Compare AI models on applied math tasks
This bank measures numerical correctness on twelve applied problems. It does not score the quality of explanations.
Last tested
2026-10-04T17:01:24.616847+00:00
Last successful source fetch
2026-10-04T09:01:57.926856+00:00
Last published
2026-10-04T18:18:57.482142+00:00
Observed leaders
gpt-6.1-sol, gemini-3.8-flash
Descriptive pass counts after offline runner correction of the original outputs. Task ambiguities described in the audit limit broader conclusions.
Tested API configurations
| Model | Task passes | Cost per pass | Processing |
|---|---|---|---|
GPT-6.1 Solgpt-6.1-sol | 30 / 36 | $0.0013 (estimated) | OpenAI direct API, Standard global Medium reasoning; 8,192-token cap |
Claude Sonnet 5.5claude-sonnet-5-5 | 3 / 36 | $0.0270 (estimated) | Claude direct API, Standard global Medium reasoning; 8,192-token cap |
Gemini 3.8 Flashgemini-3.8-flash | 30 / 36 | $0.0033 (estimated) | Gemini Developer API, paid Standard Medium reasoning; 8,192-token cap |
Three documented current direct-API models from different providers, selected for coding/math use and practical cost. Not a claim that every leading tool is included. Account access and publication terms require verification before dispatch. No web, tools, prompt caching, batch or regional processing. Medium reasoning labels are provider-specific, not equal compute.
Scores by task group
| Model | Group | Passes | Median latency |
|---|---|---|---|
| gpt-6.1-sol | Finance | 12 / 18 | 2.96 seconds (whole model) |
| gpt-6.1-sol | Optimization | 6 / 6 | 2.96 seconds (whole model) |
| gpt-6.1-sol | Probability | 6 / 6 | 2.96 seconds (whole model) |
| gpt-6.1-sol | Statistics | 6 / 6 | 2.96 seconds (whole model) |
| claude-sonnet-5-5 | Finance | 3 / 18 | 1.99 seconds (whole model) |
| claude-sonnet-5-5 | Optimization | 0 / 6 | 1.99 seconds (whole model) |
| claude-sonnet-5-5 | Probability | 0 / 6 | 1.99 seconds (whole model) |
| claude-sonnet-5-5 | Statistics | 0 / 6 | 1.99 seconds (whole model) |
| gemini-3.8-flash | Finance | 12 / 18 | 2.56 seconds (whole model) |
| gemini-3.8-flash | Optimization | 6 / 6 | 2.56 seconds (whole model) |
| gemini-3.8-flash | Probability | 6 / 6 | 2.56 seconds (whole model) |
| gemini-3.8-flash | Statistics | 6 / 6 | 2.56 seconds (whole model) |
Historical and current-price estimates
gpt-6.1-sol: original run $0.0394; same recorded usage at rates reviewed 2026-10-04T06:52:40.966997+00:00: $0.0394. Both are estimates; billing reconciliation is separate.
claude-sonnet-5-5: original run $0.0811; same recorded usage at rates reviewed 2026-10-04T06:52:40.966997+00:00: $0.0811. Both are estimates; billing reconciliation is separate.
gemini-3.8-flash: original run $0.0995; same recorded usage at rates reviewed 2026-10-04T06:52:40.966997+00:00: $0.0995. Both are estimates; billing reconciliation is separate.
The 12 tasks
Open a task to inspect its exact prompt and, after testing, every model output. Hidden coding fixtures and answer keys are not served to the models or this page.
Outputs are generated by the named AI models and may contain errors. Scores cover the declared task checks; they do not verify every statement in an output.
Separate markup from margin Finance
A shop buys 240 items at $18 each. It sells 210 at $30 and 30 at $24. Platform fees are 3% of revenue plus $0.20 per sold item. Shipping costs $2.50 per sold item. Calculate revenue, profit after these costs, and profit margin as a percentage of revenue. Return only a JSON object with these keys: revenue, profit, margin_percent. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Failed
{"revenue":7020,"profit":1841.4,"margin_percent":26.23}4.44 seconds · $0.0014 estimated
Attempt 2 · Failed
{"revenue":7020,"profit":1841.4,"margin_percent":26.23}4.83 seconds · $0.0015 estimated
Attempt 3 · Failed
{"revenue":7020,"profit":1841.4,"margin_percent":26.23}4.06 seconds · $0.0011 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Revenue: 210×30 = 6300; 30×24 = 720; total 7020.
