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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 15 points

1.On the number line shown, the marks are equally spaced. What number does the arrow point to?[3]
Text description of the figure
A number line with equally spaced tick marks. The leftmost tick is labelled 0 and the rightmost is labelled 60, with five unlabelled ticks evenly spaced between them. An arrow points to the fourth tick from the left.
- A4
- B24
- C30
- D40
- E50
2.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
- A20
- B40
- C45
- D55
- E60
3.One bus leaves every 12 minutes and another every 18 minutes. They leave together at 9:00. When do they next leave together?[3]
- A9:06
- B9:30
- C9:36
- D9:54
- E12:36
4.A jacket costs 80 pounds. In January the price rises by 20 percent. In February the new price falls by 20 percent. What is the price at the end of February?[3]
- A80 pounds
- B76.80 pounds
- C64 pounds
- D83.20 pounds
- E96 pounds
5.What is the remainder when 2 to the power 50 is divided by 7?[3]
- A1
- B2
- C4
- D6
- E0

Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 1 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.

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.C — 30KA-0006Number lines and betweenness
- AI counted the tick marks and gave the position number instead of reading the value on the scale.
- BI worked out that each gap is worth 10 but then counted only as far as the tick before the arrow.
- DI counted the tick marks rather than the gaps between them, so every gap came out one step too small.
- EI counted the gaps from the right-hand end instead of from zero.
2.E — 60KA-0026Percentages and simple discounts
- AI worked out the size of the discount and gave that as the new price instead of subtracting it.
- BI treated a quarter off as half off and took the price down to 40.
- CI applied the 25% reduction twice, taking 80 down to 60 and then 60 down to 45.
- DI subtracted 25 euros rather than 25 percent, treating the percentage as an amount of money.
3.C — 9:36KA-0041Factors, multiples, LCM and GCD by listing
- AI found the greatest common divisor of 12 and 18 instead of the least common multiple.
- BI added the two intervals together rather than looking for a time that is a multiple of both.
- DI found a common multiple but not the least one, landing on a later coincidence.
- EI multiplied the two intervals together instead of finding their least common multiple.
4.B — 76.80 poundsKA-0153Percentages and simple discounts
- AI assumed a 20 percent rise and a 20 percent fall must cancel because the percentages match.
- CI applied only the fall and forgot the rise.
- DI got the size of the change right but the direction wrong.
- EI applied only the rise and forgot the fall.
5.C — 4KA-0161Remainders and modular cycles
- AI assumed the cycle ends on 1 at every exponent that is a multiple of 2.
- BI used a remainder of 1 rather than 2 when dividing 50 by 3.
- DI doubled my way to 2 cubed = 8 and used 8 minus 2.
- EI assumed a large power of 2 must eventually be divisible by 7.

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