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 dentist says: "Children should brush their teeth for two full minutes, not just a quick scrub." Which one of these statements, if true, best supports the dentist's claim?
Show worked solution
C gives the reason two minutes works better — the effect the claim rests on.
2 Ivy, Jay and Kim line up side by side. Jay is somewhere left of Kim, and Ivy is somewhere right of Jay. Which statement is certainly true?
Show worked solution
Both Kim and Ivy are to Jay's right, so Jay is furthest left. Kim and Ivy could be in either order.
3 Four friends sit at a table for four on a train, two seats on each side facing each other. Two of them face forwards and two face backwards; two have window seats and two have aisle seats. Pip sits diagonally opposite Rae. Sol faces forwards. Tam sits next to Pip. Which one of the following do you also know?
Show worked solution
Pip and Rae are diagonal, and Tam is beside Pip, so Sol must be beside Rae — which puts Sol directly opposite Pip. Seat sides and directions cannot be fixed from these clues.
4 Two reasons were suggested for why the class tomato plants grew badly: not enough sunlight, or too little water over the holidays. Ms Bell: "I checked, and the plants were in the shadiest corner of the courtyard. So it was the lack of sunlight, not the watering." Which one of the following sentences shows that Ms Bell has made a mistake?
Show worked solution
Finding one cause does not rule out the other. B says both may be true.
5 This net folds into a cube with a letter on each face.When it is folded, which face is opposite R?
Show worked solution
Q–R–S is a row, so Q is opposite S. P hangs off one end of the row on one side and T off the other end on the other side, so P is opposite T. That leaves U, which folds over to become the lid above R: R is opposite U.
6 Every player who scores a goal at Saturday's match will get a medal.
Zac: "Ali got a medal, so Ali must have scored a goal."
Yin: "Ben did not score a goal, so Ben will not get a medal."
If the information in the box is true, whose reasoning is correct?
Zac: "Ali got a medal, so Ali must have scored a goal."
Yin: "Ben did not score a goal, so Ben will not get a medal."
If the information in the box is true, whose reasoning is correct?
Show worked solution
The rule promises medals to scorers; it does not say ONLY scorers get medals. Zac runs it backwards; Yin assumes no goal → no medal, which the rule never says. Neither.
7 A library book was borrowed on a Monday. It was returned 9 days later, and borrowed again 5 days after that. On which day was it borrowed again?
Show worked solution
Monday + 9 days = Monday + 7 + 2 = Wednesday. Wednesday + 5 days = Monday.
8 At the swimming club the weekly timetable is:
Fins are used in three sessions: freestyle, backstroke and butterfly. This week the pool is closed on Tuesday. For how many sessions are fins used this week?
| Monday | Tuesday | Wednesday | Thursday | |
| 4–5 pm | freestyle | diving | relay | freestyle |
| 5–6 pm | diving | butterfly | backstroke | relay |
| 6–7 pm | backstroke | freestyle | diving | butterfly |
Show worked solution
Monday: freestyle, backstroke (2). Wednesday: backstroke (1). Thursday: freestyle, butterfly (2). Tuesday is closed. 2 + 1 + 2 = 5.
9 A survey found that most families in the city recycle their food scraps. Kai: "That must be wrong. My family doesn't, and neither do my neighbours." Which one of the following sentences shows that Kai has made a mistake?
Show worked solution
A few households cannot outvote a city-wide survey. C names the jump; B doubts the survey without showing Kai's error.
10 A tram takes 45 minutes to travel from the beach to the city. A train on the same trip is three times as fast. Both arrive in the city at 5:00 pm. When did the train leave the beach?
Show worked solution
Three times as fast → a third of the time: 15 minutes. 5:00 pm − 15 minutes = 4:45 pm.
11 A vet says: "It is best not to touch wild animals, but pet rabbits should be handled gently every day so they grow up calm." Which one of these statements, if true, gives the vet the strongest backing?
Show worked solution
B shows the effect the vet claims for handling pets. A, C and D are nearby facts.
