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 Ella bumped into Finn on a Thursday. Their next meeting was 6 days after that, and the one after that came 9 days later still. What day of the week was their third meeting?
Show worked solution
Thursday + 6 days = Wednesday. Wednesday + 9 days = Wednesday + 7 + 2 = Friday.
2 Rosa wants to get better at chess but thinks it will take years. Ben suggests: "Join the chess club at the library — lots of strong players go there." Which one of these statements, if true, best supports Ben's suggestion?
Show worked solution
Only A links "strong players at the club" to "getting better" — the reason the suggestion would work.
3 This net folds into a normal dice.When it is folded, which face is opposite the 4?
Show worked solution
In a row of four squares, faces one apart are opposite: 2 ↔ 5 and 3 ↔ 4. The 1 above and 6 below the 3 are opposite each other.
4 The school put new lights on the oval in April. Since then, more students have played football at lunch. Mr Cole: "The new lights must be the reason more students are playing football." Which one of the following sentences shows that Mr Cole has made a mistake?
Show worked solution
Something else changed at the same time. D offers a rival cause; the others never touch the jump.
5 After school Nadia visits the snack van, but only on days when it sells a smoothie she likes. She likes mango and banana smoothies, but not apple or peach.
On which day will Nadia not visit the snack van?
| smoothie | days available |
| mango | Monday and Thursday |
| apple | Monday, Tuesday and Wednesday |
| peach | Tuesday and Friday |
| banana | Wednesday, Thursday and Friday |
Show worked solution
Mango or banana is on sale Monday, Wednesday, Thursday and Friday. Tuesday has only apple and peach.
6 The only students staying inside at lunch are the ones who have not finished their project.
Maya: "Kai has finished his project, so he will be outside at lunch."
Ola: "Lin is staying inside at lunch, so she has not finished her project."
If the information in the box is true, whose reasoning is correct?
Maya: "Kai has finished his project, so he will be outside at lunch."
Ola: "Lin is staying inside at lunch, so she has not finished her project."
If the information in the box is true, whose reasoning is correct?
Show worked solution
"The only students staying in are the unfinished ones" means: staying in → unfinished (Ola ✓), and finished → not staying in, so outside (Maya ✓). Both.
7 A school planted four seeds, one in each of four rooms. The bean (art room) came up later than the corn (library) but earlier than the pea (hall). The sunflower (office) came up on the very same day as the pea. Exactly one seed came up a full day ahead of the rest. Which seed?
Show worked solution
Order: corn, then bean, then pea and sunflower together. The corn was first.
8 Each of the six shapes in Set 2 is meant to be a copy of one of the Set 1 shapes — rotated if necessary, but never flipped over.How many shapes in the second set are NOT true copies?
Show worked solution
Set 2 in order: L turned ✓, mirror L ✗, T turned ✓, Z (mirror of S) ✗, S turned ✓, square ✗. Three are not identical.
9 Amy, Bo and Cy each scored a different number of goals: 1, 2 or 3. Knowing which ONE of the following would tell you everyone's score for certain?
Show worked solution
D: Amy 1, so Bo and Cy have 2 and 3; Bo more than Cy → Bo 3, Cy 2. Settled. Each other clue leaves at least two arrangements.
10 A netball team wins a match by scoring more goals than its opponent. Wins and draws earn ladder points; losses earn nothing. When the season ended, the Hawks had scored zero goals all year. Which statement must be true?
Show worked solution
With no goals they could never score MORE than an opponent, so no wins. They might have drawn 0–0, so B and D are not forced, and A depends on other teams.
11 Tess wants the quickest way home from the city. Tess: "The train takes 25 minutes and the bus takes 40 minutes. So I'll take the train and get home sooner." Which one of the following sentences shows that Tess has made a mistake?
Show worked solution
Tess compared ride times only. A names a time factor she left out; B–D are about cost or comfort, not time.
12 Priya, Quinn, Raj and Sana share a car with two front seats and two back seats. Quinn is either the driver or is next to Sana. Sana's seat is directly behind the driver's. Raj has a front seat and is not next to Priya. Who is driving?
Show worked solution
Raj is in the front. Raj is not beside Priya, so Priya is in the back with Sana. The front pair is Raj and Quinn. Quinn is not beside Sana, so Quinn must be driving.
13 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.
BEE is worth 4, BEG 7, GEEK 9 and KEEP 8.
How many points is BEEP worth?
BEE is worth 4, BEG 7, GEEK 9 and KEEP 8.
How many points is BEEP worth?
Show worked solution
BEE = 4 forces E = 1, B = 2. BEG = 7 → G = 4. GEEK = 9 → K = 3. KEEP = 8 → P = 3. BEEP = 2 + 1 + 1 + 3 = 7.
14 A council says: "Painting our bike lanes green will make cycling safer." Which one of these statements, if true, best supports the council's claim?
Show worked solution
D connects green lanes directly to fewer crashes — the claimed effect.
15 Whenever the town hall is booked for a concert, the car park next to it is full.
Dev: "The car park is full, so there must be a concert on."
Mia: "There is no concert today, so the car park will not be full."
If the information in the box is true, whose reasoning is correct?
Dev: "The car park is full, so there must be a concert on."
Mia: "There is no concert today, so the car park will not be full."
If the information in the box is true, whose reasoning is correct?
Show worked solution
The rule runs concert → full. Dev runs it backwards (a market could fill the car park). Mia assumes no concert → not full, which the rule never says. Neither.
16 Opposite faces of a standard dice always total 7. Which of these drawings could be a real view of one?
Show worked solution
Three faces that meet at a corner can never include an opposite pair. B shows 1 and 6 together, C shows 2 and 5, D shows 3 and 4. Only A (1, 2, 3) is possible.
