Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
30 questions · official format, shuffled order
1 A slow ferry left Port Ash at 10:00 am and reached Cove Island at 4:00 pm. A fast ferry left Port Ash later and arrived at Cove Island at the same time. The fast ferry was three times as fast as the slow ferry. Both travelled at a steady speed without stopping. When did the fast ferry leave Port Ash?
Show worked solution
The slow ferry took 6 hours. Three times as fast → a third of the time: 2 hours. Arriving at 4:00 pm means leaving at 2:00 pm.
2 Coach: "The player who scored the winning goal was wearing a red headband." Nate: "Sami wears a red headband, so Sami must have scored it." Which one of the following sentences shows that Nate has made a mistake?
Show worked solution
Matching a description does not make Sami the only match. B names the jump.
3 Ava, Ben and Cara collect stickers. Ava has stars, moons, cats, trees and cars. Ben has cats, trees and fish. Cara has stars, fish, trees, boats and cats. Which stickers does Ava have that neither Ben nor Cara has?
Show worked solution
Cross off anything Ben or Cara has: stars (Cara), cats (both), trees (both). Left: moons and cars.
4 Jo's school makes every student pick exactly one activity from each of four lists for next year:
Jo has already decided on drama, music and robotics. Which activity is impossible as her fourth?
| List 1 | List 2 | List 3 | List 4 |
| coding | drama | drama | chess |
| gardening | chess | gardening | robotics |
| music | photography | robotics | cooking |
| cooking | debating | debating | debating |
Show worked solution
Music is only in List 1, so List 1 is used. Drama must come from List 2 or 3 and robotics from List 3 or 4. If drama is List 2 and robotics List 3, the fourth comes from List 4: chess, cooking or debating. If drama is List 3, robotics is List 4 and the fourth comes from List 2: chess, photography or debating. Gardening (Lists 1 and 3) is never available.
5 A doctor says: "Children should spend at least an hour outdoors every day." Which one of these statements, if true, best supports the doctor's claim?
Show worked solution
C gives a benefit that follows from daily outdoor time — a reason for the claim.
6 Students may go on the zoo excursion only if a signed permission note is handed in by Friday.
Ola: "Kian handed his note in on Wednesday, so he is certain to be going."
Raf: "Tess lost her note and cannot get a new one signed in time, so she will not be going."
If the information in the box is true, whose reasoning is correct?
Ola: "Kian handed his note in on Wednesday, so he is certain to be going."
Raf: "Tess lost her note and cannot get a new one signed in time, so she will not be going."
If the information in the box is true, whose reasoning is correct?
Show worked solution
"Only if" makes the note necessary, not enough: Kian might be ill or choose not to go (Ola wrong). Without a note Tess cannot go (Raf right).
7 Nia marks the halfway point of a straight ribbon. She then folds the ribbon in half and marks the halfway point of the doubled strand. When she opens the ribbon out flat, neighbouring marks are 6 cm apart. What is the ribbon's full length?
Show worked solution
The first mark is at the halfway point. Folding in half and marking the middle puts marks at the quarter points. Three marks split the ribbon into 4 equal pieces of 6 cm: 24 cm.
8 This square is made from five different pieces.Which one of the following squares is made from the same five pieces? (They may be turned or turned over.)
Show worked solution
The original pieces are a T (4), a straight 4, a straight 3, an L of 3, and a domino. A has two single squares, B has an L of 4 instead of the T, C has a 2 × 2 square. Only D has exactly the same five pieces.
9 Ms Okafor: "Twelve students in my class have library books out. Only eight have brought their books back today, so the other four must have finished reading them and forgotten to bring them." Which one of the following sentences shows that Ms Okafor has made a mistake?
Show worked solution
Forgotten possibility: not returning a book does not mean it is finished. C names the open door.
10 A prize is given to the student whose mark improved the most from last year. Last year's and this year's marks:
Who won the prize?
| student | last year | this year |
| Uma | 84 | 80 |
| Finn | 82 | 89 |
| Lily | 75 | 86 |
| Arlo | 73 | 78 |
| Sophie | 69 | 78 |
| Leon | 73 | 73 |
Show worked solution
Improvements: Uma −4, Finn +7, Lily +11, Arlo +5, Sophie +9, Leon 0. Lily improved most. (Finn has the highest mark — the trap.)
