30 PMP Math Questions Answer and Explanation

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Question 1 - ID: 602854
A project manager is preparing to lead a project status meeting later that afternoon. The project is currently 75 percent complete and is reaching the most critical point. Since the project sponsor is planning on attending the meeting, the project manager decides to update the earned value calculations to present the latest performance updates in terms that the sponsor will want to see. The budget at completion (BAC) is set at $550,000, and the current estimate at completion (EAC) is at $525,000. How is the project performing in terms of the budget?
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Answer and explanation:
To determine performance against the budget, you must first calculate variance at completion. To calculate variance at completion, subtract the estimate at completion from the budget at completion (BAC – EAC): $550,000 – $525,000 = $25,000. A positive VAC means that the project is performing under the planned costs.
Question 2 - ID: 823489
You are the project manager for Kitchens Plus Inc. The latest project involves the development of an automatic dicer with unique industry features. The project uses a predictive life cycle, and you are analyzing schedule performance. Based on the information provided by the scheduling team, the current schedule performance index (SPI) is at 1.10, while the cost performance index (CPI) is at 0.80. What might be a good strategy for balancing out performance between the schedule and budget?
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Answer and explanation:
Based on the performance indexes provided, the project is 10 percent ahead of schedule but over budget. Leveling out resource usage is a strategy used to spread out costs over time. This helps in reducing sudden spikes in spending, although it may lead to lengthening the schedule.
Question 3 - ID: 813319

A small sample of your project’s PERT calculations is shown here. Activity 2 is particularly important to the project, and your stakeholders are asking for a confidence level for this activity. You tell them there is a 95.44 percent chance of completing activity 2 within how many days?

Activity Optimistic Pessimistic Likely Expected Value
1 10 14 12
2 20 30 23
3 3 3 3
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Answer and explanation:
First you need to calculate the standard deviation for this activity, which is 1.67. That is, (Pessimistic – Optimistic) ÷ 6. A 95.44 percent confidence factor is 3 standard deviations. That is, 1.67 × 3 = 5.01. The expected value is 23 days, so you have a 95.44 percent chance of completing the activity within between 18 and 28 days.
Question 4 - ID: 702934
Using the estimates provided, calculate the beta distribution: most likely estimate (ML) = 72, optimistic estimate (O) = 55, pessimistic estimate (P) = 85. Round to one decimal point.
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Answer and explanation:
A beta distribution calculation involves giving a greater weight to the most likely estimate. Simply multiply the most likely estimate by four, add the result with the other two estimates, and divide by six: (4 × (ML) $72 + (O) $55 + (P) $85) ÷ 6 = $71.3.
Question 5 - ID: 813168
If earned value = 500, planned value = 700, and actual costs = 450, what is the schedule variance?
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Answer and explanation:
To calculate schedule variance, subtract planned value from earned value (SV = EV – PV): $500 – $700 = –$200. A negative schedule variance means that the project is behind schedule.
Question 6 - ID: 923513
A project manager is working through potential options using a decision tree. Scenario A has a failure impact of –$5,000 with a probability of 25 percent, and no impact if successful; and scenario B has a failure impact of –$3,500 with a probability of 65 percent, and no impact if successful. Which scenario should the project manager choose?
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Answer and explanation:
To solve a decision tree, calculate the expected monetary value of each scenario. Expected monetary value can be calculated by multiplying the impact by the probability. Scenario A has a potential implication of –$1,250, and scenario B has a potential implication of –$2,275. Therefore, scenario A is the best choice.
Question 7 - ID: 373363
Your project has come about because of a social need. You’re calculating performance measurements and know the following information: BAC = 2400, ETC = 400, PV = 2200, EV = 2100, and AC = 2000. What are the CPI and SPI?
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Answer and explanation:
CPI = EV ÷ AC, or in this example, $2,100 ÷ $2,000 = $1.05. SPI = EV ÷ PV, or in this example, $2,100 ÷ $2,200 = $.95.
