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Critical path method in Software Engineering - Practice Problems & Coding Challenges

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Challenge - 5 Problems
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Critical Path Mastery
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🧠 Conceptual
intermediate
2:00remaining
Understanding the Critical Path

In project management, what does the critical path represent?

AThe shortest sequence of tasks that can be completed independently
BThe tasks with the most resources assigned
CThe longest sequence of dependent tasks that determines the shortest project duration
DThe sequence of tasks that can be delayed without affecting the project end date
Attempts:
2 left
💡 Hint

Think about which tasks control the overall project length.

📋 Factual
intermediate
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Identifying Slack Time

What is slack time (or float) in the context of the Critical Path Method?

AThe amount of time a task can be delayed without delaying the project completion
BThe total duration of the critical path
CThe time required to complete the longest task in the project
DThe time between the start and finish of the first task
Attempts:
2 left
💡 Hint

Slack time relates to flexibility in scheduling tasks.

🔍 Analysis
advanced
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Effect of Delays on Project Duration

Consider a project with a critical path duration of 30 days. If a non-critical task with 5 days of slack is delayed by 6 days, what happens to the project completion time?

AThe project completion time decreases by 5 days
BThe project completion time remains 30 days
CThe project completion time increases by 6 days
DThe project completion time increases by 1 day
Attempts:
2 left
💡 Hint

Compare the delay to the slack time available.

❓ Comparison
advanced
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Comparing Critical Path and Critical Chain

Which statement best distinguishes the Critical Path Method (CPM) from the Critical Chain Method (CCM) in project management?

ACPM manages resources strictly; CCM ignores resource constraints
BCPM focuses on task order and duration; CCM adds resource availability and buffers to manage uncertainties
CCPM uses probabilistic task durations; CCM uses fixed durations only
DCPM is used only for software projects; CCM is used only for construction projects
Attempts:
2 left
💡 Hint

Think about how each method handles resources and uncertainties.

❓ Reasoning
expert
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Calculating Project Duration with Multiple Paths

A project has three paths with durations: Path 1 = 20 days, Path 2 = 25 days, Path 3 = 22 days. Path 2 has a task delayed by 3 days. Which statement is true about the new project duration?

AThe project duration becomes 28 days because Path 2 is now the longest
BThe project duration remains 25 days because delays on critical path tasks do not affect total duration
CThe project duration becomes 23 days because Path 3 is now the longest
DThe project duration becomes 20 days because Path 1 is the shortest
Attempts:
2 left
💡 Hint

Identify the critical path before and after the delay.

Practice

(1/5)
1. What does the Critical Path Method (CPM) primarily help determine in a project?
easy
A. The total cost of the project
B. The longest sequence of dependent tasks that sets the project duration
C. The number of team members required
D. The quality standards for project deliverables

Solution

  1. Step 1: Understand the purpose of CPM

    The Critical Path Method is used to find the longest chain of tasks that must be completed on time to avoid delaying the project.

  2. Step 2: Identify what CPM does not measure

    CPM does not calculate cost, team size, or quality standards; it focuses on task sequencing and timing.

  3. Final Answer:

    The longest sequence of dependent tasks that sets the project duration -> Option B

  4. Quick Check:

    CPM = longest task sequence [OK]
Hint: CPM finds the longest chain of tasks to finish on time [OK]
Common Mistakes:
  • Confusing CPM with cost estimation
  • Thinking CPM calculates resources needed
  • Assuming CPM sets quality standards
2. Which of the following is the correct way to represent a task dependency in a project network diagram?
easy
A. Task A finishes before Task B starts, but they are independent
B. Task A and Task B start at the same time regardless of each other
C. Task B starts only after Task A finishes
D. Task B can start before Task A finishes

Solution

  1. Step 1: Understand task dependency in CPM

    In CPM, a task dependency means one task must finish before the next can start.

  2. Step 2: Evaluate each option

    Only Task B starts only after Task A finishes correctly states that Task B starts after Task A finishes, showing a dependency.

  3. Final Answer:

    Task B starts only after Task A finishes -> Option C

  4. Quick Check:

    Dependency = task B after task A [OK]
Hint: Dependencies mean one task waits for another to finish [OK]
Common Mistakes:
  • Assuming tasks can start simultaneously without dependency
  • Thinking tasks are independent when they have dependencies
  • Believing a task can start before its predecessor finishes
3. Given tasks with durations and dependencies:
Task A: 3 days (start)
Task B: 4 days (after A)
Task C: 2 days (after A)
Task D: 5 days (after B and C)
What is the total project duration using CPM?
medium
A. 9 days
B. 7 days
C. 14 days
D. 12 days

Solution

  1. Step 1: Calculate paths and durations

    Path 1: A (3) -> B (4) -> D (5) = 3 + 4 + 5 = 12 days
    Path 2: A (3) -> C (2) -> D (5) = 3 + 2 + 5 = 10 days

  2. Step 2: Identify the critical path

    The longest path is Path 1 with 12 days, so the project duration is 12 days.

  3. Final Answer:

    12 days -> Option D

  4. Quick Check:

    Longest path duration = 12 days [OK]
Hint: Add durations along longest dependent path [OK]
Common Mistakes:
  • Adding all tasks durations regardless of dependencies
  • Choosing the shortest path instead of longest
  • Ignoring that D depends on both B and C
4. A project has tasks:
A (2 days), B (3 days after A), C (4 days after B), D (1 day after A)
Which task dependency is incorrect if the critical path is A -> B -> C?
medium
A. Task D depends on Task C
B. Task D depends on Task A
C. Task B depends on Task A
D. Task C depends on Task B

Solution

  1. Step 1: Analyze given dependencies

    Tasks A, B, and C form the critical path with dependencies A->B->C.
    Task D depends on A, so it starts after A.

  2. Step 2: Check if Task D depends on Task C

    Since D depends on A only, not on C, Task D depends on Task C is incorrect because it states D depends on C.

  3. Final Answer:

    Task D depends on Task C -> Option A

  4. Quick Check:

    Incorrect dependency = D on C [OK]
Hint: Check if dependencies match critical path order [OK]
Common Mistakes:
  • Assuming all tasks depend on the last task
  • Mixing up which tasks depend on which
  • Ignoring the critical path sequence
5. You have tasks:
W: 2 days (start)
X: 3 days (after W)
Y: 4 days (after W)
Z: 1 day (after X and Y)
If task Y is delayed by 2 days, what is the new project duration?
hard
A. 9 days
B. 10 days
C. 8 days
D. 7 days

Solution

  1. Step 1: Calculate original paths durations

    Path 1: W (2) -> X (3) -> Z (1) = 6 days
    Path 2: W (2) -> Y (4) -> Z (1) = 7 days

  2. Step 2: Add delay to task Y and recalculate

    Y delayed by 2 days: Y duration = 4 + 2 = 6 days
    New Path 2 duration: 2 + 6 + 1 = 9 days

  3. Step 3: Determine new project duration

    Longest path is now Path 2 with 9 days, so project duration is 9 days.

  4. Final Answer:

    9 days -> Option A

  5. Quick Check:

    Delay added to longest path = 9 days [OK]
Hint: Add delay to longest path tasks only [OK]
Common Mistakes:
  • Adding delay to shortest path
  • Ignoring delay impact on critical path
  • Calculating total duration without dependencies
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