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PERT practice questions

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Question 1Project Network Modeling and Activity Sequencing

In PERT, the expected (mean) duration of an activity is calculated as which weighted average of the optimistic (O), most likely (M), and pessimistic (P) estimates?

  1. (O + 4M + P) / 6 Correct answer.
  2. (O + 2M + P) / 4
  3. (O + M + P) / 3
  4. (4O + M + P) / 6

Explanation

PERT approximates the activity duration with a beta distribution that weights the most likely value four times and each extreme once, then divides by six. This places the mean closer to M than a simple average would.

Question 2Project Network Modeling and Activity Sequencing

In PERT analysis, the standard deviation of an activity's duration estimate is calculated as:

  1. (P − O) / 3
  2. [(P − O) / 6]²
  3. (P − O) / 2
  4. (P − O) / 6 Correct answer.

Explanation

The optimistic-to-pessimistic range is treated as spanning roughly six standard deviations (three on each side of the mean), so dividing the range by six yields the standard deviation. Squaring that result gives the variance.

Question 3Project Network Modeling and Activity Sequencing

Which path through a project network determines the shortest possible project duration?

  1. The longest path in terms of total duration Correct answer.
  2. The path containing the largest number of activities
  3. The path with the greatest total float
  4. The path with the lowest total direct cost

Explanation

Project duration equals the duration of the longest path, since every path must be completed before the project finishes. That longest path is the critical path, and its activities have the least scheduling flexibility.

Question 4Project Network Modeling and Activity Sequencing

In an activity-on-node (precedence) diagram, each node represents:

  1. A dummy activity showing dependency only
  2. A single project activity with its duration Correct answer.
  3. The elapsed time between two events
  4. A milestone or event with no duration

Explanation

In activity-on-node format the activity itself sits on the node, and arrows show the logical relationships between activities. Duration and other attributes are attached to the node.

Question 5Project Network Modeling and Activity Sequencing

Total float (slack) for an activity is best defined as:

  1. The time an activity can slip without delaying any immediate successor
  2. The range between the optimistic and pessimistic duration estimates
  3. The time an activity can slip without delaying project completion Correct answer.
  4. The time by which a duration can be shortened with added resources

Explanation

Total float is the difference between an activity's late and early finish (or late and early start), meaning the schedule cushion available before the project finish date is affected. It can be shared with other activities on the same path.

Question 6Project Network Modeling and Activity Sequencing

A finish-to-start (FS) relationship between activity A and activity B means that:

  1. B may finish only after A starts
  2. A cannot finish until B has started
  3. A and B must start at the same time
  4. B cannot start until A has finished Correct answer.

Explanation

In a finish-to-start link the predecessor's finish governs the successor's start, so the successor waits for the predecessor to complete. It is the most common relationship used in precedence diagrams.

Question 7Project Network Modeling and Activity Sequencing

The forward pass through a project network is used to determine which set of values?

  1. Late start and late finish dates
  2. Early start and early finish dates Correct answer.
  3. Budgeted cost and earned value
  4. Total float and free float

Explanation

The forward pass moves from the start of the network to the finish, assigning each activity the earliest date it can begin and end given its predecessors. Float values are then derived by comparing these dates with the backward pass results.

Question 8Project Network Modeling and Activity Sequencing

In an activity-on-arrow (AOA) network, a dummy activity is used to:

  1. Show a logical dependency that consumes no time or resources Correct answer.
  2. Split a long activity into two shorter parallel activities
  3. Represent an activity that has been removed from scope
  4. Provide a placeholder for an activity whose duration is unknown

Explanation

A dummy is a zero-duration, zero-resource arrow that carries logic only, keeping the network's dependency structure correct. It is required when the pure arrow notation cannot otherwise express which activity depends on which.

Question 9Project Network Modeling and Activity Sequencing

An activity has an optimistic estimate of 4 days, a most likely estimate of 6 days, and a pessimistic estimate of 14 days. What is its PERT expected duration?

  1. 8 days
  2. 6 days
  3. 7 days Correct answer.
  4. 9 days

Explanation

Applying the PERT formula gives (4 + 4×6 + 14) / 6 = 42 / 6 = 7 days. The most likely value receives four times the weight of each extreme.