Cost of goods: 240×18 = 4320.
Platform fees: 0.03×7020 = 210.6; per-item fee: 240×0.20 = 48; total 258.6.
Shipping: 240×2.50 = 600.
Profit: 7020 − 4320 − 258.6 − 600 = 1841.4.
Margin: 1841.4/7020 = 0.262308 → 26.23%.
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}2.24 seconds · $0.0023 estimated
Attempt 2 · Failed
Revenue: 210×30 = 6300; 30×24 = 720; total 7020.
Cost of goods: 240×18 = 4320.
Platform fees: 0.03×7020 = 210.60; per item 0.20×240 = 48; total 258.60.
Shipping: 2.50×240 = 600.
Profit: 7020 − 4320 − 258.60 − 600 = 1841.40.
Margin: 1841.40/7020 = 0.262308 → 26.23%.
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}2.37 seconds · $0.0023 estimated
Attempt 3 · Failed
Revenue: 210×30 = 6300; 30×24 = 720; total 7020.
Cost of goods: 240×18 = 4320.
Platform fees: 0.03×7020 = 210.6; per item: 240×0.20 = 48; total fees 258.6.
Shipping: 240×2.50 = 600.
Profit: 7020 − 4320 − 258.6 − 600 = 1841.4.
Margin: 1841.4/7020 = 0.262308 → 26.23%.
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}2.21 seconds · $0.0023 estimated
Gemini 3.8 Flash
Attempt 1 · Failed
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}3.63 seconds · $0.0035 estimated
Attempt 2 · Failed
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}3.42 seconds · $0.0031 estimated
Attempt 3 · Failed
{"revenue": 7020, "profit": 1841.4, "margin_percent": 26.23}4.40 seconds · $0.0042 estimated
Solve a production mix Optimization
Make exactly 80 litres of a 35% concentrate from 20% and 60% stocks, with additive volumes. How many litres of each stock are needed? Return only a JSON object with these keys: litres_20, litres_60. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"litres_20":50,"litres_60":30}2.92 seconds · $0.0006 estimated
Attempt 2 · Passed
{"litres_20":50,"litres_60":30}2.50 seconds · $0.0007 estimated
Attempt 3 · Passed
{"litres_20":50,"litres_60":30}2.52 seconds · $0.0006 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Let x be litres of the 20% stock and 80 − x litres of the 60% stock.
0.20x + 0.60(80 − x) = 0.35 × 80 = 28
0.20x + 48 − 0.60x = 28, so 0.40x = 20 and x = 50.
That gives 50 litres of the 20% stock and 30 litres of the 60% stock.
{"litres_20": 50, "litres_60": 30}2.07 seconds · $0.0017 estimated
Attempt 2 · Failed
Let x be the litres of the 20% stock. Then x + y = 80 and 0.2x + 0.6y = 0.35·80 = 28.
Substituting y = 80 − x: 0.2x + 48 − 0.6x = 28, so −0.4x = −20 and x = 50. Then y = 30.
{"litres_20": 50, "litres_60": 30}1.83 seconds · $0.0015 estimated
Attempt 3 · Failed
Let x be litres of the 20% stock and 80 − x litres of the 60% stock.
0.20x + 0.60(80 − x) = 0.35 × 80
0.20x + 48 − 0.60x = 28
−0.40x = −20
x = 50
So 50 litres of the 20% stock and 30 litres of the 60% stock.
{"litres_20": 50, "litres_60": 30}1.92 seconds · $0.0016 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"litres_20": 50, "litres_60": 30}1.95 seconds · $0.0014 estimated
Attempt 2 · Passed
{"litres_20": 50, "litres_60": 30}1.93 seconds · $0.0013 estimated
Attempt 3 · Passed
{"litres_20": 50, "litres_60": 30}1.88 seconds · $0.0014 estimated
Aggregate conversion rates correctly Statistics
Campaign A has 900 visits and 45 purchases. Campaign B has 100 visits and 20 purchases. Next week A has 100 visits and 8 purchases; B has 900 visits and 162 purchases. Return each week’s total conversion percentage and next-minus-first percentage-point change. Return only a JSON object with these keys: week1_percent, week2_percent, change_points. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"week1_percent":6.5,"week2_percent":17,"change_points":10.5}2.38 seconds · $0.0008 estimated
Attempt 2 · Passed
{"week1_percent":6.5,"week2_percent":17,"change_points":10.5}2.92 seconds · $0.0008 estimated
Attempt 3 · Passed
{"week1_percent":6.5,"week2_percent":17,"change_points":10.5}3.62 seconds · $0.0008 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Week 1: total visits 1000, purchases 65, so 6.5%.
