Chatbots are useful generators of case-math drills and unreliable checkers of their own arithmetic. That is the whole game. If you treat ChatGPT, Claude, or Gemini as an answer key, you will practice the wrong habit: nodding at a confident final number while the intermediate multiply is off by a factor of ten.
I score case math from the other side of the table. The sheet rewards a clean setup, staged arithmetic you can follow, units that stay visible, and a one-line business read. The final percentage is maybe a quarter of the points. After this piece you will have a free-tier comparison as of today, copy-ready prompts for timed sets, a verification loop that catches chatbot slips, and a plain description of CoachNed's free-forever Quick Math as one option among them. CoachNed is my product; I will say so when it matters.
What the interviewer actually grades
In a typical first round of eight candidates, two or three lose points on math not because they cannot multiply, but because they bury the formula, skip units, or finish with a number and no meaning. A strong answer sounds like this: "Revenue = price times volume. Old revenue at 100 units is $5,000. At $55, flat revenue needs about 91 units, so volume can fall roughly 9 percent before revenue drops. That is a ceiling, not a profit win."
A weak answer sounds like this: "Uh, 9 percent? Yeah." Same arithmetic destination, different score.
So when you ask a free chatbot to "drill me on case math," the prompt has to grade those four moves, not just the final digit. The model will happily grade itself generous unless you force a verification pass.
Free tiers as of 2026-09-24
Limits move. Cite the vendor pages, not a prep-site rumor.
| Tool | Free access (vendor wording) | Practical use for case math | Main free-tier constraint |
|---|---|---|---|
| ChatGPT Free | Free plan for everyday chat; core features with usage limits; no set time limit on the free plan | High-volume set generation and fast prompt iteration | Tools beyond basic text (uploads, voice, image gen, analysis) have separate caps; OpenAI states free everyday text chats are unlimited subject to abuse safeguards on the Free Tier FAQ |
| Claude Free | $0, "Free for everyone"; chat on web, desktop, and mobile | Longer calculation chains and pasting a full case prompt to extract the math | Usage limits reset on a rolling five-hour window; Anthropic does not publish a fixed free message count; Free "covers everyday questions" |
| Gemini Free | $0 with a Google Account; access to Flash and varying access to Pro | Building plausible industry inputs, then drilling the staged math | Compute-based "standard limits"; Google states the free app limit refreshes every 5 hours until a weekly ceiling (see footnote 2 on the subscriptions page); free context is smaller than paid |
None of the three publishes a guaranteed daily problem count for math drills. Plan for a short morning block, not an all-day session on the free tier. When you hit a wall, wait for the reset or switch tools rather than burning the rest of the day arguing with a rate-limit screen.
Why chatbots slip on arithmetic
This is not folklore. OpenAI's own GSM8K work on grade-school math word problems notes that language models still struggle with robust multi-step mathematical reasoning and that samples frequently contain critical mistakes even when the problems are conceptually simple (OpenAI on GSM8K; Cobbe et al., arXiv:2110.14168). The paper's authors explicitly call out calculation failures as a common error source and trained models to call a calculator for that reason.
Case math is shorter than GSM8K, but the failure mode is the same: fluent prose, wrong intermediate product. In an interview you cannot outsource the multiply. On a chatbot drill you must make the model show every stage and recompute before it grades you.
Ned's rule. Never accept a chatbot's final case-math number until it has restated the formula, recomputed each line with units, and given a one-sentence business read. If any of those three is missing, the grade is noise.
How to make them verify
Use a two-pass loop. Pass one generates or grades. Pass two is a cold check with no praise language.
Pass one (generate or grade): Ask for five timed problems. Require messy numbers, a 45-second target, and a rubric: equation, staged calc, units, business meaning.
Pass two (verify): Paste your answer (or the model's own "correct" key) and say: "Do not agree with me. Recompute each arithmetic step independently. Flag any line where the product or quotient does not match. Then score setup, units, and business read separately from the final number."
If the model changes its mind between passes, trust the recompute, not the first confident answer. For chained profitability math, ask it to rebuild the table from the inputs alone rather than editing its previous reply.
Worked example you can reproduce
Invented company: HarborLine Apparel, a mid-market outerwear brand. Price rises from $80 to $88. What volume loss keeps revenue flat?
Setup: hold old volume at 100 jackets so the arithmetic is transparent.
- Old revenue = 100 × $80 = $8,000
- Flat-revenue volume at $88 = $8,000 ÷ $88 = 90.91 jackets
- Maximum volume loss ≈ 9.1 percent
Business read: a 9 percent volume drop keeps revenue flat; it says nothing yet about margin, returns, or lifetime value. In the room I care that you said "ceiling," not that you claimed a win.
Run the same problem through a free chatbot, then force Pass two. Watch whether it invents a different percentage on the recompute. That gap is the point of the drill.
Copy-ready prompts for timed math sets
Paste these into ChatGPT, Claude, or Gemini. Change the industry if you want; keep the grading rules.
Prompt A — five-problem timed set
Act as a case interviewer. Give me exactly 5 case-math problems, one at a time.
Constraints: messy numbers (no round tens), no calculator, 45-second target each.
