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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 15 points

1.A class of 12 scored an average of 8. Another class of 18 scored an average of 13. What is the average for all 30 students together?[5]
- A10.5
- B11
- C11.5
- D12
- E21
2.A jug holds 900 ml of juice. A third is poured out, then 150 ml is added. How many millilitres are in the jug?[5]
- A450
- B600
- C750
- D900
- E1050
3.One tap fills a tank in 6 hours. A second tap fills the same tank in 4 hours. Both taps are opened together on an empty tank. How long does it take to fill?[5]
- A2 hours 24 minutes
- B5 hours
- C10 hours
- D2 hours
- E1 hour 12 minutes

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Answer key — Math Kangaroo practice

Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.

1.B — 11KA-0112Mixtures and weighted averages
- AI averaged the two averages, ignoring that the classes are different sizes.
- CI weighted the averages but used the wrong class size against each one.
- DI leaned towards the larger class's average without computing the totals.
- EI added the two averages together instead of combining them.
2.C — 750KA-0137Multi-step arithmetic word problems
- AI poured out half instead of a third and then forgot to add the 150 ml back.
- BI poured out the third correctly but never added the 150 ml.
- DI assumed the 150 ml added back was the same as the amount poured out, so nothing changed.
- EI added the 150 ml to the full jug without pouring anything out first.
3.A — 2 hours 24 minutesKA-0159Combined work rates
- BI averaged the two times, but two taps together must be faster than either one alone.
- CI added the two times, which would be right for filling two tanks one after the other.
- DI halved the smaller of the two times, guessing that two taps must simply be twice as fast as one.
- EI found 2 hours 24 minutes correctly and then halved it a second time.

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