Week 2: total visits 1000, purchases 170, so 17%.
Change: 17 - 6.5 = 10.5 percentage points.
{"week1_percent": 6.5, "week2_percent": 17, "change_points": 10.5}1.74 seconds · $0.0014 estimated
Attempt 2 · Failed
Week 1: total visits 1000, purchases 65, so 6.5%.
Week 2: total visits 1000, purchases 170, so 17%.
Change: 10.5 percentage points.
{"week1_percent": 6.5, "week2_percent": 17, "change_points": 10.5}1.70 seconds · $0.0013 estimated
Attempt 3 · Failed
Week 1: total visits = 1000, purchases = 65, so 6.5%.
Week 2: total visits = 1000, purchases = 170, so 17%.
Change: 17 − 6.5 = 10.5 percentage points.
{"week1_percent": 6.5, "week2_percent": 17, "change_points": 10.5}1.81 seconds · $0.0014 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"week1_percent": 6.5, "week2_percent": 17.0, "change_points": 10.5}3.09 seconds · $0.0013 estimated
Attempt 2 · Passed
{"week1_percent": 6.5, "week2_percent": 17.0, "change_points": 10.5}1.61 seconds · $0.0012 estimated
Attempt 3 · Passed
{"week1_percent": 6.5, "week2_percent": 17, "change_points": 10.5}1.64 seconds · $0.0014 estimated
Interpret a screening result Probability
A defect affects 2% of units. A detector flags 95% of defective units and 4% of nondefective units. Given a flag, calculate the probability the unit is defective, as a decimal from 0 to 1. Return only a JSON object with these keys: probability. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"probability":0.32646048109965636}2.71 seconds · $0.0007 estimated
Attempt 2 · Passed
{"probability":0.32646048109965636}2.81 seconds · $0.0007 estimated
Attempt 3 · Passed
{"probability":0.32646048109965636}2.44 seconds · $0.0006 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
P(defective | flag) = (0.02 × 0.95) / (0.02 × 0.95 + 0.98 × 0.04)
The numerator is 0.019 and the second term in the denominator is 0.0392, so the denominator is 0.0582.
0.019 / 0.0582 = 0.326460...
{"probability": 0.3265}1.77 seconds · $0.0014 estimated
Attempt 2 · Failed
P(D)=0.02, P(F|D)=0.95, P(F|not D)=0.04.
Numerator: 0.02*0.95=0.019
Denominator: 0.019+0.98*0.04=0.019+0.0392=0.0582
Probability = 0.019/0.0582 = 0.326460...
{"probability": 0.32646}1.84 seconds · $0.0014 estimated
Attempt 3 · Failed
P(D)=0.02, P(F|D)=0.95, P(F|not D)=0.04.
Numerator: 0.02*0.95=0.019
Denominator: 0.019+0.98*0.04=0.019+0.0392=0.0582
Probability=0.019/0.0582=0.326460...
0.0582*0.3265=0.01900; so ≈0.32646.
{"probability": 0.32646}1.96 seconds · $0.0016 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"probability": 0.32646048109965636}2.47 seconds · $0.0018 estimated
Attempt 2 · Passed
{"probability": 0.32646048109965635}2.47 seconds · $0.0016 estimated
Attempt 3 · Passed
{"probability": 0.32646048109965636}2.23 seconds · $0.0016 estimated
Calculate an amortizing payment Finance
A $12000 loan charges a nominal annual rate of 12%, compounded monthly, repaid with 24 equal end-of-month payments. Calculate the monthly payment and total interest, without intermediate rounding. Return only a JSON object with these keys: payment, interest. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Failed
{"payment":564.88,"interest":1557.16}6.37 seconds · $0.0019 estimated
Attempt 2 · Failed
{"payment":564.88,"interest":1557.16}12.10 seconds · $0.0042 estimated
Attempt 3 · Failed
{"payment":564.88,"interest":1557.16}8.04 seconds · $0.0021 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Monthly rate i = 0.01, n = 24.
Payment = 12000 · i / (1 − (1+i)^−24).
1.01^24 = 1.2697346485 (known value: 1.269734649).
1/1.269734649 = 0.787566 (more precisely 0.78756606).
1 − 0.78756606 = 0.21243394.
