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

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