Question 10Project Network Modeling and Activity Sequencing

An activity has an optimistic estimate of 3 days and a pessimistic estimate of 15 days. What is its PERT standard deviation?

  1. 4 days
  2. 2 days Correct answer.
  3. 1 day
  4. 3 days

Explanation

The standard deviation is (15 − 3) / 6 = 2 days. The 12-day range is treated as six standard deviations wide.

Question 11Project Network Modeling and Activity Sequencing

An activity has an early start of day 5, a duration of 4 days, and a late start of day 8. What is its total float?

  1. 4 days
  2. 12 days
  3. 3 days Correct answer.
  4. 5 days

Explanation

Total float equals late start minus early start, or equivalently late finish minus early finish. Here 8 − 5 = 3 days, matching a late finish of day 12 against an early finish of day 9.

Question 12Project Network Modeling and Activity Sequencing

Activity P has an early finish of day 10. Its two immediate successors have early starts of day 12 and day 15 respectively. What is P's free float?

  1. 1 day
  2. 5 days
  3. 0 days
  4. 2 days Correct answer.

Explanation

Free float equals the earliest start among the immediate successors minus the activity's early finish, so 12 − 10 = 2 days. Using the later successor start would overstate how far P can slip before affecting any successor.

Question 13Project Network Modeling and Activity Sequencing

Activities A (3 days) and B (4 days) can start at project start. Activity C (2 days) depends only on A. Activity D (5 days) depends on both A and B. Activity E (2 days) depends on both C and D. What is the minimum project duration?

  1. 7 days
  2. 10 days
  3. 11 days Correct answer.
  4. 9 days

Explanation

Enumerating the paths gives A-C-E = 3+2+2 = 7, A-D-E = 3+5+2 = 10, and B-D-E = 4+5+2 = 11 days. The longest path, B-D-E at 11 days, sets the project duration.

Question 14Project Network Modeling and Activity Sequencing

In a precedence diagram, a finish-to-start relationship with a lag of 3 days means that:

  1. The successor can start 3 days after the predecessor finishes Correct answer.
  2. The two activities must overlap by at least 3 days
  3. The successor can start 3 days before the predecessor finishes
  4. The predecessor must finish 3 days after the successor starts

Explanation

A lag adds waiting time to a relationship, so the successor's start is pushed three days beyond the predecessor's finish. A negative lag, by contrast, would pull the successor earlier.

Question 15Project Network Modeling and Activity Sequencing

Which of the following is a mandatory dependency?

  1. Scheduling landscaping after the roofing crew becomes available
  2. Waiting for poured concrete to cure before framing on top of it Correct answer.
  3. Choosing to write the user manual before the training materials
  4. Starting interior painting after the client's furniture delivery

Explanation

Mandatory (hard) dependencies are inherent in the nature of the work, such as a physical or contractual requirement that cannot be reordered. Concrete must cure before framing can bear on it, regardless of management preference.

Question 16Project Network Modeling and Activity Sequencing

A project network has two parallel critical paths of equal duration. Which statement is true?

  1. Only the path with more activities is truly critical
  2. Both paths must be shortened to reduce the project duration Correct answer.
  3. One of the two paths must contain a logic error
  4. Shortening either path alone will shorten the project

Explanation

When two paths share the longest duration, each independently controls the project finish date. Reducing only one leaves the other still driving the end date, so compression must address both.

Question 17Project Network Modeling and Activity Sequencing

During the backward pass, the late finish of an activity is set to:

  1. The smallest late start among its immediate successors Correct answer.
  2. The early finish date of the project
  3. The largest late start among its immediate successors
  4. Its own late start plus its duration

Explanation

An activity must finish in time for the most constrained successor to start late, so its late finish is the minimum of its successors' late starts, adjusted for any lag. Using the largest value would allow the activity to finish too late.

Question 18Project Network Modeling and Activity Sequencing

A project has an expected duration of 40 days and a standard deviation of 4 days. What z-value corresponds to completing the project within 46 days?

  1. 10.0
  2. 6.0
  3. 1.5 Correct answer.
  4. 0.67

Explanation

The z-value is the difference between the target and the mean divided by the standard deviation: (46 − 40) / 4 = 1.5. It expresses the target date in units of standard deviation.