Question 8 - ID: 903334
Mike is a seasoned project manager who has been tasked with mentoring Bernard, a junior project manager. During a mentoring session, Mike stresses the importance of managing lines of communication and then asks Bernard how many stakeholders are engaged in his project. Bernard responds with 15. How many lines of communication must Bernard manage for his project?
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Answer and explanation:
To calculate lines of communication, use the following formula, where n represents total number of stakeholders: n(n – 1) ÷ 2. Next, plug in 15 in place of the n to get the answer: 15(15 – 1) ÷ 2 = 105.
Question 9 - ID: 333189
You are the project manager for Kitchens Plus Inc. The latest project involves the development of an automatic dicer with unique industry features and has a project budget of $95,000. Based on the latest data, the project has a planned value of $70,200, an earned value of $59,000, and an actual cost of $65,500. How is the project currently performing according to the schedule and budget?
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Answer and explanation:
To answer this question, you will need to calculate the cumulative SPI and CPI. All values needed to do this have been provided within the question. The formula for calculating SPI, which will tell us how the project is performing according to the schedule, is EV ÷ PV. Plug in the values provided to result in the following: ($59,000 / $70,200) = 0.84. Anything less than 1.0 means that the project is behind schedule. Now, calculate CPI by using the following formula: EV ÷ AC. Plug in the values provided to result in the following: ($59,000 / $64,500) = 0.91. A CPI under 1.0 means that the project is over budget. Therefore, the project is behind schedule and over budget.
Question 10 - ID: 643166
Yazzy is a junior project manager for a fitness company that is developing a new franchise model. She is currently working under the guidance of a senior project manager over her parent project, who asks that she calculate the expected costs to finish the remaining project work. The work is proceeding as planned. She determines that the EAC is $75,000, and the cumulative actual costs to date are $50,000. What will Yazzy communicate to the senior project manager?
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Answer and explanation:
The project manager has asked Yazzy to calculate estimate to complete (ETC). When the work is proceeding as planned, use the following ETC formula: EAC – AC. Plug in the values to get the following: $75,000 – $50,000 = $25,000.
Question 11 - ID: 543328
Calculate the to-complete performance index (TCPI) based on the current EAC, using the following values: BAC = 15,000, AC = 12,000, EV = 10,000, EAC = 17,000.
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Answer and explanation:
The formula for TCPI when targeting EAC is as follows: TCPI = (BAC – EV) ÷ (EAC – AC). Plug in the values to get the following: ($15,000 – $10,000) ÷ ($17,000 – $12,000) = $1.0.
Question 12 - ID: 122841
You are a project manager for Community Trends, a nonprofit organization. Your project has come about because of a social need. You’re calculating performance measurements and using actual costs to date, and you assume that ETC work will be completed at the budgeted rate. You know the following information: BAC = 900, ETC = 65, PV = 500, EV = 475, and AC = 425. Which of the following is the correct expected total cost at completion, given this situation?
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Answer and explanation:
Since EAC is based on actual costs to date and assuming ETC work will be completed at the budgeted rate, the equation to use for EAC is EAC = AC + (BAC – EV). In this case, your formula looks like this: $425 + ($900 – $475) = $850.
Question 13 - ID: 922773
Your project has a total of 35 stakeholders. How many lines of communication exist?
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Answer and explanation:

The formula for calculating lines of communication is as follows, where n represents the total number of stakeholders (you are already assumed to have been included in the number): Plug in the numbers to get the following: 35(35 - 1) ÷ 2 = 595.

Question 14 - ID: 972888
If earned value = 500, planned value = 700, and actual costs = 450, what is the cost variance?
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Answer and explanation:
To calculate schedule variance, subtract planned value from earned value (CV = EV – AC): $500 – $450 = $50. A positive cost variance means that the project is under budget.
Question 15 - ID: 213300
Your project selection committee is meeting later this week and is considering initiating one of two projects. They’ve asked you to recommend the project that will benefit the organization the most. The information you’ve gathered shows the initial investment for Project 1 is $795,000. Monthly cash inflows for the first year are $44,000, and expected cash inflows beginning in year 2 are $156,000 per quarter. Project 2 has an initial investment of $845,000. Expected quarterly inflows for the first year are $180,000. Beginning in the second year, inflows are expected to be $136,000 per quarter. Which project should you recommend to the committee and why?