Types to mix: price-volume tradeoff, contribution margin, CAGR-style growth, break-even volume, simple share shift.
After each of my answers, grade ONLY these four: (1) formula, (2) staged arithmetic, (3) units, (4) one-line business meaning.
Do not praise. If any stage is wrong, show the correct stage with units.
Wait for my answer before the next problem.
Prompt B — force verification
Here is my answer to the last problem:
[paste]
Recompute every arithmetic line from the inputs alone. Do not reuse your previous final number.
List each step as: inputs → operation → result with units.
Then tell me which of the four grading dimensions would lose points in a first-round case.
If your recompute differs from your earlier key, say so in one sentence.
Prompt C — build plausible inputs, then drill
I am about to size a specialty coffee market in a mid-size US city.
Give me 6 plausible input assumptions with units (population, adult share, weekly purchase rate, average ticket).
Do not invent sources you cannot name; label estimates as estimates.
Then quiz me on the staged calculation only: adults → buyers → weekly cups → annual revenue.
Grade setup and units harder than the final dollar figure.
Prompt C fits Gemini's freer search grounding; Prompts A and B fit any of the three. Claude's free tier is the one I reach for when the chain is long (sensitivity across three drivers), because the five-hour usage pool still covers a full pasted case for most candidates before it throttles everyday use.
Where CoachNed Quick Math sits
CoachNed is an AI case-interview practice product I built. I am not a neutral reviewer of my own tool. Here is the honest placement.
Quick Math is free forever. It is a timed drill surface for the short calculations that show up mid-case: margins, growth, break-evens, share math. It does not replace a full interviewer-led case, and it does not pretend ChatGPT cannot generate similar prompts. What it does differently from a general chatbot is hold a fixed consulting-shaped format so you are not rewriting the rubric every morning.
Everything else on CoachNed is open for seven days with no card; then $120 for a recruiting season or $49 a month. Use Quick Math as the daily speed layer. Use a free chatbot when you want custom industries or Pass-two verification. Use a full math drill or a live case on /interview when you need setup-plus-synthesis scored together.
A one-week free stack that actually fits a calendar
| Day | Tool | Assignment | Time |
|---|---|---|---|
| Mon | ChatGPT Free | Prompt A, five problems | 20 min |
| Tue | Claude Free | Same five answers through Prompt B | 15 min |
| Wed | Gemini Free | Prompt C on a new industry | 20 min |
| Thu | ChatGPT or Claude | Sensitivity: change one driver, recompute | 15 min |
| Fri | Quick Math | Timed set until accuracy holds under pace | 15 min |
| Sat | Optional | One full case on /start or /interview | 20–40 min |
| Sun | Off or light | Re-run only the problem types you missed | 10 min |
That is roughly two hours across the week. Enough to make the setup muscle automatic without burning free-tier caps in one sitting.
Practice this today
Open whichever free chatbot you already use. Run Prompt A for five problems. Immediately run Prompt B on your weakest answer. Then do one set on Quick Math. Write down which of the four grading dimensions failed most often. Tomorrow, only drill that dimension.
If you want a graded consulting math rep with a fixed rubric after that, use the math drill. If you want the full voice case, go to /interview.
Frequently asked questions
Is ChatGPT, Claude, or Gemini best for free case math practice?
None is best for every job. ChatGPT Free is strongest for high-volume set generation under OpenAI's everyday-chat free access. Claude Free is strongest for longer chains inside Anthropic's five-hour usage window. Gemini Free is strongest when you need plausible industry inputs before the arithmetic. Pick by the job, not by the brand.
Do free AI chatbots make arithmetic mistakes on case math?
Yes. Multi-step math is a known weak spot for language models; OpenAI documented calculation failures even on grade-school word problems in the GSM8K work. Always force a recompute pass before you treat a chatbot as an answer key.
Can I practice case math for free without creating many accounts?
Yes. One chatbot account plus Quick Math is enough for a week of timed sets. Add a second chatbot only when you want an independent Pass-two check.
How long should a free case-math session take?
Fifteen to twenty minutes. Five timed problems with a verification pass beats an hour of untimed chatting. Free tiers also refresh on rolling windows (Claude and Gemini both use five-hour style limits), so short blocks fit the product design.
Is CoachNed affiliated with McKinsey, BCG, Bain, or the other firms named in prep content?
No. CoachNed is independent and not affiliated with McKinsey, BCG, Bain, Deloitte, or any firm named here.
Sources
- ChatGPT Free plan — OpenAI's free-plan description and stated limitations. Checked 2026-09-24.
- ChatGPT Free Tier FAQ — everyday text-chat access and separate tool limits on Free. Checked 2026-09-24.
- Claude plans and pricing — Free plan features and Anthropic's five-hour usage-window wording. Checked 2026-09-24.
- Gemini subscriptions (Free vs paid) — Free tier positioning and footnote 2 on compute-based limits, 5-hour refresh, and weekly ceiling. Checked 2026-09-24.
- Solving math word problems (OpenAI) — GSM8K motivation and multi-step reasoning failures. Checked 2026-09-24.
- Training Verifiers to Solve Math Word Problems (arXiv:2110.14168) — Cobbe et al. on calculation errors and verification. Checked 2026-09-24.