11 When the school siren sounds it is either a real emergency or a practice drill. Practice drills can happen on any day, but always at exactly 2:00 pm.
Yuki: "If the siren sounds in the morning, it must be a real emergency."
Bindi: "Even if the siren is not sounding, that does not prove there is no emergency."
If the information in the box is true, whose reasoning is correct?
Yuki: "If the siren sounds in the morning, it must be a real emergency."
Bindi: "Even if the siren is not sounding, that does not prove there is no emergency."
If the information in the box is true, whose reasoning is correct?
Show worked solution
A morning siren cannot be a drill, so it is real (Yuki ✓). The box never says every emergency sets off the siren, so silence proves nothing (Bindi ✓). Both.
12 A squad has four players: Ari, Bel, Cass and Dan. The coach's two rules for tomorrow: "Should Ari sit out, Bel plays. Should Ari play, Cass takes the spot rather than Dan." Bel ends up sitting out. Which of the other three take the field?
Show worked solution
Bel is not playing, so Ari must be playing (otherwise Bel would play). Ari playing means Cass plays instead of Dan. Ari and Cass.
13 Opposite faces of a standard dice always total 7. Which net folds up into a standard dice?
Show worked solution
In a row of four squares, faces one apart end up opposite, and the two squares hanging above and below are opposite each other. A: 2 is opposite 4 (6, not 7). B: 1 is opposite 2. C: 2 is opposite 6. D: 2 ↔ 5, 3 ↔ 4 and 1 ↔ 6 all add to 7.
14 An environmental officer says: "Litter in the creek is not just ugly — it harms the platypuses that live there." Which one of these statements, if true, best supports the officer's claim?
Show worked solution
B shows the litter actually harming platypuses — the claim's point.
15 Six villages are labelled P to U. Q lies due north of R and north-east of P. R lies due north of S and due west of T. U lies due east of T. Which village is north-west of S?
Show worked solution
Sketch: R above S; Q above R; P is south-west of Q, so P sits west of the Q–R–S line and above S (Q and R are north of S; P is below Q on the western side). T and U are east. The village north-west of S is P.
16 Three cups stand in a row, each either blue or green. A marble starts in the first cup, which is blue. It is passed to the middle cup, then from the middle cup to the last cup, which is green. Which one of the following must be true?
Show worked solution
If the middle cup is green, the first pass is blue → green. If it is blue, the second pass is blue → green. Either way D is true; A and C depend on the middle cup.
17 One batch of 6 muffins uses 150 g flour, 100 g sugar, 50 g butter and 1 egg. Dana's pantry holds 600 g flour, 350 g sugar, 250 g butter and 5 eggs. At most, how many muffins can she bake?
Show worked solution
Batches: flour 4, sugar 3½, butter 5, eggs 5. Sugar runs out first: 3½ batches × 6 = 21 muffins.
18 Ms Lee: "To have any chance of being chosen for the debating team you must have spoken in at least three practice debates." Omar: "I have spoken in five practice debates, so I am sure to be chosen." Which one of the following sentences shows that Omar has made a mistake?
Show worked solution
A minimum is an entry ticket, not a prize. C names the jump.
19 Five lockers, each a different colour, stand in a row, and a prize is hidden in one of them. The white locker is two places from the prize locker. The black locker is at the far left, two places from the white one. The red locker is not beside the prize locker. The yellow locker is somewhere right of the white one. The green locker is beside neither the black nor the white locker. Which locker holds the prize?
Show worked solution
Black is position 1, so white is position 3. Green is beside neither 1 nor 3, so green is position 5; yellow is right of white, so position 4; red is position 2. The prize is two places from white: position 1 or 5. Position 1 is beside red, which is not allowed, so the prize is in position 5 — the green locker.
20 Class 4B voted between three possible pets: rabbit, fish and lizard. Each student had two votes and had to give them to two different animals. A pet is bought only if one animal is chosen by every single student; otherwise none is. Each animal received at least one vote. Which ONE extra fact would settle whether a pet is bought?