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Answer and explanation:
Project 1’s payback period is 19 months. Year 1 inflows are $528,000. Year 2 inflows are $39,000 per month, making the total payback period 19 months. Project 2’s payback period is 16 months. Year 1 inflows are $72,000. Year 2 inflows are $45,000 per month, which makes the payback period 16 months.
Question 16 - ID: 813153
You are a project manager for Wedding Planners, Inc. Since every wedding is unique, your organization believes in managing each one as a project. You’ve come up with a great idea for a new event that you’re certain customers will love and that will also profit the company. Your boss asks you to investigate alternative methods for implementing the new idea and come back with a recommendation. You discover that Alternative A could yield revenues of $21 million over the next two years, while Alternative B could yield revenues of $29 million over three years. The finance manager told you to use 5 percent as the cost of capital. Which project should you choose and why?
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Answer and explanation:
This question requires discounted cash flow analysis to compare the value of Alternative A to Alternative B. Applying the present value formula to Alternative A, the formula is calculated this way: $21,000,000 / (1 + .05)2 = $19,047,619. Alternative B is calculated this way: $29,000,000 / (1 + .05)3 = $25,051,831.
Question 17 - ID: 573497
A project with a CPI of 1.12 and an SPI of 0.90 is performing:
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Answer and explanation:
A CPI of greater than 1 is performing under budget; an SPI of less than 1 is performing behind schedule. Remember that generally an index > 1 is good, an index = 1 is perfect, and an index of < 1 is bad.
Question 18 - ID: 763384
Given the following information, are project costs ahead or behind what was planned for this period? EV = 95, PV = 85, AC = 100.
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Answer and explanation:
Cost variance tells you whether costs are above or below what was planned for this period and are calculated by subtracting AC from EV. In this case, the formula looks like this: $95 – $100 = –$5. The resulting number is negative, which means the project costs are lower than what was planned for this time period.
Question 19 - ID: 723161
The project management team is coordinating the decision between making or buying a product. Making the product would require an initial investment of $35,000 and has a probability of 15 percent failure and a probable impact of $15,000. Buying the product would require an initial investment of $25,000 but has a probability of 35 percent failure and $10,000 impact. What is the expected monetary value of making the product?
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Answer and explanation:
Getting this question correct involves knowing how to calculate the expected monetary value, as well as understanding decision tree analysis. The correct answer is $37,250. Based on the question, our focus is on the make scenario. To calculate the expected monetary value, take the impact of $15,000 and multiply it by the probability of 15 percent, and then add the initial investment of $35,000.
Question 20 - ID: 663206
If you know that EV = 114, PV = 120, and AC = 103, what are CPI and SPI, respectively?
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Answer and explanation:
The formula for CPI is EV ÷ AC; therefore, 114 ÷ 103 = 1.1. The formula for SPI is EV ÷ PV; therefore, 114 ÷ 120 = .95.
Question 21 - ID: 213440
Using the following three-point estimates, calculate the expected value using the beta distribution formula: Optimistic = 25, Pessimistic = 50, Most Likely = 35.
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Answer and explanation:
Expected value can be calculated using a triangular distribution (simple average) or beta distribution (weighted average). The three-point estimating formula that uses a beta distribution is as follows: (Optimistic + Pessimistic + (4 × Most Likely)) ÷ 6. Plug in the values provided to calculate the following: ($25 + $50 + ($35 × 4)) ÷ 6 = $35.8, or 36 when rounded to the nearest whole number.
Question 22 - ID: 283399
You are a project manager working for Mail House King. Your company processes orders for several mail-order catalog companies. Your project is to install new mail-sorting equipment and software. You’ve had some problems and experienced some variances during the project. You expect these variances to continue throughout the life of the project and expect they will be similar to the variances you’ve seen so far. You know the following information: PV = 900, BAC = 1400, EV = 925, AC = 925. Which of the following is the correct ETC given the circumstances?