Payment = 120 / 0.21243394 = 564.8672...
Check: 0.21243394 × 565 = 120.02512, so the excess is 0.02512 / 0.21243394 = 0.11825. Payment = 565 − 0.11825 = 564.88175.
More precisely, the known payment factor for 1%, 24 months is 0.0470734722, so 12000 × 0.0470734722 = 564.8816664.
Total paid = 564.8816664 × 24 = 13557.16 (564.8816664 × 24 = 13557.1599936).
Interest = 1557.16 (about 1557.1599936).
{"payment": 564.8816664, "interest": 1557.15999}4.07 seconds · $0.0038 estimated
Attempt 2 · Failed
Monthly rate i = 0.01, n = 24.
Payment = 12000 · 0.01 / (1 − 1.01^-24).
1.01^24 = 1.269734648531914, so 1.01^-24 = 0.787566178...
Check: 1/1.269734648531914 ≈ 0.78756618. Then 1 − 0.78756618 = 0.21243382.
Payment = 120 / 0.21243382 ≈ 564.8707.
More precisely: 0.21243382 × 565 = 120.0241, which is 0.0241 too high; 0.0241/0.21243 = 0.1134, so payment ≈ 564.8866. Recompute: 0.21243382 × 564.8866 = 0.21243382×564 = 119.81 (0.21243382×500 = 106.21691, ×64 = 13.59576, sum 119.81267), plus 0.21243382×0.8866 = 0.18835, total 120.00102. Slightly high by 0.00102, which is 0.0048 in payment. So payment ≈ 564.8818.
Refine 1.01^-24 more precisely: 1/1.269734648531914. 1.269734648531914 × 0.7875 = 0.99991 (1.269734648×0.7875 = 0.999915...). Compute: 1.269734648×0.78 = 0.990393025; ×0.0075 = 0.009523010; sum 0.999916035. Remainder 0.000083965/1.269734648 = 0.00006613. So the inverse is 0.78756613. Then 1 − that = 0.21243387.
Payment = 120/0.21243387. 0.21243387×564.88 = 0.21243387×564 = 119.812 (0.21243387×564: ×500 = 106.216935, ×64 = 13.595768, sum 119.812703), plus ×0.88 = 0.186941, total 119.999644. Remainder 0.000356/0.21243 = 0.001676. Payment ≈ 564.881676.
The known value is 564.8734? Check against the standard: the payment on 12000 at 1% for 24 months is 564.87 (the factor 0.0470735 × 12000 = 564.88). The factor 0.04707347 × 12000 = 564.8816. Good.
Total interest = 24 × 564.8817 − 12000 = 13557.16 − 12000 = 1557.16.
24 × 564.881676 = 13557.160. Interest ≈ 1557.16.
{"payment": 564.88, "interest": 1557.16}6.79 seconds · $0.0087 estimated
Attempt 3 · Failed
Monthly rate i = 0.01, n = 24.
Payment = 12000 · 0.01 / (1 − 1.01^−24).
1.01^24 = 1.269734648531914...
1.01^−24 = 1/1.269734648531914 = 0.787566...
Compute: 1/1.2697346485 ≈ 0.78756691. Check: 1.2697346485 × 0.78756691 = 1.0000000 (1.2697346485×0.78 = 0.99039302; ×0.00756691 = 0.00960800; total 1.00000102, slightly high). Adjust: 0.00000102/1.26973 ≈ 0.0000008, so 0.7875661.
Then 1 − 0.7875661 = 0.2124339.
Payment = 120 / 0.2124339 = 564.8...
Compute: 0.2124339 × 565 = 120.0242. Excess 0.0242/0.2124339 = 0.1139. So the payment ≈ 564.886.
More precisely, the known value is 564.8671 for a 24-month 1% loan per 12000 (the factor 0.0470735 × 12000 = 564.882). The standard payment factor for 1%, 24 months is 0.04707347. Times 12000 = 564.88164.
Check: 0.04707347 × 12000 = 564.88164. This agrees with the estimate of about 564.886 within the rounding error of the hand calculation.
Total paid = 564.88164 × 24 = 13557.159; interest ≈ 1557.159.
More digits: the factor 0.0470734722 gives 564.88167 and 13557.1601, so the interest is 1557.16.
