ISAT - International Student Admissions Mathematical Problem-Solving 2

Question 1

A cylindrical tank: radius 3m, height 5m. Pump rate: 2 cubic meters/min. Time to fill to 80%? (pi=3.14)

Accepted Answer

56.5 minutes

Answer

Volume = 3.14 x 9 x 5 = 141.3. 80% = 113.04. Time = 113.04/2 = 56.5 minutes.

Question 2

Blend A: $12/kg. Blend B: $8/kg. Want 5kg at $9.60/kg. How much of each?

Accepted Answer

2 kg A, 3 kg B

Answer

12x + 8(5-x) = 48. 4x = 8. x = 2kg A, 3kg B.

Question 3

Revenue function R(x) = -2x^2 + 120x - 400. How many units (thousands) maximize revenue?

Accepted Answer

30,000 units; $1,400

Answer

Vertex at x = -120/(2*-2) = 30. R(30) = -1800+3600-400 = 1400.

Question 4

Anna pays 1/3 of a dinner bill, Ben pays 1/4. Carla pays the remaining $25. What was the total?

Accepted Answer

$60

Answer

Anna+Ben = 1/3+1/4 = 7/12. Remaining: 5/12 = $25. Total = 25 x 12/5 = $60.

Question 5

A boat: 24km upstream in 3 hours, 24km downstream in 2 hours. Find boat speed and current speed.

Accepted Answer

Boat: 10 km/h, Current: 2 km/h

Answer

Upstream: 8 km/h. Downstream: 12 km/h. Boat = (8+12)/2 = 10. Current = (12-8)/2 = 2.

ISAT - International Student Admissions Test Practice Test