qwen3.7-plus × math

PASS10.0

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Prompt

math1.2K tok cap

A SaaS product has 1,000 users.

60% use the free plan.
Of free-plan users, 8% convert to paid each month.
Paid users have a 4% monthly churn rate.
No new users join.
Conversion happens before churn each month.
A converted user cannot churn during the same month they convert.

Question: After one month, how many free users and paid users are expected to remain?

Show the calculation clearly. Do not round intermediate values.

Output format: { "free_users_after_month_1": number, "paid_users_after_month_1": number, "calculation": ["...", "...", "..."], "assumptions": ["..."] }

Candidate — qwen/qwen3.7-plus

done

{
  "free_users_after_month_1": 552,
  "paid_users_after_month_1": 432,
  "calculation": [
    "Initial free users: 1000 * 0.60 = 600",
    "Initial paid users: 1000 * 0.40 = 400",
    "Free users converting to paid: 600 * 0.08 = 48",
    "Free users after conversion: 600 - 48 = 552",
    "Paid users after conversion (before churn): 400 + 48 = 448",
    "Converted users are exempt from churn this month, so churn applies only to original paid users",
    "Paid users churning: 400 * 0.04 = 16",
    "Paid users after churn: 448 - 16 = 432"
  ],
  "assumptions": [
    "No new users join the product during the month",
    "Conversion is calculated on the starting free-user base for the month",
    "Churn is calculated on the starting paid-user base for the month, excluding newly converted users",
    "Conversion happens before churn within the month"
  ]
}

Tokens1.1K

Cost$0.0011

Latency14.9s

Finishstop

Judges

median 10.0

grok-4.5scored

PASS10.0

gpt-5.6-luna-proscored

PASS10.0

claude-sonnet-5scored

PASS9.9

8/8 checks passed

Output parses as JSON
expected "valid JSON object" · got "parsed"
No prose outside the JSON object
expected "JSON only (optional single fence)" · got "clean"
All required keys present
expected ["free_users_after_month_1","paid_users_after_month_1","calculation","assumptions"] · got ["free_users_after_month_1","paid_users_after_month_1","calculation","assumptions"]
Values have the expected types
expected {"free_users_after_month_1":"number","paid_users_after_month_1":"number","calculation":"array","assumptions":"array"} · got {"free_users_after_month_1":"number","paid_users_after_month_1":"number","calculation":"array","assumptions":"array"}
Arrays have the exact required counts
expected {} · got {}
Free-plan count present as an integer
expected 552 · got 552
Paid-plan count present as an integer
expected 432 · got 432
Exact answers — free = 552, paid = 432
expected {"free":552,"paid":432} · got {"free":552,"paid":432}

Loading cell…

{ "free_users_after_month_1": 552, "paid_users_after_month_1": 432, "calculation": [ "Initial free users: 1000 * 0.60 = 600", "Initial paid users: 1000 * 0.40 = 400", "Free users converting to paid: 600 * 0.08 = 48", "Free users after conversion: 600 - 48 = 552", "Paid users after conversion (before churn): 400 + 48 = 448", "Converted users are exempt from churn this month, so churn applies only to original paid users", "Paid users churning: 400 * 0.04 = 16", "Paid users after churn: 448 - 16 = 432" ], "assumptions": [ "No new users join the product during the month", "Conversion is calculated on the starting free-user base for the month", "Churn is calculated on the starting paid-user base for the month, excluding newly converted users", "Conversion happens before churn within the month" ] }