{"payment": 564.8816, "interest": 1557.16}5.71 seconds · $0.0060 estimated
Gemini 3.8 Flash
Attempt 1 · Failed
{"payment": 564.88, "interest": 1557.16}13.20 seconds · $0.0120 estimated
Attempt 2 · Failed
{"payment": 564.88, "interest": 1557.16}12.40 seconds · $0.0102 estimated
Attempt 3 · Failed
{"payment": 564.88, "interest": 1557.16}10.19 seconds · $0.0091 estimated
Calculate break-even with fees Finance
A product sells for $40. Variable costs are $17 production, $3 shipping, and a payment fee of 2.5% of sale price plus $0.30. Fixed monthly costs are $1870. Return the minimum whole units needed to break even and profit at that unit count. Return only a JSON object with these keys: units, profit. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"units":100,"profit":0}2.34 seconds · $0.0007 estimated
Attempt 2 · Passed
{"units":100,"profit":0}2.76 seconds · $0.0010 estimated
Attempt 3 · Passed
{"units":100,"profit":0}2.57 seconds · $0.0007 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Payment fee per unit: 0.025*40 + 0.30 = 1.00 + 0.30 = 1.30.
Variable cost per unit: 17 + 3 + 1.30 = 21.30.
Contribution margin: 40 - 21.30 = 18.70.
Break-even units: 1870 / 18.70 = 100 exactly.
Profit at 100 units: 100*18.70 - 1870 = 0.
{"units": 100, "profit": 0}1.94 seconds · $0.0019 estimated
Attempt 2 · Failed
Payment fee per unit = 0.025*40 + 0.30 = 1.00 + 0.30 = 1.30.
Variable cost per unit = 17 + 3 + 1.30 = 21.30.
Contribution margin = 40 - 21.30 = 18.70.
Break-even units = 1870 / 18.70 = 100 exactly.
Profit at 100 units = 100*18.70 - 1870 = 0.
{"units": 100, "profit": 0}1.84 seconds · $0.0019 estimated
Attempt 3 · Failed
Payment fee per unit = 0.025*40 + 0.30 = 1.00 + 0.30 = 1.30.
Variable cost per unit = 17 + 3 + 1.30 = 21.30.
Contribution margin = 40 − 21.30 = 18.70.
Break-even units = 1870 / 18.70 = 100 exactly.
Profit at 100 units = 100 × 18.70 − 1870 = 0.
{"units": 100, "profit": 0}1.87 seconds · $0.0019 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"units": 100, "profit": 0}2.89 seconds · $0.0021 estimated
Attempt 2 · Passed
{"units": 100, "profit": 0}2.26 seconds · $0.0019 estimated
Attempt 3 · Passed
{"units": 100, "profit": 0}1.77 seconds · $0.0013 estimated
Calculate independent service reliability Probability
Each of three independent services succeeds with probability 0.98. A workflow requires all three. It retries the complete workflow once if the first attempt fails; attempts are independent. Calculate eventual success probability and expected number of complete attempts. Return only a JSON object with these keys: success_probability, expected_attempts. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"success_probability":0.996541619136,"expected_attempts":1.058808}3.99 seconds · $0.0012 estimated
Attempt 2 · Passed
{"success_probability":0.996541619136,"expected_attempts":1.058808}2.70 seconds · $0.0011 estimated
Attempt 3 · Passed
{"success_probability":0.996541619136,"expected_attempts":1.058808}3.04 seconds · $0.0010 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
p = 0.98^3 = 0.941192
Failure = 0.058808
Success probability = 1 - 0.058808^2 = 1 - 0.003458... compute: 0.058808^2 = 0.003458380864 (0.058808*0.058808: 0.058808*0.05=0.0029404; *0.008808=0.000517981...; sum: 0.0029404+0.00051798=0.00345838). So success = 0.996541619136.
Expected attempts = 1 + 0.058808 = 1.058808.
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}2.68 seconds · $0.0023 estimated
Attempt 2 · Failed
p = 0.98^3 = 0.941192
Failure = 0.058808
Success probability = 1 - 0.058808^2 = 1 - 0.003458700864 = 0.996541299136
Check 0.058808^2: 0.058808*0.058808 = 0.0034587... 0.058808^2 = (0.0588)^2 + 2*0.0588*0.000008 + 6.4e-11 = 0.00345744 + 0.0000009408 + 0.000000000064 = 0.003458380864. Recompute: 0.0588^2 = 0.00345744. Add 0.0000009408 → 0.0034583808, plus 6.4e-11 → 0.003458380864.
