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1.How many two-digit numbers have digits that add up to 8?[5]
A4
B7
C8
D9
E16
2.Ana says "Bo is lying." Bo says "Cal is lying." Cal says "Ana and Bo are both lying." How many of the three are telling the truth?[5]
A0
B1
C2
D3
Eit cannot be decided
3.A three-digit code uses only the digits 1, 2 and 3, and digits may repeat. How many such codes contain at least one 3?[5]
A8
B9
C12
D19
E27
4.A square sheet is folded in half top to bottom, then in half left to right. One hole is punched through all the layers. How many holes are in the unfolded sheet?[5]
Text description of the figure
Three steps in a row: a square sheet, the same sheet folded in half top to bottom into a wide rectangle, and that rectangle folded in half left to right into a small square with a single punched hole near its centre.
A1
B2
C4
D6
E8
5.How many squares of any size can be found on a 3 by 3 board?[5]
A9
B10
C12
D13
E14
6.A square sheet is folded in half, then in half again. Two holes are punched through all the layers. How many holes are there when it is unfolded?[5]
A2
B4
C6
D8
E16
7.How many two-digit numbers have both of their digits odd?[5]
A10
B20
C25
D45
E50
8.Four children stand in a line. Ana is not first. Bo stands directly behind Ana. Cal is last. Who is first?[5]
AAna
BBo
CCal
DDee
Eit cannot be decided
9.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
10.Squares of dots grow: 1 dot, then 4, then 9, then 16. How many dots are in the seventh square?[5]
A25
B36
C42
D49
E64
11.On a die, opposite faces add to 7. A die rests on a table with 3 on top. What do the four side faces add up to?[5]
A10
B12
C14
D17
E18
12.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 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 — 8KA-0012Casework
AI counted each pair of digits once instead of counting both orders, such as 17 and 71.
BI listed the pairs starting from 1 and 7 and forgot the number 80, where the second digit is zero.
DI included 08 as a two-digit number, but a two-digit number cannot start with zero.
EI counted both orders of every pair and then counted the pairs that reverse to themselves twice as well.
2.B — 1KA-0017Truth-tellers and liars
AI assumed everyone could be lying at once without checking that Cal's statement would then be true.
CI found one consistent truth-teller and added another without testing whether both could hold together.
DI assumed everyone was telling the truth without noticing that Ana's statement then contradicts Bo's.
EI gave up after one assumption led to a contradiction, instead of trying the other assumption.
3.D — 19KA-0018Complementary counting
AI counted the codes that avoid 3 entirely and gave that as my answer without subtracting.
BI counted the codes with a 3 in the first position only and forgot the other two positions.
CI counted the codes with exactly one 3 and forgot the ones with two or three of them.
EI counted every possible code and forgot to remove the ones with no 3 at all.
4.C — 4KA-0020Paper folding and hole punching
AI forgot that the punch goes through every layer at once, not just the top one.
BI undid only one of the two folds before counting the holes.
DI doubled for the first fold and then added two more rather than doubling a second time.
EI counted a fold that was never made, doubling three times instead of twice.
5.E — 14KA-0133Counting shapes hidden inside a figure
AI counted the nine small squares and stopped, missing every larger one.
BI counted the small squares and the whole board, forgetting the middle size entirely.
CI found the 2 by 2 squares by splitting the board into blocks, getting two instead of four.
DI slid the 2 by 2 square across and down but missed one of its four positions.
6.D — 8KA-0134Paper folding and hole punching
AI forgot that the punch goes through every layer, not just the top one.
BI undid only one of the two folds before counting.
CI doubled twice for the folds but added the second hole instead of doubling for it too.
EI counted three folds instead of two, doubling one time too many.
7.C — 25KA-0135Digit-constraint puzzles
AI counted the odd numbers in one row of ten and treated that as the whole answer.
BI used four odd digits instead of five, forgetting that 9 is odd.
DI counted every two-digit number that is itself odd, which only fixes the last digit.
EI let the first digit be any of ten values rather than only the five odd ones.
8.D — DeeKA-0136Ordering and ranking from clues
AI ignored the very first clue, which rules Ana out of the front directly.
BI put Bo at the front, but Bo must have Ana immediately in front of him.
CI forgot that Cal is fixed at the back of the line.
EI stopped once two arrangements seemed possible, without testing whether the second one actually fits every clue.
9.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.
10.D — 49KA-0138Growth patterns and figurate numbers
AI continued the pattern to the fifth square instead of the seventh.
BI stopped one square short, giving the sixth instead of the seventh.
CI added 6 to the sixth square's 36, treating the differences as constant.
EI continued one square too far and gave the eighth.
11.C — 14KA-0139Dice and cube face relationships
AI subtracted only the top face from 21, forgetting the hidden bottom face as well.
BI guessed four middling numbers and added them without using the total of all six faces.
DI subtracted only the bottom face of 4 from the total of 21.
EI added the four largest numbers on the die rather than the four that are actually at the sides.
12.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.