Question 19Project Network Modeling and Activity Sequencing

Which statement distinguishes the critical path method from PERT?

  1. CPM uses one deterministic duration per activity Correct answer.
  2. CPM cannot handle networks with more than one critical path
  3. CPM replaces the network diagram with a bar chart
  4. CPM requires three duration estimates per activity

Explanation

CPM treats activity durations as known, single values, which suits repetitive work with reliable historical data. PERT adds uncertainty by using three-point probabilistic estimates.

Question 20Project Network Modeling and Activity Sequencing

A project is behind schedule and the manager wants to shorten the overall duration at the lowest added cost. Which activity should be crashed first?

  1. A critical-path activity with the lowest crash cost per time unit Correct answer.
  2. A noncritical activity that is nearly finished
  3. The longest-duration activity in the network regardless of path
  4. Any activity with the largest total float

Explanation

Only critical activities control the finish date, so compression must start there. Among critical activities, the one with the lowest cost per unit of time saved gives the cheapest reduction.

Question 21Project Network Modeling and Activity Sequencing

Activity X has an early finish of day 12. Every path from X to the end of the network has a duration of 5 days, and the project duration is 20 days. What is X's total float?

  1. 3 days Correct answer.
  2. 5 days
  3. 0 days
  4. 8 days

Explanation

X's late finish is the project duration minus the longest remaining path: 20 − 5 = 15. Total float is late finish minus early finish, so 15 − 12 = 3 days.

Question 22Project Network Modeling and Activity Sequencing

Three activities on the critical path have duration variances of 4, 9, and 4 square days. What is the standard deviation of the total project duration?

  1. Approximately 17 days
  2. Approximately 3.0 days
  3. Approximately 5.67 days
  4. Approximately 4.12 days Correct answer.

Explanation

Variances of activities along a path are additive, giving 4 + 9 + 4 = 17, and the standard deviation is the square root of that sum, about 4.12 days. Standard deviations themselves would not be added directly.

Question 23Project Network Modeling and Activity Sequencing

Under the PERT three-point method, the expected duration exceeds the most likely duration when which condition holds?

  1. The most likely estimate equals the average of the optimistic and pessimistic
  2. The optimistic estimate is farther from the most likely than the pessimistic is
  3. The optimistic and pessimistic estimates are equidistant from the most likely
  4. The pessimistic estimate is farther from the most likely than the optimistic is Correct answer.

Explanation

The expected time minus the most likely time equals [(P − M) − (M − O)] / 6, so the mean is pulled above M whenever the pessimistic side is more stretched. That corresponds to a right-skewed distribution of possible durations.

Question 24Project Network Modeling and Activity Sequencing

The backward pass on a network produces negative total float for several activities. What does this indicate?

  1. An imposed finish date precedes what the network can achieve Correct answer.
  2. Those activities lie on a path shorter than the critical path
  3. The calculations are invalid, because float cannot be negative
  4. Those activities have more resources assigned than are available

Explanation

Negative float appears when a target or contractual finish date is earlier than the date the network logic can deliver. It signals that the plan must be compressed, resequenced, or the date renegotiated.

Question 25Project Network Modeling and Activity Sequencing

An activity has a total float of 6 days and a free float of 2 days. If it is delayed by 4 days, what is the effect?

  1. The project finish date is delayed by 4 days
  2. The project finish date is delayed by 2 days
  3. Neither the successor nor the project finish date is affected
  4. A successor is delayed by 2 days; the project finish is not Correct answer.

Explanation

A delay consumes free float first; anything beyond it pushes the earliest start of the immediate successors, here by 4 − 2 = 2 days. Because the 4-day delay remains within the 6 days of total float, the project finish date is unchanged.

Question 26Project Network Modeling and Activity Sequencing

In a precedence diagram, a start-to-start relationship with zero lag between Activity A and Activity B means that:

  1. The predecessor must finish before the successor can finish
  2. The predecessor can begin once the successor has begun
  3. The successor can begin once the predecessor has finished
  4. The successor can begin once the predecessor has begun Correct answer.