Success = 1 - 0.003458380864 = 0.996541619136
Expected attempts = 1 + 0.058808 = 1.058808
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}2.98 seconds · $0.0034 estimated
Attempt 3 · Failed
p = 0.98^3 = 0.941192
Failure = 0.058808
Success probability = 1 - 0.058808^2 = 1 - 0.003458540864 = 0.996541459136
0.058808^2: 0.058808*0.058808 = 0.003458 (0.058808*0.05=0.0029404; *0.008808=0.00051798...). Compute precisely: 0.058808*0.008808 = 0.000517980... 0.058808*0.008=0.000470464; *0.000808=0.0000475168 (0.058808*0.0008=0.0000470464; *0.000008=0.000000470464; sum 0.000047516864). Total 0.000517980864. Plus 0.0029404 = 0.003458380864.
So success = 1 - 0.003458380864 = 0.996541619136.
Expected attempts = 1 + 0.058808 = 1.058808
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}3.34 seconds · $0.0035 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}2.64 seconds · $0.0022 estimated
Attempt 2 · Passed
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}3.91 seconds · $0.0035 estimated
Attempt 3 · Passed
{"success_probability": 0.996541619136, "expected_attempts": 1.058808}3.42 seconds · $0.0035 estimated
Compare sequential and additive discounts Finance
An item is $250 before discounts and tax. Apply 20% off, then a further 15% off the discounted price, then 8% tax. Return the final price and effective pretax discount percentage. Return only a JSON object with these keys: final_price, discount_percent. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"final_price":183.6,"discount_percent":32}2.13 seconds · $0.0006 estimated
Attempt 2 · Passed
{"final_price":183.6,"discount_percent":32}3.50 seconds · $0.0006 estimated
Attempt 3 · Passed
{"final_price":183.6,"discount_percent":32}1.93 seconds · $0.0006 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
250 × 0.8 = 200; × 0.85 = 170; × 1.08 = 183.6.
Effective pretax discount: (250 − 170)/250 = 32%.
{"final_price": 183.6, "discount_percent": 32}1.61 seconds · $0.0011 estimated
Attempt 2 · Failed
250 × 0.8 = 200; × 0.85 = 170; × 1.08 = 183.6. Effective pretax discount: (250 − 170)/250 = 32%.
{"final_price": 183.6, "discount_percent": 32}1.60 seconds · $0.0010 estimated
Attempt 3 · Failed
250 × 0.8 = 200; × 0.85 = 170; × 1.08 = 183.6. The effective pretax discount is (250 − 170) / 250 = 32%.
{"final_price": 183.6, "discount_percent": 32}1.77 seconds · $0.0011 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"final_price": 183.6, "discount_percent": 32}1.70 seconds · $0.0012 estimated
Attempt 2 · Passed
{"final_price": 183.6, "discount_percent": 32}2.05 seconds · $0.0014 estimated
Attempt 3 · Passed
{"final_price": 183.6, "discount_percent": 32}2.18 seconds · $0.0015 estimated
Optimize a constrained production plan Optimization
Product A uses 3 labour hours and 2 machine hours and earns $40 contribution. B uses 2 labour and 4 machine hours and earns $50. Weekly limits are 120 labour and 160 machine hours. Products must be whole units. Maximize contribution; if tied choose more A. Return A, B and contribution. Return only a JSON object with these keys: a, b, contribution. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"a":20,"b":30,"contribution":2300}4.77 seconds · $0.0012 estimated
Attempt 2 · Passed
{"a":20,"b":30,"contribution":2300}4.13 seconds · $0.0011 estimated
Attempt 3 · Passed
{"a":20,"b":30,"contribution":2300}4.35 seconds · $0.0011 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Maximize 40A + 50B subject to 3A + 2B ≤ 120 and 2A + 4B ≤ 160, with A and B whole numbers.
The two constraints intersect where 3A + 2B = 120 and A + 2B = 80. Subtracting gives 2A = 40, so A = 20 and B = 30. The contribution there is 800 + 1500 = 2300.
Checking the other corner points:
- A = 0, B = 40 gives 2000.
- A = 40, B = 0 gives 1600.
The intersection is integer-valued and gives the highest contribution found. The objective slope (40:50) lies between the constraint slopes, so the optimum is at the vertex. Ties are not a concern, since the objective is not parallel to either constraint: 40/50 = 0.8, versus 3/2 = 1.5 and 2/4 = 0.5.
{"a":20,"b":30,"contribution":2300}3.58 seconds · $0.0034 estimated
Attempt 2 · Failed
Maximize 40A + 50B subject to 3A + 2B ≤ 120 and 2A + 4B ≤ 160, with A and B whole numbers.
