Love it, loathe it, or somewhere in between — you have to know your math for the PMP exam. Fortunately, none of the arithmetic is very hard, and PMI provides you with a virtual calculator. Unfortunately, you really need to know the formulas. PMP math questions don’t require calculus, just some solid algebra (or memory) skills.

You can use this article in two ways:

- If you’re just getting started, use it as an overview of the types of math questions you’ll encounter. I’ve tried to offer a variety of questions, which means you’ll encounter breadth but not depth.
- If you’ve been studying for a while, do a quick quiz with these. If you get any wrong, focus your studies in these area listed in answers.

Also, when you’re studying, you’ll want to use these resources:

**Designing Your PMP Brain Dump**– Having a well-design brain dump that you practice regularly is key to mastering PMP math questions.**Sample Earned Value Management (EVM) Questions**– EVM is the most complex question with math that you’ll encounter on the PMP exam. Spend most of your prep time here.

## PMP Math Questions

For the first three questions, assume you are managing the following project:

*You are the project manager of a project that is budgeted to cost $1 million at completion. The project will last ten months and its budget is spread evenly across each month. It is currently 50% complete and has so far cost $750K but only produced value of $500K.*

1. What is the schedule variance (SV) of the project?

A. $0

B. $200K

C. $500K

D. $750K

2. What is the cost performance index (CPI) of the project?

A. 0.67

B. 1

C. 1.5

D. 2

3. If the variance is not expected to continue, what is the expected estimate at completion (EAC) of the project?

A. $500K

B. $750K

C. $1 million

D. $1.25 million

4. You want to estimate the duration of an activity on your project. Your pessimistic estimate is 10 days, your most likely estimate is 5 days, and your optimistic estimate is 3 days. Using a triangular PERT distribution, what is your duration estimate?

A. 4.6 days

B. 5 days

C. 6 days

D. 9.3 days

5. You are the project manager for a medium-sized project. There are 14 team members, and everyone communicates with everyone else on the project team. How many communication channels are there?

A. 91

B. 105

C. 182

D. 210

6. You are negotiating an FPIF contract. The ceiling price is $2 million, and the target price is $1.8 million. The buyer’s share ratio is 75% for overruns. What is the target profit for the seller if the target cost for the buyer is $1.5 million?

A. $150K

B. $200K

C. $300K

D. $1.5 million

7. Activity X takes 4 days and is followed by Activity Y, which takes 3 days. The early start of Activity X is day 20, and the early start of Activity Y is day 27. What is the free float of Activity X?

A. 0

B. 3

C. 7

D. 10

8. A project is expected to result in $2 million in five years. The current interest rate is 5%. What is the PV of the project?

A. $1,359,252

B. $1,567,398

C. $1,784,972

D. $2 million

9. You must select one and only one project to take on on for your company. The net present value (NPV) for each project is as follows: Project A’s NPV is $10K, Project B’s NPV is $20K, and Project C’s NPV is $30K.

A. Project A

B. Project B

C. Project C

D. This problem cannot be solved without knowing the interest rate for each project.

10. A new state-of-the-art computer for your project costs $10K. You expect for it to last for four years and to sell it for $1K for parts. How much should you book in depreciation each year for the computer? Assume you are using straight-line depreciation.

A. $1250

B. $2000

C. $2250

D. $2500

## PMP Math Answers

The toughest of your PMP math will relate to EVM, or earned value management. That’s why the first three questions are on EVM. These questions weren’t so tough, but you can visit 7 Example PMP Earned Value Questions for more information. Get to know it really well!

1. **A. $0** – Schedule Variance = Earned Value – Planned Value, or SV = EV – PV. The project’s current value at 50% completion is stated in the problem as $500K. To determine the Planned Value, use the project’s original BAC times percentage complete: $1 million * 50% = $500K. SV = EV – PV = $500K – $500K = $0. The project is on schedule.

2. **A. 0.67** – Cost Performance Index = CPI = EV/AC. You determined EV in the previous problem at $500K. The problem tells you that the project has so far cost $750K, which is the AC. CPI = EV/AC = $500K/$750K = 0.67. The project is over budget.

3. **D. $1.25 million** – The variance is expected to go away, so use the formula AC + BAC – EV = $700K + $1 million – $500K = $1.2 million.

4. **C. 6 days** – Your typical PERT estimate is shown by the formula (P + 4L + O)/6, but this problem wants you to use the triangular PERT estimate instead. (P + L + O)/3 = (10 + 5 + 3)/3 = 18/3 = 6 days. Did you use the wrong formula because you were moving too fast? Remember to slow down!

5. **B. 105** – The formula for determining the number of communication channels on a project is [n(n-1)]/2, where *n* is the number of project team members. Don’t forget to include the project manager! In this problem, *n*=15, but you may have accidentally said *n*=14 if you forgot the PM.

