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Math Kangaroo practice

Name: ______________________Date: ____________3 questions · 12 points

1.A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?[4]
- A56
- B336
- C24
- D112
- E28
2.Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?[4]
- A30 sq cm
- B50 sq cm
- C45 sq cm
- D10.8 sq cm
- E90 sq cm
3.Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?[4]
- A40 percent
- B37.5 percent
- C75 percent
- D35 percent
- E30 percent

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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.A — 56KA-0163Selections of a few objects
- BI counted ordered selections, so I counted the same three people once for every order they could stand in.
- CI multiplied the 8 members by the 3 places, which counts something quite different from a selection.
- DI divided the 336 ordered selections by 3 instead of by 3 factorial.
- EI chose 2 people rather than 3.
2.B — 50 sq cmKA-0164Scaling and similar figures
- AI scaled the area by 5/3, using the side ratio directly instead of its square.
- CI multiplied the area by 2.5, halfway between the side ratio and its square.
- DI scaled by 3/5 instead of 5/3, making the larger triangle smaller.
- EI multiplied by 5 and ignored the 3 in the ratio entirely.
3.A — 40 percentKA-0165Mixtures and weighted averages
- BI averaged 25 and 50 without weighting by how much of each solution there was.
- CI added the two percentages together, which cannot be right because a mixture can never be stronger than its strongest ingredient.
- DI weighted the percentages by the wrong volumes, giving the 25 percent solution the larger share.
- EI used only the acid from the weaker solution and spread it over all ten litres.

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