Explanation

A start-to-start link ties the successor's start to the predecessor's start, so with zero lag the successor may begin as soon as the predecessor begins (subject to its other constraints). The predecessor's finish date plays no part in this logic.

Question 27Project Network Modeling and Activity Sequencing

In a precedence diagram, a finish-to-finish relationship with zero lag between Activity A and Activity B means that:

  1. The successor cannot finish until the predecessor finishes Correct answer.
  2. The predecessor cannot start until the successor has started
  3. Both activities must have identical durations
  4. The successor cannot start until the predecessor has finished

Explanation

A finish-to-finish link constrains the successor's finish to occur on or after the predecessor's finish. It does not force equal durations, and it limits the successor's start only indirectly through its own duration.

Question 28Project Network Modeling and Activity Sequencing

A negative lag applied between two linked activities is best described as:

  1. An error in the network logic that must be corrected
  2. A constraint that fixes the successor's start date
  3. A lead allowing the successor to overlap Correct answer.
  4. A delay applied to the successor activity

Explanation

Lag is time inserted between linked activities, so a negative lag works in the opposite direction and permits the successor to start or finish ahead of the predecessor's corresponding point. This overlap is called a lead and is legitimate logic when work can genuinely proceed concurrently.

Question 29Project Network Modeling and Activity Sequencing

Which statement correctly describes an activity-on-node (precedence) diagram?

  1. Activities are drawn as nodes and dependencies as arrows Correct answer.
  2. The nodes store only the early and late event times
  3. Activities are drawn on the arrows and the nodes represent events
  4. Dummy activities are required for every dependency

Explanation

In an activity-on-node diagram each activity occupies its own node (box) and precedence is shown by arrows between nodes. This is why AON networks generally need no dummy activities to preserve activity identity.

Question 30Project Network Modeling and Activity Sequencing

An activity that lies on the critical path of a network with no imposed date constraints has:

  1. Total float equal to the project's total float
  2. Float that cannot be determined without resource loading
  3. Zero total float Correct answer.
  4. Total float equal to its own duration

Explanation

The critical path is the longest path through the network, so any slippage on it moves the project finish date. Such activities therefore have zero total float, while activities on shorter paths carry positive float.

Question 31Project Network Modeling and Activity Sequencing

In a precedence network, the earliest time at which the whole project can be completed equals:

  1. The longest path through the network Correct answer.
  2. The sum of all activity durations in the network
  3. The duration of the path with the most activities
  4. The average of all path durations

Explanation

The project cannot finish until every path from start to finish is complete, so the longest path governs the completion date. Summing all durations double-counts activities that run in parallel.

Question 32Project Network Modeling and Activity Sequencing

An activity that has two or more immediate successors in a network is termed:

  1. A burst activity Correct answer.
  2. A dummy activity
  3. A merge activity
  4. A hammock activity

Explanation

Terminology distinguishes nodes by their degree: a burst releases more than one successor, while a merge receives more than one predecessor. Both are ordinary logic features and require no special treatment in the calculation.

Question 33Project Network Modeling and Activity Sequencing

A start-to-finish relationship is most appropriate when:

  1. Two activities must end on the same day
  2. A successor must wait for a predecessor to finish before starting
  3. Two activities must begin on the same day
  4. A successor's finish depends on another activity's start Correct answer.

Explanation

A start-to-finish link ties the successor's completion to the start of the predecessor, so the successor cannot be finished until the predecessor has begun. It is the least common relationship and suits handover logic, such as retiring an old system once its replacement is switched on.

Question 34Project Network Modeling and Activity Sequencing

Activity A has an early start of day 5 and a duration of 10 days. Activity B is linked to A by a start-to-start relationship with a lag of 3 days and has no other predecessors. What is B's early start?

  1. Day 18
  2. Day 8 Correct answer.
  3. Day 15
  4. Day 5

Explanation

A start-to-start link with lag states that the successor's start is at least the predecessor's start plus the lag: 5 + 3 = 8. The predecessor's duration is irrelevant because the link references only its start date.

Question 35Project Network Modeling and Activity Sequencing

Activity X has an early start of day 6 and a duration of 4 days. Activity Y follows X under a finish-to-finish relationship with a lag of 2 days and has a duration of 3 days, with no other constraints. What is Y's early start?

