Anna=$20, Ben=$15, Carla=$25.
Question 5: A boat: 24km upstream in 3 hours, 24km downstream in 2 hours. Find boat speed and current speed.
- Boat: 10 km/h, Current: 2 km/h (Correct answer)
- Boat: 12, Current: 4
- Boat: 8, Current: 4
- Boat: 10, Current: 4
Correct answer: Boat: 10 km/h, Current: 2 km/h
Upstream: 8 km/h. Downstream: 12 km/h. Boat = (8+12)/2 = 10. Current = (12-8)/2 = 2.
b-c=8, b+c=12. Adding: 2b=20, b=10. Subtracting: 2c=4, c=2.
Question 6: Rectangular prism: 8cm x 6cm x 4cm. What is the space diagonal length?
- sqrt(116) = 10.8 cm (Correct answer)
- sqrt(100) = 10 cm
- sqrt(80) = 8.9 cm
- sqrt(136) = 11.7 cm
Correct answer: sqrt(116) = 10.8 cm
d = sqrt(64+36+16) = sqrt(116) = 10.77 cm.
d = sqrt(8^2 + 6^2 + 4^2) = sqrt(116) = 10.77 cm.
ISAT - International Student Admissions Mathematical Problem-Solving 2
A cylindrical tank: radius 3m, height 5m.
Pump rate: 2 cubic meters/min.
Time to fill to 80%? (pi=3.14)