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Answer and explanation:
The formula for ETC when variances are expected to continue is ETC = (BAC – EV) ÷ CPI. First you need to calculate CPI, which is $925 ÷ $925 = $1. Now you can plug in the numbers: ($1,400 – $925) ÷ 1 = $475.
Question 23 - ID: 233338
A project manager managing a small project has a total of 45 active stakeholders. How many lines of communication exist?
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Answer and explanation:
The formula for calculating lines of communication is as follows, where n represents the total number of stakeholders (you are already assumed to have been included in the number): n(n – 1) ÷ 2. Plug in the numbers to get the following: 45(45 - 1) ÷ 2 = 990.
Question 24 - ID: 713158
Using a triangular distribution formula, calculate the cost estimate based on the following three-point estimates: Optimistic = $2,500, Most Likely = $3,500, Pessimistic = $7,200.
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Answer and explanation:
The triangular distribution formula using the three-point estimating technique is (Optimistic + Most Likely + Pessimistic) ÷ 3. Plugging in the values provided yields the following: ($2,500 + $3,500 + $7,200) ÷ 3 = $4,400.
Question 25 - ID: 803584
You work for Rory’s, a golf equipment manufacturer. Your organization is installing some new manufacturing equipment, and you are managing the project. Your project sponsor has asked for an EAC and has told you that he wants you to consider ETC work performed at the present CPI. If EV = 145, PV = 162, AC = 138, and BAC = 200, what is EAC?
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Answer and explanation:
The EAC formula for this question is BAC ÷ CPI. First, calculate CPI, which is EV ÷ AC: 145 ÷ 138 = 1.05. Plugging in the numbers from the question, you get 200 ÷ 1.05 = 190
Question 26 - ID: 142897
Leticia is a project manager working for Dancing Apron, a company that combines cooking with simple children’s cooking recipes and music. Her latest project involves the release of the company’s first digital product that parents will be able to purchase and download online. Kip, who is the sponsor of the project, asks her to calculate the EAC assuming that the work will be accomplished at the planned rate. Leticia knows that they have spent $15,000 to date of the $20,000 budgeted and that the earned value of the project has already been calculated at $18,000. What is the EAC that she will communicate to Kip?
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Answer and explanation:
To calculate EAC when the future work will be accomplished at the planned rate, use the following formula: AC + BAC – EV. Plug in the values provided in the question to arrive at the following: $15,000 + $20,000 – $18,000 = $17,000.
Question 27 - ID: 803463
Activity A has a probability of 10 percent and an impact of $4,000. What is the expected monetary value of Activity A?
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Answer and explanation:
The formula for calculating expected monetary value is probability times impact. Plug in the values to get the following: 10% × $4,000 = $400.
Question 28 - ID: 752992
What is the present value of $8,000 received three years from the present using a 7 percent interest rate? Assume all options are rounded to the nearest whole dollar.
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Answer and explanation:
The formula for present value is PV = FV / (1 + i)n. Plugging in the information from the question, the formula becomes $8,000 / (1 + .07)3 = $6,530.
Question 29 - ID: 442982
Yasmin is a senior project manager who has just taken on a project that will produce a new line of medical widgets for a Fortune 100 company. The entire industry is buzzing with excitement over this project, which is estimated to span three years and require an investment of $1.5 billion from the company. What type of project is this?
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Answer and explanation:
A megaproject is defined as a large multiyear project that costs more than $1 billion and affects 1 million or more people.
Question 30 - ID: 183187
During a status meeting, the project manager informs the team that the project has spent a total of $7,500 to date and that the earned value is $5,000. How is the project currently performing?
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Answer and explanation:
To calculate the project’s performance using the information provided, you can use the cost performance index (CPI) earned value calculation. The formula for calculating CPI is CPI = EV ÷ AC. Plug in the values to calculate the following: $5,000 ÷ $7,500 = $0.67. A CPI of less than 1 means that the project is performing over budget.

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