Sample Question Pack — 13 Questions with Worked Explanations | Cognora
Try 13 real questions from the free library across Thinking Skills, Mathematical Reasoning and Reading. Every question includes a full explanation — not just the answer, but why each wrong option is tempting.
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These questions come directly from the free seed bundle inside the app. No account, no card — just click and practise.
How to use: Sit the pack cold (no notes, no help) in ~30 minutes. The score doesn't matter. What matters is the review:
sort every wrong answer into "didn't know it" (teaching problem → add to planner) or
"knew it, misread" (habit problem → slow down on the stem).
Q1Thinking Skills Medium Logical Reasoning
The council says the community garden should be closed because its maintenance costs are too high. Since the garden is the only green space where neighbourhood children can play, closing it will significantly reduce the amount of outdoor activity they get.
Which of the following, if true, most weakens the argument?
Explanation
The argument assumes the garden is the only green space for children. Option A shows another park nearby, so closing the garden need not reduce outdoor activity — the assumption collapses. B and C describe other benefits and other programmes, neither of which touches the assumption. D disputes the cost claim, not the reasoning about green space.
Q2Thinking Skills Easy Logical Reasoning
A recent survey shows that only 5% of local residents visit Riverside Park each month. The council believes the land would be better used for new housing to address the town's shortage of homes. Therefore, the council should close the park and sell the land.
Which of the following, if true, most weakens the argument?
Explanation
The argument assumes that low visitor numbers mean the park has little value, justifying its sale. Option B shows the park has essential ecological importance, undermining that assumption and weakening the conclusion. Option A merely mentions more funding – it does not affect the park's value. Option C supports the idea that the park is underused. Option D reinforces the need for housing, which actually strengthens the council's plan.
Q3Thinking Skills Easy Logical Reasoning
Emma, the manager of a local bike shop, wants to know whether customers are happy with the new safety helmets. She asks the 80 customers who bought the new helmet last month to rate their satisfaction on a scale of 1 to 10. The average rating is 9.2, so she concludes that the new helmet makes all customers very satisfied.
What is the main weakness in Emma's survey?
Explanation
The survey only asked people who already bought the helmet, so the results cannot be generalised to all customers – the sample is biased. The sample size of 80 is reasonably large, the 1‑to‑10 scale is a standard clear measure, and there is no indication that respondents were pressured.
Q4Thinking Skills Easy Numerical Reasoning
A school fundraiser sells two types of tickets. A standard ticket costs $2 and gives 1 raffle entry. A premium ticket costs $5 and gives 4 raffle entries. The school wants to raise exactly $27 and give out exactly 15 raffle entries. How many of each ticket must be sold?
Explanation
Let s = number of standard tickets and p = number of premium tickets.
Cost equation: 2s + 5p = 27.
Entry equation: s + 4p = 15.
From the entry equation, s = 15 – 4p.
Substitute into the cost equation: 2(15 – 4p) + 5p = 27 → 30 – 8p + 5p = 27 → 30 – 3p = 27 → 3p = 3 → p = 1.
Then s = 15 – 4·1 = 11.
So the school must sell 11 standard tickets and 1 premium ticket.
Q5Mathematical Reasoning Medium Number & Algebra
Liam thinks of a number. He multiplies it by 3, adds 12, then divides the result by 2. If the final result is 21, what number did he first think of?
Explanation
Work backwards, undoing each step in reverse order. Start at 21 and multiply by 2 to undo the division: 42. Subtract 12 to undo the addition: 30. Divide by 3 to undo the multiplication: 10. Option D is the trap — it is the value reached one step early, before the final division is undone.
Q6Mathematical Reasoning Easy Statistics & Probability
A jar contains 2 red, 3 blue and 5 yellow beads. Two beads are drawn at random without replacement. What is the probability that at least one of the two beads drawn is red?
