July 2016 Logic & Maths Problems – Solutions
1. 1 in 10 or 10%
2. 8
3. 50 salutes
4. Alice is 10, Bill is 5, Charlie is 9
5. day 20
6. $30
7. 517 inhabitants
8. Answer: 1 minute early:
SOLUTION:
Journey 1:
Speed = 20km/hr = 1/3 km/min
Time = 20 mins late
Journey 2:
Speed = 30km/hr = ½ km/min
Time = 15 mins early
Journey 3:
Speed = 25km/hr = 5/12 km/min
y = the distance to work
speed (s) = distance (d) / time (t)
If the distance to work was (1/3 x 20) km shorter for journey 1 and (1/2 x 15) km longer for journey 2 both journeys would take the same time. Therefore, using s=d/t:
t = (y – 1/3 x 20) / (1/3) = (y + 1/2 x 15) / (1/2)
therefore the distance to work (y) = 35km.
therefore Journey 1 took 35/(1/3) = 35 x 3 = 105 mins.
105 mins is 20 mins late therefore the journey should take 85 mins.
Journey 3 takes 35 / (5/12) = 35 x 12/5 = 84 mins. Therefore he’s 1 minute early for work.
9. 10 teams
10. a. 10 b. 15 c. 9 d. 20 e. 12