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1.A jacket costs 80 euros. Its price is reduced by 25%. What is the new price?[3]
A20
B40
C45
D55
E60
2.A cat walks 3 m north, then 4 m east, then 3 m south. How many metres is it now from where it started?[3]
A0
B3
C4
D7
E10
3.A pack of 24 pencils is shared equally among 4 children. Each child then gives 2 pencils to a teacher. How many pencils do the children have left altogether?[4]
A4
B6
C16
D18
E22
4.A password is one letter from A, B, C followed by two digits from 1 to 5. Digits may repeat. How many passwords are possible?[4]
A13
B30
C60
D75
E125
5.An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?[4]
A20
B40
C45
D80
E100
6.A diagonal joins two corners of a shape that are not next to each other. How many diagonals does a hexagon have?[4]
A6
B9
C12
D15
E18
7.The numbers 1 to 9 are placed in a row in some order. Can every neighbouring pair add up to an odd number?[5]
AYes, and many orders work
BYes, but only one order works
CNo, there are too many odd numbers
DNo, nine places is an odd number of places
EOnly if the row starts with an even number
8.Five children sit in a row. Two of them are twins who insist on sitting next to each other. In how many orders can the five sit?[5]
A12
B24
C48
D60
E120
9.Five beads of five different colours are threaded on a circular bracelet. Two bracelets count as the same if one can be turned or flipped into the other. How many different bracelets are there?[5]
A12
B20
C24
D60
E120
10.A code uses the letters A, B and C, each exactly once. How many codes do not start with A?[5]
A2
B3
C4
D6
E9
Kangaroo Atlas · https://kangaroo-atlas.vercel.app · seed 3 · 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.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.
2.C — 4KA-0120Draw the diagram
AI assumed the walk was a loop because the north and south distances match.
BI gave one of the distances walked rather than the distance from the start.
DI added the two different directions together instead of drawing where the cat ends up.
EI added up the whole distance walked, which is not the same as the distance from the start.
3.C — 16KA-0019Multi-step arithmetic word problems
AI found what one child has left and gave that instead of the total for all four.
BI divided 24 by 4 and then subtracted 2 twice, mixing up per-child steps with total steps.
DI subtracted 2 pencils once from the whole pack instead of once from each of the four children.
EI subtracted the 2 before sharing, so only one lot of 2 ever came out of the total.
4.D — 75KA-0023The multiplication principle
AI added the number of options at each step instead of multiplying them.
BI treated the two digits as one choice of ten rather than two independent choices of five.
CI assumed the two digits had to be different, so I used 5 times 4 for them.
EI used 5 choices for the letter position as well, forgetting there are only three letters.
5.B — 40KA-0080Properties of triangles and quadrilaterals
AI subtracted 100 from 180 and then divided by four instead of by two.
CI assumed the two equal angles are always 45 degrees.
DI gave what is left after taking 100 from 180 without splitting it between the two angles.
EI made the 100 one of the equal pair, which would already exceed 180 degrees on its own.
6.B — 9KA-0150Try small cases first
AI counted one diagonal from each corner and stopped there.
CI counted three diagonals from each corner but forgot that each one gets counted from both ends.
DI counted every line joining two corners, including the six sides.
EI multiplied six corners by three diagonals each and never halved.
7.A — Yes, and many orders workKA-0049Parity of numbers (odd/even behavior)
BI found one arrangement that works and assumed a problem this fiddly could only have one answer.
CI saw five odd numbers against four even ones and called that a mismatch, when a row of nine needs exactly five of one and four of the other.
DI blamed the length of the row rather than checking how many odd and even numbers it has to hold.
EI decided the first number settles it without checking that starting even would need five even numbers, and only four exist.
8.C — 48KA-0070Counting with restrictions
AI treated the twins as one child and forgot they can also swap places with each other.
BI glued the twins together into a single block but then forgot that the block can be arranged with the others in more ways than I counted.
DI halved the 120 total, assuming the twins are together in exactly half the arrangements.
EI counted every arrangement of five children and forgot the twins' condition entirely.
9.A — 12KA-0071Overcount, then correct
BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
CI allowed for turning the bracelet but forgot it can also be flipped over.
DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
EI counted every arrangement in a line, as if the bracelet had a fixed first bead.
10.C — 4KA-0140The multiplication principle
AI counted the codes that do start with A rather than the ones that do not.
BI counted the letters available for the first position instead of counting whole codes.
DI counted every arrangement of the three letters and forgot the restriction.
EI allowed letters to repeat, which the words each exactly once rule out.