Cognitive Reflection Test Problem Decomposition Strategies 2 — Questions and Answers
Question 1: A widget and a box cost $2.20 together. The box costs $2.00 more than the widget. Decomposing this into two equations, how much does the widget cost?
- $0.10 (Correct answer)
- $0.20
- $0.11
- $0.22
Correct answer: $0.10
Widget = x, box = x + 2.00, so 2x + 2.00 = 2.20 gives x = $0.10.
Question 2: When decomposing a problem, what is the primary purpose of identifying independent sub-problems?
- To make the problem look harder
- So they can be solved separately without affecting each other (Correct answer)
- To increase the number of steps
- To avoid using logic
Correct answer: So they can be solved separately without affecting each other
Independent sub-problems can be solved in isolation because their solutions do not interfere.
Question 3: If 5 machines take 5 minutes to make 5 widgets, decomposing the rate, how long do 100 machines take to make 100 widgets?
- 100 minutes
- 5 minutes (Correct answer)
- 20 minutes
- 1 minute
Correct answer: 5 minutes
Each machine makes one widget in 5 minutes, so 100 machines make 100 widgets in 5 minutes.
Question 4: Which step comes first in a top-down decomposition strategy?
- Solve the smallest detail
- Break the overall goal into major components (Correct answer)
- Combine all solutions
- Test the final answer
Correct answer: Break the overall goal into major components
Top-down decomposition starts by splitting the overall goal into large components before detailing each.
Question 5: A lily pad patch doubles each day and covers the lake in 48 days. Decomposing the growth backward, on what day is it half covered?
- Day 24
- Day 47 (Correct answer)
- Day 46
- Day 12
Correct answer: Day 47
Since it doubles daily, the lake is half covered the day before full coverage, on day 47.
Question 6: What is a key advantage of decomposing a complex problem before solving it?
- It guarantees no mistakes ever occur
- It makes each piece smaller and easier to reason about (Correct answer)
- It removes the need for verification
- It always reduces the answer to one step
Correct answer: It makes each piece smaller and easier to reason about
Decomposition reduces cognitive load by making each sub-piece simpler to handle.
Question 7: In problem decomposition, what does 'dependency mapping' help you determine?
- The color of the diagram
- Which sub-problems must be solved before others (Correct answer)
- How many people to hire
- The final cost only
Correct answer: Which sub-problems must be solved before others
Dependency mapping reveals the order in which sub-problems must be solved.
Cognitive Reflection Test Problem Decomposition Strategies 2
A widget and a box cost $2.20 together.
The box costs $2.00 more than the widget.
Decomposing this into two equations, how much does the widget cost?