17 A circus performs every evening from Tuesday the 5th to Friday the 22nd of the same month. On Wednesdays and Sundays there is an afternoon show as well. How many shows are there altogether?
Show worked solution
Evenings: 22 − 5 + 1 = 18. Wednesdays in that span: 6th, 13th, 20th (3). Sundays: 10th, 17th (2). 18 + 3 + 2 = 23.
18 A report says that nearly half of Australian households have a pet dog. Jun: "That can't be right — nobody in my apartment building has a dog." Which one of the following sentences shows that Jun has made a mistake?
Show worked solution
One building cannot outvote a national figure. B says his sample is untypical; C doubts the report without showing Jun's error.
19 Trainee wizards follow this timetable every week:
Wands must be carried to spells, charms and herbology, but to no other class. Friday is always free. A festival wipes out every Thursday class this week. How many wand-carrying classes are left this week?
| Monday | Tuesday | Wednesday | Thursday | |
| 9–10 | astronomy | brewing | charms | herbology |
| 10–11 | star maps | herbology | flying | astronomy |
| 11–12 | spells | charms | herbology | spells |
Show worked solution
Monday: spells (1). Tuesday: herbology, charms (2). Wednesday: charms, herbology (2). Thursday is cancelled. 1 + 2 + 2 = 5.
20 Kit stacks four fillings — ham, tomato, cheese and lettuce — into a sandwich for his sister, who insists: lettuce and ham must not be touching; cheese sits immediately above tomato; ham and tomato must not be touching. Which filling ends up on top?
Show worked solution
Tomato-then-cheese is a fixed pair. If it is at the bottom or top, ham and lettuce must touch each other — not allowed. So it is in the middle: lettuce, tomato, cheese, ham. Ham is on top.
21 Ms Reed says: "Reading stories is fun, but it is reading non-fiction that builds the knowledge students need for school tests." Which one of these statements, if true, best supports Ms Reed's claim?
Show worked solution
The claim's point is that non-fiction builds test knowledge. D shows exactly that effect.
22 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
In every wall tile the quarter-circle sits in a corner NEXT TO the stripe's edge, and each tile has one stripe and a curved corner. Only A matches all three features under rotation.
23 Uma has to get a key back to Zed before the day ends, though she will not see him herself. These meetings are already fixed for today:
Uma meets Vic at 9:00. Wes meets Xav at 10:00. Xav meets Yara at 11:00. Yara meets Zed at 12:00.
Which extra meeting would let the key reach Zed today?
Uma meets Vic at 9:00. Wes meets Xav at 10:00. Xav meets Yara at 11:00. Yara meets Zed at 12:00.
Which extra meeting would let the key reach Zed today?
Show worked solution
Uma → Vic at 9:00. B: Vic → Xav at 10:30, Xav → Yara at 11:00, Yara → Zed at 12:00 ✓. Wes never has the key (A, C fail); D is after Yara has already met Zed.
24 Two possible reasons were suggested for why the school hens laid fewer eggs last month: the cold weather, or a fox frightening them at night. Mr Ali: "Last month was very cold, so the cold is the reason. There is no need to worry about a fox." Which one of the following sentences shows that Mr Ali has made a mistake?
Show worked solution
Confirming one cause does not rule out the other. A says both may be true.
25 Four drawings each show two objects drawn to one shared scale, though each drawing uses its own scale. Real heights: car 1.5 m, person 2 m, swing 2.5 m, shed 3 m.Which of the unknown objects is tallest in real life?
Show worked solution
Statue = 2 × car = 3 m. Sign = 1¾ × person = 3.5 m. Tree = 1.6 × swing = 4 m. Truck = 1.2 × shed = 3.6 m. The tree is tallest.
26 A teacher says the best way to reduce the school's paper waste is to set every printer to print double-sided unless told otherwise. Which one of these statements, if true, gives the teacher the strongest backing?
Show worked solution
D shows that single-sided printing is the biggest source, so fixing it is the BEST way. A and C are true but do not single out double-siding.
27 Ada, Ben and Cal line up side by side. Ada is somewhere right of Ben, and Cal is somewhere left of Ada. Which statement is certainly true?
Show worked solution
Both Ben and Cal are somewhere to Ada's left, so Ada is furthest right. Ben and Cal could be in either order, so B is not forced.
28 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 half touches the 6; the bottom domino's right half touches the 4; the two new dominoes touch each other at the corner. Domino 1 (6|6) cannot go on the left (a 6 would touch the 6), so it goes on the bottom with a 6 at the corner — and domino 3 (6|4) must then put its 6 at the top (touching the 6) or at the corner (touching the other 6). Every placement fails. The other pairs all fit.
29 Poster: "Every student in the school choir can read music." Ivy: "Tom can read music, so Tom must be in the choir." Which one of the following sentences shows that Ivy has made a mistake?
Show worked solution
The poster runs choir → reads music, not the reverse. B shows readers of music who are not in the choir.
30 Round one of a tennis tournament gives every player 4 matches, and only players with 3 or more wins go through to round two. Bea and Cam are both on 2 wins from 2, and their third match is against each other. A tennis match always has a winner.
Ria: "At least one of Bea and Cam will reach the second round."
Ken: "Bea and Cam cannot both reach the second round."
If the information in the box is true, whose reasoning is correct?
Ria: "At least one of Bea and Cam will reach the second round."
Ken: "Bea and Cam cannot both reach the second round."
If the information in the box is true, whose reasoning is correct?
Show worked solution
Whoever wins this match has 3 wins and is through — Ria is right. The loser still has 2 wins and one match left, so could also reach 3 — Ken is wrong.