12 Five lockers stand in a row. One holds a prize. Clues: The grey locker is at the far left. The blue locker is next to the grey locker. The green locker is 2 places from the blue locker. The pink locker is next to the blue locker. The prize is 2 places from the orange locker. Which locker holds the prize?
Show worked solution
Grey is 1, blue is 2. Green is 2 places from blue: position 4 (there is no position 0). Pink is next to blue and 1 is taken, so pink is 3. Orange gets the last place, 5. The prize is 2 places from orange: position 3 — the pink locker.
13 Four drawings each show two objects drawn to one shared scale, though each drawing uses its own scale. Real heights: bike 1 m, door 2 m, giraffe 5 m, bus 3 m.Which of the unknown objects is tallest in real life?
Show worked solution
Post = 2.5 × bike = 2.5 m. Flag = 1.6 × door = 3.2 m. Tree = 0.9 × giraffe = 4.5 m. Crane = 1.6 × bus = 4.8 m. The crane is tallest — even though the tree is drawn taller on the page.
14 Rules: "If the river rises above the bridge, the road is closed. If the road is closed, the school bus does not run." The river has risen above the bridge this morning. Which one of the following must be true?
Show worked solution
Chain the rules: river up → road closed → bus does not run. Nothing forces the school to close or says why the river rose.
15 Ranger: "The animal that raided the campsite left large paw prints. Dingoes have large paws, so it must have been a dingo." Which one of the following sentences shows that the ranger has made a mistake?
Show worked solution
Matching the description does not make the dingo the only candidate. C names the more-than-one-match jump.
16 A health teacher says: "Eating breakfast every day helps students learn." Which one of these statements, if true, gives the teacher the strongest backing?
Show worked solution
C reports the learning benefit itself. The others are facts about breakfast, not reasons.
17 The only people allowed backstage at the concert are the performers and their teachers.
Nora: "Mr Diaz is backstage, so he must be a performer or a teacher."
Eli: "Sara is a performer, so she is allowed backstage."
If the information in the box is true, whose reasoning is correct?
Nora: "Mr Diaz is backstage, so he must be a performer or a teacher."
Eli: "Sara is a performer, so she is allowed backstage."
If the information in the box is true, whose reasoning is correct?
Show worked solution
Backstage → performer or teacher (Nora ✓). Performer → allowed (Eli ✓ — he says "allowed", not "is there"). Both.
18 Hana has to get a message to Kofi before the day ends, though she will not see him herself. These meetings are already fixed for today:
Hana meets Ivo at 10:00. Jun meets Kofi at 11:00. Ivo meets Lea at 11:30. Lea meets Jun at 12:00.
Which extra meeting would let the message reach Kofi today?
Hana meets Ivo at 10:00. Jun meets Kofi at 11:00. Ivo meets Lea at 11:30. Lea meets Jun at 12:00.
Which extra meeting would let the message reach Kofi today?
Show worked solution
Hana → Ivo at 10:00. A: Ivo → Jun at 10:30, then Jun → Kofi at 11:00 ✓. B is too late to be useful (Lea meets Jun at 12:00 but Jun has already seen Kofi). C is before Ivo has the message. D: Lea does not have the message until 11:30.
19 Four dominoes will form a square frame, numbers showing. The rule: a domino may go down only if neither of its numbers touches a matching number on a domino already placed. Two dominoes are down; the bottom and left of the frame are still empty.Spare dominoes 1 to 5 are available, each usable once. Which pair of spares CANNOT finish the frame?
Show worked solution
The left domino's top touches the 5; the bottom domino's right end touches the 2; the two new dominoes touch at the corner. Domino 3 (5|5) cannot go on the left (a 5 would touch the 5), so it goes on the bottom with a 5 at the corner — then domino 1 (2|5) on the left must put its 5 at the corner (touching a 5) or at the top (touching the 5). Every placement fails. The other pairs fit.
20 A councillor says: "The town should turn the empty car park into a skate park." Which one of these statements, if true, best supports the councillor's claim?
Show worked solution
D gives both a need and a reason this site fits — a direct reason for the plan.