  1. Day 9 Correct answer.
  2. Day 6
  3. Day 15
  4. Day 12

Explanation

A finish-to-finish link with lag sets Y's early finish at X's early finish plus the lag: (6 + 4) + 2 = 12. Y's own duration of 3 days converts that finish constraint into an early start of 12 − 3 = 9.

Question 36Project Network Modeling and Activity Sequencing

Activity C has an early start of day 10 and a duration of 5 days. Its only successor has an early start of day 18. What is C's free float?

  1. 8 days
  2. 3 days Correct answer.
  3. 0 days
  4. 5 days

Explanation

Free float is the slip an activity can absorb without delaying any immediate successor: successor early start minus the activity's early finish, or 18 − (10 + 5) = 3 days. Total float would add the successors' own float on top of this gap.

Question 37Project Network Modeling and Activity Sequencing

While reviewing a precedence diagram you find that Activity K depends on L, L depends on M, and M depends on K. What is the correct treatment of this situation?

  1. Treat the loop as a single activity with the sum of the durations
  2. Revise the logic so that the network contains no cycle Correct answer.
  3. Replace the three links with dummy activities
  4. Keep the loop and let the forward pass resolve it iteratively

Explanation

A precedence network must be acyclic; a cycle has no valid calculation order and implies that each activity waits on itself. Such a loop almost always signals mis-stated logic, such as a missing phase or a sequence that has been reversed.

Question 38Project Network Modeling and Activity Sequencing

An activity has predecessors but no successor, and it is not the final activity of the project. What does this most likely indicate?

  1. The activity has zero total float
  2. The activity must be removed from the network as an error
  3. A logical link to the rest of the network is missing Correct answer.
  4. The activity is a hammock activity

Explanation

Apart from the project's finishing activity, every activity should lead somewhere; a dangling end usually means a missing dependency. Until the link is added, the activity can slip without pushing the computed project finish, and the completion date will be understated.

Question 39Project Network Modeling and Activity Sequencing

In an activity-on-arrow network, what does a node represent?

  1. A cost account to which activities are coded
  2. A point in time marking an activity's start or finish Correct answer.
  3. A resource assignment shared by the following activities
  4. An activity that consumes both time and resources

Explanation

In the AOA convention, arrows carry the activities and nodes are events, meaning instants at which incoming work has finished and outgoing work may begin. Events themselves take no time and hold no resources.

Question 40Project Network Modeling and Activity Sequencing

Activity D has an early finish of day 22 and a late finish of day 27. What is D's total float?

  1. 27 days
  2. 5 days Correct answer.
  3. 0 days
  4. 22 days

Explanation

Total float equals late finish minus early finish, or 27 − 22 = 5 days. It is the delay the activity can absorb without moving the project completion date past its planned finish.

Question 41Project Network Modeling and Activity Sequencing

Activity E has an early start of day 8 and a duration of 6 days. It has two successors whose early starts are day 16 and day 20. What is E's free float?

  1. 12 days
  2. 0 days
  3. 2 days Correct answer.
  4. 6 days

Explanation

E's early finish is day 14, and free float is measured against the earliest-starting successor: min(16, 20) − 14 = 2 days. Using the later successor would overstate the float and would delay the day-16 activity.

Question 42Project Network Modeling and Activity Sequencing

A contract requires completion by day 60, while the network's calculated early finish is day 55. Relative to the imposed date, the project has:

  1. Zero float, because the contract date is a constraint
  2. Minus 5 days, because the date is earlier than the computed finish
  3. 5 days of project float Correct answer.
  4. Float that cannot be determined without the activity durations

Explanation

When an imposed finish date falls later than the calculated early finish, the difference (60 − 55) is project float available before the contract is breached. The constraint reduces that buffer but does not, by itself, make the plan late.

Question 43Project Network Modeling and Activity Sequencing

Two activities are linked only by a start-to-start relationship with a lag of 4 days. If the predecessor's duration is increased by 5 days, what happens to the successor's early start, all else being equal?

