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1.Red and blue counters are in the ratio 3 to 5. There are 40 counters altogether. How many are red?[4]
A5
B8
C13
D15
E24
2.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
3.How many different four-letter arrangements can be made from the letters of the word MATH, using each letter once?[4]
A4
B12
C16
D24
E256
4.One pipe fills a pool in 12 hours and another fills it in 4 hours. With both running, how many hours does the pool take to fill?[4]
A3
B4
C6
D8
E16
5.A 4 by 4 board has two opposite corner squares removed, leaving 14 squares. Each domino covers exactly two squares that share an edge. Can 7 dominoes cover the board?[5]
Text description of the figure
A 4 by 4 chessboard-style grid coloured in alternating light and dark squares, with the top-left and bottom-right squares removed. Both removed squares were the same colour.
AYes, and there is exactly one way
BYes, and there are several ways
CNo, because 14 is not divisible by 2
DIt depends which corners are removed
ENo, because the colours do not balance
6.On a 4 by 4 board, how many aligned squares of any size are there, counting 1 by 1, 2 by 2, 3 by 3 and 4 by 4?[5]
A16
B20
C26
D30
E36
7.How many three-digit whole numbers contain at least one digit 7?[5]
A243
B252
C271
D280
E648
8.A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?[5]
Text description of the figure
The floor of a room, 8 metres by 4 metres, drawn flat, with one 8-metre-by-2-metre wall unfolded upwards from its far edge. A straight line joins the ant's starting corner on the floor to the opposite corner on the unfolded wall.
A9.2
B10
C11
D12
E14
9.The numbers 1 to 10 stand in a row. A move swaps two neighbours. After exactly 45 moves, can the row be back in its starting order?[5]
AYes, always
BYes, if the swaps are chosen well
CNo, because 45 is not a multiple of 10
DNo, because the number of moves is odd
EIt depends which numbers are swapped
10.What is the value of (1 - 1/2) x (1 - 1/3) x (1 - 1/4) x ... x (1 - 1/10)?[5]
A1/10
B1/9
C1/2
D9/10
E1
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.D — 15KA-0024Ratio as parts of a whole
AI found what one part is worth and gave that as my answer instead of multiplying it back up.
BI divided 40 by the five blue parts instead of by the eight parts that make the whole.
CI read the ratio 3 to 5 as meaning 3 out of every 5 and worked from that.
EI found the value of one part correctly but then multiplied by 5 instead of 3, giving the blue counters.
2.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.
3.D — 24KA-0073Arrangements of a few objects
AI counted the letters rather than their arrangements.
BI multiplied 4 by 3 and stopped, forgetting the last two positions.
CI used 4 choices for every position, as if letters could repeat.
EI used 4 choices in each of four positions, which allows every letter to repeat.
4.A — 3KA-0116Combined work rates
BI gave the faster pipe's time on its own, forgetting the slower one helps as well.
CI halved the slower pipe's time rather than adding the two rates.
DI averaged the two times, which would only be right if the pipes took turns.
EI added the two times, which makes two pipes slower than one - an impossible answer.
5.E — No, because the colours do not balanceKA-0034Coloring arguments
AI assumed that because 14 is even, seven dominoes must fit somehow.
BI tried a few arrangements, got most of the board covered, and assumed a full covering existed.
CI claimed the right answer for the wrong reason, since 14 is in fact divisible by 2.
DI thought removing a different pair of opposite corners could change the colour balance, but opposite corners always share a colour.
6.D — 30KA-0047Counting by position (sliding window)
AI counted only the sixteen smallest squares and stopped there.
BI counted the small squares and the single big one, and forgot every size in between.
CI counted the 2 by 2 squares as four rather than nine, splitting the board into blocks.
EI used 4 by 4 positions for every size instead of shrinking the range as the square grows.
7.B — 252KA-0075Complementary counting
AI counted the numbers made entirely of digits other than 7 in every position, including a leading zero.
CI counted the numbers with a 7 in each position separately and forgot that some were counted twice.
DI added three lots of 90 and one extra hundred, double counting the 700s.
EI counted the numbers with no 7 at all and gave that instead of subtracting it.
8.B — 10KA-0082Shortest paths on and around shapes
AI measured the straight line through the middle of the room, but the ant has to stay on the surfaces.
CI unfolded the room but folded out the short wall rather than the one that makes the shortest route.
DI chose an unfolding that gives a longer straight line and did not compare it with the others.
EI walked along the edges of the room, 8 then 4 then 2, instead of cutting straight across the surfaces.
9.D — No, because the number of moves is oddKA-0097Parity arguments
AI assumed enough moves can undo anything, without asking what each move preserves.
BI tried a few sequences that nearly worked and assumed a better choice would finish the job.
CI reached for the number of items rather than for what a single swap actually changes.
EI thought the choice of swaps could change the outcome, when every swap has the same effect.
10.A — 1/10KA-0125Spot the trick vs. decide to grind
BI cancelled the chain but stopped one factor early, leaving a 9 on the bottom.
CI worked out the first bracket and assumed the rest made no difference.
DI gave the last bracket on its own instead of the whole product.
EI assumed everything cancels completely, leaving nothing behind.