Explanation
Step 1: Total beads = 2 + 3 + 5 = 10. The number of ways to draw any 2 beads is C(10,2) = 45.
Step 2: Find the complement – the probability that no red bead is drawn. There are 8 non‑red beads, so the number of ways to choose 2 non‑red beads is C(8,2) = 28. Thus P(no red) = 28/45.
Step 3: Required probability = 1 – P(no red) = 1 – 28/45 = (45‑28)/45 = 17/45.
Q7Mathematical Reasoning Easy Number & Algebra
A number machine follows a rule: it first multiplies the input number by 3, then subtracts 4 from the result. If the number 8 is put into the machine, what number comes out?
Explanation
The rule involves two sequential steps:
1. First, multiply the input number by 3. Given input = 8 → 8 × 3 = 24
2. Then, subtract 4 from the result. 24 - 4 = 20
Therefore, the number that comes out is 20.
Q8Mathematical Reasoning Easy Ratio & Proportion
For a school fete, cupcakes are sold in boxes. Each box contains 3 chocolate cupcakes and 5 vanilla cupcakes. If a baker prepares 24 chocolate cupcakes, how many vanilla cupcakes will they need to prepare to fill the boxes?
Explanation
Each box has 3 chocolate cupcakes. With 24 chocolate cupcakes, the baker can fill 24 ÷ 3 = 8 boxes.
Each box also needs 5 vanilla cupcakes, so 8 boxes × 5 = 40 vanilla cupcakes needed.
Q9Reading Medium Figurative Language
In the saying "break the ice", the phrase most closely means:
Explanation
The idiom is figurative: it describes easing tension and getting a conversation started when people feel uneasy. Option A takes the words literally, which is the mistake the question is testing. C and D attach a negative meaning the idiom does not carry.
Q10Reading Easy Reading Comprehension
The word 'crackling' (in line 8) tells us that the fire was:
[Passage context: "When night fell, the fire crackling in the centre of the circle became our focus. The sound was steady, like a heartbeat..."]
Explanation
The passage describes "the fire crackling in the centre of the circle" and adds, "The sound was steady, like a heartbeat." Therefore "crackling" describes a continuous, sharp sound. Option B is correct.
Q11Reading Medium Vocabulary in Context
The word "bleak" in the passage suggests that the landscape felt:
[Passage context: "Mawson's diary described the scene as 'a bleak landscape where the snow drifts seem to swallow the horizon'."]
Explanation
"Bleak" here conveys desolation and hopelessness, matching option C. The other options describe feelings not aligned with the usual meaning of 'bleak' in this context of Antarctic exploration.
Q12Reading Hard Inference
Why does the writer mention "the tide's gentle retreat" before describing the glow?
[Passage context: "As the tide's gentle retreat pulls the water back over the sand, a faint shimmer begins at the shoreline..."]
Explanation
The detail connects the retreat of the tide with the onset of movement that disturbs the plankton, triggering the bioluminescence. It does not state that glow is limited to low tide, nor does it suggest exclusive tourist access.
Q13Abstract Reasoning Easy Pattern Recognition
These five shapes can be put in order based on rotation. The shape rotates 45° clockwise each step. Which one is the middle of the sequence?
(Imagine arrow shapes rotated at: 315°, 270°, 0°, 180°, 225°)
Explanation
Put the five shapes in order of rotation: 315° → 270° → 0° → 180° → 225° (each step rotates 45° clockwise). The middle one (3rd position) is the upright arrow at 0° rotation.
Answer key & worked explanations
Mark the pack after all 13 questions are attempted, not as you go. Sort every
wrong answer into "didn't know it" or "knew it, misread" — the two need different fixes.
A — A public park is located a five-minute walk from the neighbourhood. Logical Reasoning
The argument assumes the garden is the only green space for children. Option A shows another park nearby, so closing the garden need not reduce outdoor activity — the assumption collapses. B and C describe other benefits and other programmes, neither of which touches the assumption. D disputes the cost claim, not the reasoning about green space.
