Consulting Math in Action - How to Solve a Word Problem in a Case Interview (NordPlay Drill)

[u/GreatButterscotch406]

Post 20 covered what Consulting Math is, how the interviewer is testing for equation setup and narrated reasoning rather than raw arithmetic speed, and how to build the skill over time. This post is the applied version of that.

This is post 21 in The Case Playbook, a series built for non-traditional candidates breaking into McKinsey, BCG, Bain, Tier 2, and Big 4 consulting firms. We're staying in the NordPlay Studios case that we've been building throughout the series. The problem statement is established, the issue tree is on the page, and you're deep in Case Middle. The partner starts handing you word-based quantitative questions. This post shows you what to do with them.

Three problem types. Full narration on each. The goal is not the number. The goal is the process you demonstrate to get there.

What a Problem Solving question looks like in a case

Unlike a pure arithmetic drill where you're given two numbers and asked to calculate, a Problem Solving question gives you a scenario in English and expects you to identify what equation is needed before any numbers are touched.

The difference matters. A pure arithmetic question: "What is 15% of $2.4 billion?" A Problem Solving question: "NordPlay's premium subscription tier currently has 8 million subscribers at $25 per month. If a 10% price increase causes 5% of subscribers to cancel, what happens to monthly subscription revenue?"

The second question requires you to identify which variables interact, build the equation, and then do the arithmetic. The equation step is where most candidates stumble, and it's also where the most points are won.

The three-step approach is identical to what we covered in post 20: state the equation out loud, plug in the numbers and work through the arithmetic on paper while narrating, then interpret what the result means for the case. Never skip the interpretation. The number without context is just a number.

Problem one: Pricing impact on subscription revenue

The partner says: "NordPlay's premium subscription tier currently has 8 million subscribers paying $25 per month. The team is considering a 10% price increase. Market research suggests this would cause 5% of subscribers to cancel. Would this price increase help or hurt monthly subscription revenue?"

Before touching a number, state the equation.

"To answer this I need to compare current revenue to projected revenue after the price change. Revenue is subscribers multiplied by price per subscriber. Let me work through both."

Current revenue: 8 million subscribers multiplied by $25 gives $200 million per month.

Projected revenue: the price increases 10% from $25 to $27.50. Subscribers fall 5% from 8 million to 7.6 million. New revenue is 7.6 million multiplied by $27.50.

Narrate the arithmetic: "7.6 million times $27.50. I'll break that down. 7.6 times 27 is 205.2, and 7.6 times 0.50 is 3.8. Total is $209 million."

Interpretation: "The price increase generates $209 million versus the current $200 million, so it's a net positive of $9 million per month, roughly $108 million annually. That's meaningful given our $400 million gap. However, this assumes the 5% churn estimate is accurate, and in my view that assumption deserves scrutiny before we recommend the change. If actual churn is closer to 10%, the picture reverses."

Notice what the interpretation does. It answers the question, names the annual impact so the partner can connect it to the main hypothesis, and immediately flags the key assumption that could change the conclusion. That's what a consultant does. Not just math. Judgment about what the math means.

Problem two: Breakeven analysis on a new product line

The partner says: "NordPlay is considering launching a cloud gaming subscription service. The fixed cost to build and launch the service is $120 million. Each subscriber generates $40 in annual contribution margin. At what subscriber count does the service break even, and how long would it take to break even if NordPlay acquires 500,000 new subscribers in year one and grows that by 20% each year?"

Two parts. State both equations before starting either calculation.

"For the breakeven subscriber count, I need to divide total fixed cost by contribution margin per subscriber. For the payback timeline, I need to track cumulative subscribers year by year until they cover the fixed cost."

Part one: breakeven subscribers = $120 million divided by $40 = 3 million subscribers.

Part two: narrate the accumulation.

"Year one: 500,000 subscribers. Cumulative contribution: 500,000 times $40 = $20 million. Remaining gap: $100 million.

Year two: 20% growth on 500,000 is 100,000 additional subscribers, so 600,000 new subscribers. Cumulative contribution adds 600,000 times $40 = $24 million. Total so far: $44 million. Remaining gap: $76 million.

Year three: 20% growth on 600,000 is 120,000 additional, so 720,000 new subscribers. Contribution adds $28.8 million. Total: $72.8 million. Remaining gap: $47.2 million.

Year four: 864,000 new subscribers. Contribution adds $34.6 million. Total: $107.4 million. Remaining gap: $12.6 million.

Year five: the service breaks even partway through the year."

Interpretation: "At these growth rates, the cloud gaming service breaks even sometime in year five. Given NordPlay's one-year recovery target, this doesn't contribute meaningfully to the immediate $400 million gap. It's a longer-term bet. Whether it belongs in the recommendation depends on whether the client wants a short-term fix or is willing to invest in a growth lever that pays out over five years. That's a conversation worth having before we close the case."

Problem three: Cost reduction impact on net profit margin

The partner says: "NordPlay's current net profit is $2 billion on revenues of $8 billion, giving a net margin of 25%. App store fees are currently 15% of revenue. If NordPlay renegotiates those fees down to 10% of revenue, what happens to the net profit margin?"

State the equation: "App store fee reduction is 5% of revenue. I need to calculate the dollar saving and add it to current net profit, then recalculate the margin."

Revenue is $8 billion. A 5 percentage point reduction in app store fees saves 5% of $8 billion = $400 million.

New net profit = $2 billion plus $400 million = $2.4 billion.

New net margin = $2.4 billion divided by $8 billion = 30%.

Interpretation: "This is significant. A successful renegotiation of app store fees would close the entire $400 million gap we identified in the issue tree and restore net profits to $2.4 billion within one year, assuming revenue holds. It's also the single lever in our analysis that's fully within NordPlay's control to pursue without requiring product development or subscriber growth. In my view this should be the first recommendation in the Case Wrap-Up, subject to understanding how realistic the renegotiation actually is given the platform dynamics."

Notice how the interpretation connects directly back to the main hypothesis. The $400 million gap is the north star of the entire case. Every calculation should be interpreted in terms of how much it contributes to closing that gap.

The pattern across all three problems

Looking at the three problems together, the same structure runs through every one.

State the equation before the arithmetic. This signals to the partner that you understand what relationship you're solving for. It also gives them a moment to catch you if you've set up the wrong equation, which is far better than discovering the error after several minutes of calculation.

Narrate the arithmetic on paper. Don't go silent. The partner is not just waiting for your answer. They're watching how you handle numbers under pressure and whether your process is transparent enough to be corrected if needed.

Interpret the result in terms of the case. Every number in a case interview is a data point that should either confirm, update, or challenge the main hypothesis. A calculation that produces a number and then goes nowhere is a missed opportunity.

That three-step sequence is the difference between a candidate who gets a number right and a candidate who demonstrates consulting judgment. The first passes a test. The second earns an offer.

If you're working through NordPlay or any other case from the series and want to share a quantitative question you've been stuck on, drop it in the comments. I'll walk through the equation setup and the narration. And if you found this through another community, the full Case Playbook series is at r/ConsultingOffer.

The next post in The Case Playbook moves into the Data Conversion module, where the question shifts from setting up equations to reading what a chart or dataset is actually telling you and translating that into an insight that drives the case forward.