The two constraints intersect where 3A + 2B = 120 and A + 2B = 80. Subtracting gives 2A = 40, so A = 20 and B = 30. The contribution there is 800 + 1500 = 2300.
Checking the other corner points:
- A = 40, B = 0: 1600
- A = 0, B = 40: 2000
The intersection is integer-valued and gives the highest contribution, 2300. To check for ties, the objective ratio 40:50 differs from both constraint ratios (3:2 and 2:4), so no other point matches 2300.
{"a":20,"b":30,"contribution":2300}3.01 seconds · $0.0030 estimated
Attempt 3 · Failed
Maximize 40A + 50B subject to 3A + 2B ≤ 120 and 2A + 4B ≤ 160, with A and B whole numbers.
The two constraints intersect where 3A + 2B = 120 and A + 2B = 80. Subtracting gives 2A = 40, so A = 20 and B = 30. The contribution there is 800 + 1500 = 2300.
Checking the other corners:
- A = 0, B = 40 gives 2000.
- A = 40, B = 0 gives 1600.
Since 2300 is the largest and the intersection is already whole numbers, it is optimal. The ratios 40/50 and 3/2 do not match, so there are no ties along an edge.
{"a":20,"b":30,"contribution":2300}3.14 seconds · $0.0029 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"a": 20, "b": 30, "contribution": 2300}3.02 seconds · $0.0022 estimated
Attempt 2 · Passed
{"a": 20, "b": 30, "contribution": 2300}3.26 seconds · $0.0028 estimated
Attempt 3 · Passed
{"a": 20, "b": 30, "contribution": 2300}3.58 seconds · $0.0030 estimated
Discount a project cash flow Finance
Pay $1000 now, then receive $400 at each year end for three years. Use a 10% annual discount rate. Return net present value without rounding intermediate values. Return only a JSON object with these keys: npv. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"npv":-5.259203606311044}4.86 seconds · $0.0016 estimated
Attempt 2 · Passed
{"npv":-5.259203606311044}8.02 seconds · $0.0027 estimated
Attempt 3 · Passed
{"npv":-5.259203606311044}4.58 seconds · $0.0017 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
NPV = -1000 + 400*(1/1.1 + 1/1.21 + 1/1.331)
Annuity factor = 2.486851991...
Exactly: 1/1.1 = 0.909090909091, 1/1.21 = 0.826446280992, 1/1.331 = 0.751314800902. Sum = 2.486851990985.
Times 400 = 994.740796394.
NPV = -5.259203606
{"npv": -5.259203606}2.49 seconds · $0.0018 estimated
Attempt 2 · Failed
NPV = -1000 + 400 × (1/1.1 + 1/1.21 + 1/1.331)
Annuity factor = (1 - 1.1^-3)/0.1 = 2.486851991...
Exact: 1/1.1 = 0.909090909..., 1/1.21 = 0.826446281, 1/1.331 = 0.751314801. Sum = 2.486851991.
Times 400 = 994.7407964
NPV = -5.2592036
More precisely, the sum is 2.4868519909842 (since 1.1^3 = 1.331, the exact sum is (1.21 + 1.1 + 1)/1.331 = 3.31/1.331 = 2.48685199098...). Times 400 = 1324/1.331 = 994.740796...; 1324/1.331 = 994.7407964...; NPV = -5.2592036.
Check: 1.331 × 994.7408 = 1324.0000 (1.331 × 994.7408 = 994.7408 + 0.331×994.7408 = 994.7408 + 329.2593 = 1324.0001). Good.
{"npv": -5.259203606311}3.87 seconds · $0.0040 estimated
Attempt 3 · Failed
NPV = -1000 + 400 × (1/1.1 + 1/1.21 + 1/1.331)
Annuity factor = (1 - 1.1^-3)/0.1. 1.1^3 = 1.331, so 1/1.331 = 0.7513148009...
Annuity factor = (1 - 0.7513148009)/0.1 = 2.486851991
400 × 2.486851991 = 994.7407963
NPV = -5.2592037
More precisely: 1/1.331 = 0.75131480090157..., 1 - that = 0.24868519909843, factor = 2.4868519909843, times 400 = 994.74079639372, NPV = -5.25920360628.
