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Math Kangaroo practice

Name: ______________________Date: ____________10 questions · 37 points

1.Ana adds up the first seven odd numbers: 1 + 3 + 5 + 7 + 9 + 11 + 13. Is her total odd or even, and what is it?[3]
- Aodd, 47
- Bodd, 49
- Ceven, 48
- Deven, 49
- Eodd, 45
2.In the number 4073, what is the value of the digit 7?[3]
- A3
- B7
- C70
- D700
- E4000
3.A tap drips about 3 times a minute. Roughly how many drips is that in one day?[3]
- A180
- B720
- C1080
- D4320
- E43200
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 7 to the power 100 is divided by 5?[3]
- A1
- B2
- C3
- D4
- E0
6.What is the remainder when 2 to the power 30 is divided by 7?[4]
- A1
- B2
- C4
- D5
- E6
7.Which of these numbers can be divided exactly by both 4 and 9?[4]
- A96
- B117
- C132
- D144
- E153
8.A price goes up by 20%, then down by 20%. Compared with the original price, the final price is:[4]
- A20% lower
- B4% lower
- Cthe same
- D4% higher
- E40% higher
9.What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?[5]
- Ait cannot be found without a calculator
- B1
- C3
- D7
- E9
10.A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?[5]
- A3
- B6
- C11
- D12
- E13

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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 — odd, 49KA-0002Parity of numbers (odd/even behavior)
- AI decided that adding odd numbers always keeps the total odd, and made an arithmetic slip as well.
- CI paired the numbers up and forgot that with seven numbers one is left over, so I expected an even total.
- DI added correctly but then labelled 49 as even because I had already decided the pairs would make it even.
- EI added only the first six numbers and stopped before including the thirteen.
2.C — 70KA-0055Place value and digit positions
- AI gave the last digit of the number instead of looking at the 7 at all.
- BI gave the digit itself rather than what it is worth in the position it sits in.
- DI counted the positions from the left, so I read the 7 as being in the hundreds place.
- EI gave the value of the largest digit instead of the value of the 7.
3.D — 4320KA-0059Estimation and order of magnitude
- AI worked out the drips in an hour and stopped there.
- BI multiplied by the 24 hours but forgot the 60 minutes in each one.
- CI used 6 hours in a day, thinking of waking hours rather than a whole day.
- EI used 600 minutes in an hour rather than 60.
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.A — 1KA-0169Remainders and modular cycles
- BI reduced 7 to 2 correctly but then used a remainder of 1 when dividing 100 by 4.
- CI read the cycle backwards and landed on the entry before the right one.
- DI used 100 divided by 4 giving 25 and read off the 25th entry as if the cycle had length 25.
- EI assumed a power that large must be divisible by 5.
6.A — 1KA-0053Remainders and modular cycles
- BI found the cycle 2, 4, 1 but read the remainder of 30 divided by 3 as one instead of zero.
- CI counted the cycle positions from zero, which shifted my answer one step along.
- DI divided 30 by 7 and used that remainder rather than the remainder of the powers.
- EI assumed the remainder would be one less than the divisor because the power is large.
7.D — 144KA-0063Divisibility rules: 2, 3, 4, 5, 9, 10
- AI checked that it divides by 4 and stopped without testing the 9.
- BI checked the digit sum for 9 and stopped without testing the 4.
- CI saw an even number with a digit sum of 6 and treated 6 as good enough for 9.
- EI tested 9 with the digit sum and assumed any odd multiple of 9 also divides by 4.
8.B — 4% lowerKA-0065Percentages and simple discounts
- AI applied only the decrease and forgot that the price had already risen.
- CI assumed a rise and a fall of the same percentage cancel each other out exactly.
- DI got the size of the change right but the direction wrong.
- EI added the two percentages together instead of applying them one after the other.
9.E — 9KA-0037Last-digit behavior of products and powers
- AI assumed a number this large has no reachable last digit and gave up on the cycle.
- BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
- CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
- DI assumed the units digit of any power of 7 is always 7.
10.D — 12KA-0060Operation puzzles and cryptarithms
- AI added the digits of 132 instead of working out what A and B must be.
- BI found A + B correctly and then halved it, as if the question wanted one digit.
- CI spotted the 11 in the working and gave that instead of the sum it multiplies.
- EI found a pair of digits by trial and misadded them by one.

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