21 Four books are stacked in a pile: an atlas, a dictionary, a comic and a novel. The comic must not touch the atlas. The dictionary must be directly on top of the novel. The atlas must not touch the novel. Which book is at the bottom of the pile?
Show worked solution
Novel-then-dictionary is a fixed pair. If it is at the bottom or the top, the atlas and comic must touch — not allowed. So the pair is in the middle: the atlas cannot be next to the novel, so the atlas is on top and the comic is at the bottom: comic, novel, dictionary, atlas.
22 Milo wants the cheapest way to buy 12 pencils. "Shop A sells pencils for 50 cents each. Shop B sells them for 40 cents each. So I will buy them at Shop B and pay less." Which one of the following sentences shows that Milo has made a mistake?
Show worked solution
Milo compared the price per pencil only. B names a cost factor he left out; A, C and D are about other things.
23 Liam, Mei and Noor each play some instruments. Liam plays drums, guitar, piano and flute. Mei plays piano, violin and drums. Noor plays flute, harp, drums and cello. Which instruments does Liam play that neither Mei nor Noor plays?
Show worked solution
Cross off drums (both), piano (Mei), flute (Noor). Only the guitar is left.
24 In a word game each letter is worth a whole number of points (at least 1), and a word is worth the sum of its letters.
MOO is worth 5, MOP 7, POOL 8 and LOOM 8.
If A is worth 2, how many points is LAMP worth?
MOO is worth 5, MOP 7, POOL 8 and LOOM 8.
If A is worth 2, how many points is LAMP worth?
Show worked solution
MOO = 5 means M + 2O = 5, so either O = 1 and M = 3, or O = 2 and M = 1. The second fails: MOP = 7 would give P = 4 and then POOL = 8 would give L = 0, which is not allowed. So O = 1, M = 3, P = 3, L = 3 (check LOOM = 3 + 1 + 1 + 3 = 8 ✓). LAMP = 3 + 2 + 3 + 3 = 11.
25 Identical square tiles cover a wall; some were turned before being laid. Below is a patch of the wall showing four whole tiles.Which design could be printed on every tile?
Show worked solution
Every wall tile has one curved corner and one stripe along the edge next to that corner. A has a square corner, B has two stripes, D puts the stripe on the far edge. Only C matches under rotation.
26 Tia's secret number is 12, 15 or 20. Knowing which ONE of the following would tell you her number for certain?
Show worked solution
D leaves only 20. A fits all three; B leaves 12 or 20; C leaves 15 or 20.
27 Whenever the bakery makes croissants, it opens early. When the bakery opens early, the café next door also opens early.
Ana: "The bakery is making croissants today, so the café will open early."
Ravi: "The café opened early today, so the bakery must be making croissants."
If the information in the box is true, whose reasoning is correct?
Ana: "The bakery is making croissants today, so the café will open early."
Ravi: "The café opened early today, so the bakery must be making croissants."
If the information in the box is true, whose reasoning is correct?
Show worked solution
Ana runs the chain forwards ✓. Ravi runs it backwards — the café may open early for other reasons. Ana only.
28 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: left max(1, 0, 2) = 2, middle max(2, 3, 0) = 3, right max(0, 1, 1) = 1. Heights 2, 3, 1.
29 Sign: "All students on the robotics team wear a blue lanyard." Omar: "Lucy is wearing a blue lanyard, so Lucy must be on the robotics team." Which one of the following sentences shows that Omar has made a mistake?
Show worked solution
The sign runs team → blue lanyard, not the reverse. C shows non-team students with blue lanyards.
30 Sam's school makes each student pick one club from each of three lists:
Sam has already decided on chess and drama. Which club is impossible as the third?
| List 1 | List 2 | List 3 |
| art | chess | chess |
| chess | drama | art |
| music | science | drama |
Show worked solution
Sam wants chess and drama once each. Chess from List 1 and drama from List 2 leaves List 3: chess, art or drama — but chess and drama are already taken, so art. Chess from List 1, drama from List 3 leaves List 2: science (chess and drama taken). Chess from List 2 and drama from List 3 leaves List 1: art or music. So art, music and science are all possible; a second drama is not.