{"npv": -5.25920360628}2.97 seconds · $0.0026 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"npv": -5.259203606311044}3.07 seconds · $0.0027 estimated
Attempt 2 · Passed
{"npv": -5.25920360631106}3.32 seconds · $0.0032 estimated
Attempt 3 · Passed
{"npv": -5.259203606311044}2.97 seconds · $0.0027 estimated
Allocate a shared expense Finance
Allocate exactly $10.00 to three departments with weights 1, 1, 1. Work in cents: floor shares, then allocate remaining cents by descending fractional remainder, ties to lower index. Return integer cents for departments A, B and C. Return only a JSON object with these keys: a_cents, b_cents, c_cents. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"a_cents":334,"b_cents":333,"c_cents":333}1.61 seconds · $0.0004 estimated
Attempt 2 · Passed
{"a_cents":334,"b_cents":333,"c_cents":333}1.65 seconds · $0.0007 estimated
Attempt 3 · Passed
{"a_cents":334,"b_cents":333,"c_cents":333}2.99 seconds · $0.0006 estimated
Claude Sonnet 5.5
Attempt 1 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}1.33 seconds · $0.0006 estimated
Attempt 2 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}1.23 seconds · $0.0006 estimated
Attempt 3 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}1.21 seconds · $0.0006 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}2.24 seconds · $0.0015 estimated
Attempt 2 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}2.08 seconds · $0.0016 estimated
Attempt 3 · Passed
{"a_cents": 334, "b_cents": 333, "c_cents": 333}2.75 seconds · $0.0015 estimated
Calculate sample uncertainty Statistics
For observations 4, 7, 7, 10, 12 calculate the arithmetic mean, unbiased sample variance (denominator n-1), and standard error of the mean. Return only a JSON object with these keys: mean, sample_variance, standard_error. Numeric fields must be numbers. No Markdown or explanation.
GPT-6.1 Sol
Attempt 1 · Passed
{"mean":8,"sample_variance":9.5,"standard_error":1.378404875209022}2.57 seconds · $0.0009 estimated
Attempt 2 · Passed
{"mean":8,"sample_variance":9.5,"standard_error":1.378404875209022}4.16 seconds · $0.0009 estimated
Attempt 3 · Passed
{"mean":8,"sample_variance":9.5,"standard_error":1.378404875209022}2.66 seconds · $0.0009 estimated
Claude Sonnet 5.5
Attempt 1 · Failed
Sum = 4+7+7+10+12 = 40, so the mean is 8.
Squared deviations: 16, 1, 1, 4, 16, which sum to 38. Sample variance = 38/4 = 9.5.
Standard error = sqrt(9.5/5) = sqrt(1.9) ≈ 1.378405.
{"mean": 8, "sample_variance": 9.5, "standard_error": 1.3784048752090222}2.16 seconds · $0.0017 estimated
Attempt 2 · Failed
Mean = (4+7+7+10+12)/5 = 40/5 = 8.
Squared deviations: 16, 1, 1, 4, 16, which sum to 38.
Sample variance = 38/4 = 9.5.
Standard error = sqrt(9.5/5) = sqrt(1.9) ≈ 1.378405.
{"mean": 8, "sample_variance": 9.5, "standard_error": 1.3784048752090222}2.03 seconds · $0.0017 estimated
Attempt 3 · Failed
Mean = (4+7+7+10+12)/5 = 40/5 = 8.
Squared deviations: 16, 1, 1, 4, 16, which sum to 38. Sample variance = 38/4 = 9.5.
Standard error = sqrt(9.5/5) = sqrt(1.9) ≈ 1.378405.
{"mean": 8, "sample_variance": 9.5, "standard_error": 1.378405}1.90 seconds · $0.0017 estimated
Gemini 3.8 Flash
Attempt 1 · Passed
{"mean": 8, "sample_variance": 9.5, "standard_error": 1.378404875209022}1.97 seconds · $0.0014 estimated
Attempt 2 · Passed
{"mean": 8.0, "sample_variance": 9.5, "standard_error": 1.378404875209022}2.05 seconds · $0.0015 estimated
Attempt 3 · Passed
{"mean": 8, "sample_variance": 9.5, "standard_error": 1.378404875209022}2.22 seconds · $0.0015 estimated
Reproduce this run
Download original JSON evidence · Download original CSV results
Scoring audit: 2026-10-04T18:18:02.762014+00:00 · 0 verdicts changed · zero new provider requests. Download appended correction.
Run history
- 2026-10-04T08:20:14.082456+00:00 · complete · 108 / 108 required trials initiated · Archived evidence
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