Show worked solution
Each student chose two of three animals. If nobody chose rabbit + lizard together, every student's pair included the fish, so every student voted for the fish — a pet is bought. The other clues leave both outcomes open.
21 A librarian says: "Children who read at home for twenty minutes a day do better at school." Which one of these statements, if true, best supports the librarian's claim?
Show worked solution
C reports the claimed effect from a large study. The others are nearby facts.
22 The plan shows a model made of cubes seen from above. Each number tells how many cubes high that column is. The front of the model is at the bottom of the plan.Which one of the following is the FRONT view?
Show worked solution
From the front you see the tallest column in each vertical line of the plan: left column max(3, 1, 2) = 3, middle max(0, 2, 1) = 2, right max(1, 0, 1) = 1. Heights 3, 2, 1.
23 Every time Coach Bell's team loses, she is grumpy the next day, and whenever she is grumpy she makes the squad run extra laps.
Wei: "If her team loses on Saturday, we are certain to run extra laps on Monday."
Dylan: "We ran extra laps today, so her team must have lost."
If the information in the box is true, whose reasoning is correct?
Wei: "If her team loses on Saturday, we are certain to run extra laps on Monday."
Dylan: "We ran extra laps today, so her team must have lost."
If the information in the box is true, whose reasoning is correct?
Show worked solution
Wei runs the chain forwards: lose → grumpy → extra laps ✓. Dylan runs it backwards — extra laps may have another cause. Wei only.
24 Jed's model-car set is missing just two cars: the silver one and the green one. Packs of three cost $10 each:
A friend owns a spare green car and has offered it in exchange for a pink one. Which single pack lets Jed finish the set?
| pack 1 | silver | blue | yellow |
| pack 2 | green | pink | purple |
| pack 3 | silver | yellow | pink |
| pack 4 | blue | orange | pink |
Show worked solution
He needs silver AND green. Pack 3 gives silver plus a pink car to swap for the friend's green. Pack 1 has silver but no pink; pack 2 has green but no silver; pack 4 has neither.
25 A report says that most Year 4 students in the state can swim 50 metres. Tara: "That can't be true. Hardly anyone in my class can swim that far." Which one of the following sentences shows that Tara has made a mistake?
Show worked solution
One class cannot outvote a state-wide figure. A names the jump; C doubts the report without showing Tara's error.
26 Four chests, W, X, Y and Z, hold different amounts of gold. Idris knows three facts:
• X has more than Z.
• W has more than Y.
• W has more than X.
There is one more fact, not shown, and with it Idris can rank all four chests. Which could be the missing fact?
• X has more than Z.
• W has more than Y.
• W has more than X.
There is one more fact, not shown, and with it Idris can rank all four chests. Which could be the missing fact?
Show worked solution
From clues 1–3: W > X > Z and W > Y, but Y could sit anywhere below W. B places Y above X: W > Y > X > Z — a full order. A adds nothing new; C and D contradict clue 2 or 3.
27 Four friends sit at a square table with three objects on it, seen here from above.One friend sees this view:Which friend has this view?
Show worked solution
Nina sits on the east side looking west. Her left is south (bottom of the plan), her right is north: she sees the cone (bottom row), then the cube (middle row), then the tall block (top row).
28 Six puzzle pieces build a block in three layers, and every layer is a 2 × 3 rectangle formed from exactly two pieces.Which pairing of pieces makes the three layers?
Show worked solution
Each pair must total 6 squares and fit a 2 × 3. 1 and 4 (two L-shapes) fit; 2 and 6 (two straight threes) fit; 3 and 5 (domino plus the 4-piece) fit. In A and D some pairs do not total 6; in B, 1 and 6 make an L-shape with a straight three that leaves a gap.
29 Advertisement: "Every child who loves dinosaurs will love the new film Roar Valley." Pia: "My cousin loved Roar Valley, so she must be a dinosaur fan." Which one of the following sentences shows that Pia has made a mistake?
Show worked solution
The advertisement runs dinosaur fan → loves the film, not the reverse. C shows non-fans can love it too.
30 A sports scientist says: "Stretching after exercise is more important than stretching before it." Which one of these statements, if true, best supports the scientist's claim?
Show worked solution
D gives the benefit of stretching AFTER — exactly the comparison the claim makes.