6. **C. $300K** – This problem is a good example of (1) not just memorizing the formula but knowing what goes into it and (2) avoiding extraneous information. The problem sets you up to think that you’ll be using this formula: PTA = [(Ceiling – Target)/Buyer’s Share Ratio] + Target. Actually, you just need to know that the Target Price is made up of both the Buyer’s Target Cost and the Seller’s Target Profit. $1.8 million – $1.5 million = $300K in target profit for the seller.

7. **B. 3** – Network diagram math questions can be tricky, because they are almost like logic questions rather than math. For this one, know that free float (which is float on an activity) = ES of following activity – ES of present activity – present activity duration. We are determining the free float for Activity X. ES of following is easy because it is stated as 27. The duration of Activity X is also stated as four days. You need to use the ES information (day 20) and the duration (4 days). So since free float = ES of following activity – ES of present activity – present activity duration = 27 – 20 – 4 = 3.

8. **B. $1,567,398** – Get those PV & FV formulas on your brain dump. Again, this is one of those problems that may or may not surface on your exam. It did for me! (But depreciation didn’t.) Present Value = FV / [(1 + r)^n], where r is the rate of return and n is the number of years = $2 million / [(1 + .05)^5].

9. **C. Project C** – For project evaluation dealing with internal rate of return (IRR), return on investment (ROI), and net present value (NPV), simply pick the greatest value. Easy!

10. **C. $2250** – (Asset Cost – Scrap Value) / Useful Life = ($10K – $1K) / 4 = $2250 per year. It is possible, though not certain, that you will encounter a depreciation problem on your PMP exam, though I happened not to encounter one. Add the formulas to your brain dump anyway — a point is a point.

*Still feeling queasy about the PMP math questions? Let us know what’s stressing you out — we’re here to help!*

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Shouldn’t #2 be CPI = 0.667 ?

Yes! My editing error… I wrote the original question, then changed the numbers. Thanks for catching it.

7 the answer should be 3 I guess as per https://www.deepfriedbrainproject.com/2009/08/total-float-vs-free-float-cpm-network-diagram.html

Again from your answer it is unclear what did you do ?

you need to use the ES information (day 20) and the duration (4 days), which get you an EF of day 23 for Activity Shouldn’t this 24?

Hi Sruti — you’re right! I accidentally used EF of the present activity instead of ES. Thanks for catching this, and I’ve updated my post.

C- Answer:

How did you arrive on 700 K when AC is 750 K as per your question.

D. $1.25 million – The variance is expected to go away, so use the formula AC + BAC – EV = $700K + $1 million – $500K = $1.2 million.

Hi Raj, that was an editing error. I made a mistake when changing some numbers around, so I’m glad you caught it. Thanks!

Why do you (and PMI in general) purposely OBFUSCATE the question to make the wrong answer right and the right answer wrong?

If, for example, “THERE ARE … 14 team members,” but a project manager is, of course, ALWAYS a team member on any project, so 14 would include the project manager. If, on the other hand, you used language which says “You are a project manager leading a team of 14” or “You are the project manager for a team of 14,” then the exclusion of the project manager is clear. I know the formula in my sleep; what I can’t know is what you are trying to ask because you could make up either answer to the question and justify that you meant the opposite. That makes no sense.

Secondly, there is NO such terminology as “Triangular PERT” ANYWHERE in the PMBOK. It is either Triangular (3 point average) distribution or Beta (traditional PERT) distribution to be used for estimation of durations (or costs).

Make your questions hard, but don’t make them wrong. Trying to make people miss the answer when they know the material is one of the LAMEST aspects in all of PMI. They illegitimize themselves with silliness like this, and I have seen it in hundreds of questions.

That’s 5 errors on this one page; you have so many errors in your questions and answers, why don’t you just correct the page? It doesn’t raise confidence in what you are advertising for sale.

Can you explain to me how there is a “new budget” at completion? To me that was a trick question…the EAC is the estimate or new forecast. The budget is the budget.

Hi Stephanie!

Thanks for reaching out to us. 🙂 It looks like you’re right: Question 3 should be asking for an “Estimate at Completion” (EAC) and not a BAC. 😀 We’ll be looking into this a little further. Thanks again for pointing that out!

Thank you for the questions, however I do not appreciate the confusion… PERT is PERT, this is not the correct answer nor the correct method… If you want to answer and calculate using this formula in question 4, use TRIANGULAR distribution. This is just simply confusing! There are two methods one is Triangular distribution, the other is PERT which is also a triangular distribution….

Hi Sal,

I just checked with Rich to get his thoughts on this, and he says:

“”There’s at least two PERT methods that PMBOK addresses, triangular and beta. That’s why I specified triangular PERT in the problem.

Here is a related article: https://www.pmchamp.com/3-point-estimate-triangular-distribution-vs-beta-distribution-pert/ “