B — If true, Riverside Park contains the only breeding ground for a protected frog species. Logical Reasoning
The argument assumes that low visitor numbers mean the park has little value, justifying its sale. Option B shows the park has essential ecological importance, undermining that assumption and weakening the conclusion. Option A merely mentions more funding – it does not affect the park's value. Option C supports the idea that the park is underused. Option D reinforces the need for housing, which actually strengthens the council's plan.
A — survey only includes customers who purchased the helmet (selection bias) Logical Reasoning
The survey only asked people who already bought the helmet, so the results cannot be generalised to all customers – the sample is biased. The sample size of 80 is reasonably large, the 1‑to‑10 scale is a standard clear measure, and there is no indication that respondents were pressured.
A — 11 standard tickets and 1 premium ticket Numerical Reasoning
Let s = number of standard tickets and p = number of premium tickets.
Cost equation: 2s + 5p = 27.
Entry equation: s + 4p = 15.
From the entry equation, s = 15 – 4p.
Substitute into the cost equation: 2(15 – 4p) + 5p = 27 → 30 – 8p + 5p = 27 → 30 – 3p = 27 → 3p = 3 → p = 1.
Then s = 15 – 4·1 = 11.
So the school must sell 11 standard tickets and 1 premium ticket.
E — 10 Number & Algebra
Work backwards, undoing each step in reverse order. Start at 21 and multiply by 2 to undo the division: 42. Subtract 12 to undo the addition: 30. Divide by 3 to undo the multiplication: 10. Option D is the trap — it is the value reached one step early, before the final division is undone.
A — A) 17/45 Statistics & Probability
Step 1: Total beads = 2 + 3 + 5 = 10. The number of ways to draw any 2 beads is C(10,2) = 45.
Step 2: Find the complement – the probability that no red bead is drawn. There are 8 non‑red beads, so the number of ways to choose 2 non‑red beads is C(8,2) = 28. Thus P(no red) = 28/45.
Step 3: Required probability = 1 – P(no red) = 1 – 28/45 = (45‑28)/45 = 17/45.
C — C) 20 Number & Algebra
The rule involves two sequential steps:
1. First, multiply the input number by 3. Given input = 8 → 8 × 3 = 24
2. Then, subtract 4 from the result. 24 - 4 = 20
Therefore, the number that comes out is 20.
D — D) 40 Ratio & Proportion
Each box has 3 chocolate cupcakes. With 24 chocolate cupcakes, the baker can fill 24 ÷ 3 = 8 boxes.
Each box also needs 5 vanilla cupcakes, so 8 boxes × 5 = 40 vanilla cupcakes needed.
B — To start a friendly conversation in an uncomfortable situation Figurative Language
The idiom is figurative: it describes easing tension and getting a conversation started when people feel uneasy. Option A takes the words literally, which is the mistake the question is testing. C and D attach a negative meaning the idiom does not carry.
B — B) Making a continuous, sharp sound. Reading Comprehension
The passage describes "the fire crackling in the centre of the circle" and adds, "The sound was steady, like a heartbeat." Therefore "crackling" describes a continuous, sharp sound. Option B is correct.
C — C) Desolate and hopeless. Vocabulary in Context
"Bleak" here conveys desolation and hopelessness, matching option C. The other options describe feelings not aligned with the usual meaning of 'bleak' in this context of Antarctic exploration.
B — B) To link the timing of the glow with a physical process. Inference
The detail connects the retreat of the tide with the onset of movement that disturbs the plankton, triggering the bioluminescence. It does not state that glow is limited to low tide, nor does it suggest exclusive tourist access.
C — C) 0° rotation (upright) Pattern Recognition
Put the five shapes in order of rotation: 315° → 270° → 0° → 180° → 225° (each step rotates 45° clockwise). The middle one (3rd position) is the upright arrow at 0° rotation.
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