Cognitive Reflection Test Problem Decomposition Strategies 3 — Questions and Answers
Question 1: Which strategy solves a problem by breaking it into cases and handling each case separately?
- Case analysis (Correct answer)
- Random guessing
- Ignoring edge cases
- Averaging
Correct answer: Case analysis
Case analysis partitions the problem into exhaustive cases solved individually.
Question 2: A bat and ball cost $1.10; the bat costs $1.00 more than the ball. What does the ball cost?
- $0.10
- $0.05 (Correct answer)
- $0.15
- $1.00
Correct answer: $0.05
Ball = x, bat = x + 1.00, so 2x + 1.00 = 1.10 gives x = $0.05.
Question 3: When you solve a smaller version of a problem first to understand the pattern, this strategy is called:
- Solving a simpler related problem (Correct answer)
- Skipping the problem
- Memorizing the answer
- Guess and check only
Correct answer: Solving a simpler related problem
Tackling a simpler analogous problem reveals structure applicable to the full problem.
Question 4: In bottom-up decomposition, how do you build toward the solution?
- Start from the goal and split down
- Combine small solved pieces into larger structures (Correct answer)
- Ignore the small parts
- Solve only the top level
Correct answer: Combine small solved pieces into larger structures
Bottom-up assembles small verified components into progressively larger solutions.
Question 5: Why is verifying each sub-solution important during decomposition?
- It wastes time
- Errors in a sub-part can propagate to the final answer (Correct answer)
- Verification changes the question
- It is never needed
Correct answer: Errors in a sub-part can propagate to the final answer
An unchecked sub-error can cascade and corrupt the overall result.
Question 6: If it takes 3 painters 3 hours to paint 3 fences, decomposing the rate, how long do 6 painters take to paint 6 fences?
- 6 hours
- 3 hours (Correct answer)
- 1.5 hours
- 9 hours
Correct answer: 3 hours
One painter paints one fence in 3 hours, so 6 painters paint 6 fences in 3 hours.
Question 7: What does 'abstraction' contribute to problem decomposition?
- Adds irrelevant details
- Focuses on essential structure while hiding non-essential detail (Correct answer)
- Makes the problem longer
- Removes all steps
Correct answer: Focuses on essential structure while hiding non-essential detail
Abstraction highlights the core structure so you can reason without distraction.
Cognitive Reflection Test Problem Decomposition Strategies 3
Which strategy solves a problem by breaking it into cases and handling each case separately?