  1. It moves later by 4 days
  2. It moves earlier by 1 day
  3. It does not change Correct answer.
  4. It moves later by 5 days

Explanation

A start-to-start link constrains the successor's start by the predecessor's start plus the lag, so the predecessor's duration is irrelevant to that tie. The added duration would propagate only through a finish-based relationship or a shared successor constraint.

Question 44Project Network Modeling and Activity Sequencing

Activity F has a total float of 4 days and is delayed by 7 days. Assuming no other changes, what is the effect on the project?

  1. The project finish is delayed by exactly 4 days
  2. The project is unaffected because F still has float remaining
  3. The project finish is delayed by the full 7 days
  4. The finish slips 3 days and F's path becomes critical Correct answer.

Explanation

Total float must be consumed before the project finish moves, so the first 4 days of delay absorb the float and the remaining 3 days push the completion date. F's path then has zero float and joins the critical path.

Question 45Project Network Modeling and Activity Sequencing

A team schedules integration testing only after every code review is complete, although the two could overlap. This dependency is best classified as:

  1. External, because it involves another organization
  2. Resource-driven, because both use the same team
  3. Discretionary, because it reflects a chosen practice Correct answer.
  4. Mandatory, because testing cannot start without reviewed code

Explanation

Discretionary (soft) logic reflects preferred practice, policy, or convenience and can be re-sequenced if the schedule demands it. Mandatory dependencies arise from hard physical or contractual limits, which this situation does not describe.

Question 46Project Network Modeling and Activity Sequencing

A network has four start-to-finish paths with durations of 18, 24, 21, and 24 days, with no imposed dates. What is the earliest project completion time, and which paths are critical?

  1. 87 days; the sum of all paths is critical
  2. 24 days; the two 24-day paths are critical Correct answer.
  3. 21 days; the path of median length is critical
  4. 18 days; the shortest path is critical

Explanation

Earliest completion equals the longest path, which is 24 days, and every path achieving that length has zero float and is therefore critical. The presence of two critical paths means a delay on either one delays the project.

Question 47Project Network Modeling and Activity Sequencing

Activity H has an early start of day 12 and a duration of 8 days. Its successor J has an early start of day 25 and a total float of 4 days. What are H's free float and total float?

  1. Free float 0 days; total float 4 days
  2. Free float 5 days; total float 9 days Correct answer.
  3. Free float 9 days; total float 5 days
  4. Free float 5 days; total float 5 days

Explanation

H's early finish is day 20, so its free float is the gap to J's early start: 25 − 20 = 5 days. Total float adds the successor's own float to that gap, giving 5 + 4 = 9 days.

Question 48Project Network Modeling and Activity Sequencing

A project has a critical path of 30 days and a second path of 28 days. One critical activity is shortened by 4 days with no other changes. What is the new project duration?

  1. 30 days
  2. 24 days
  3. 28 days Correct answer.
  4. 26 days

Explanation

Shortening the critical path by 4 days reduces it to 26 days, at which point the 28-day path becomes the longest and governs the finish. The project duration can fall further only if that path is also compressed.

Question 49Project Network Modeling and Activity Sequencing

A hammock activity spans the time between two points in a network. What duration does it take in the schedule?

  1. The duration of the longest single activity among those it spans
  2. Zero, because a hammock consumes no work of its own
  3. The elapsed span from first spanned start to last spanned finish Correct answer.
  4. The arithmetic sum of the durations of all the activities it spans

Explanation

A hammock is a summary (level-of-effort) element whose length is the elapsed time between the start of the earliest activity it covers and the finish of the latest. It recalculates automatically as the spanned activities move, which makes it a reporting device rather than a work package.

Question 50Project Network Modeling and Activity Sequencing

A strict finish-to-start chain of repetitive activities is replaced by a laddered sequence using start-to-start links with lags. What is the effect on the schedule?

  1. Every link must be converted back to finish-to-start before calculation
  2. Overlap between consecutive activities compresses the overall duration Correct answer.
  3. The overall duration lengthens because more links are drawn
  4. The critical path becomes undefined until resources are assigned

Explanation

Laddering staggers the start of each trade or unit so downstream work begins before its predecessor is entirely complete, shortening the total duration. The network remains acyclic and fully calculable, so the critical path is still derived normally.