qwen3.7-max × 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-max

done

{
  "free_users_after_month_1": 552,
  "paid_users_after_month_1": 432,
  "calculation": [
    "Initial free users = 60% of 1000 = 600",
    "Initial paid users = 40% of 1000 = 400",
    "Converted users = 8% of 600 = 48",
    "Free users after conversion = 600 - 48 = 552",
    "Paid users after conversion = 400 + 48 = 448",
    "Churn applies only to original paid users (converted users are exempt this month)",
    "Churned users = 4% of 400 = 16",
    "Paid users after churn = 448 - 16 = 432"
  ],
  "assumptions": [
    "The 4% churn rate applies only to the 400 original paid users, since the 48 newly converted users cannot churn in the same month they convert.",
    "No new users join the system, so total user count only decreases due to churn.",
    "Conversion is calculated on the starting free user count at the beginning of the month."
  ]
}

Tokens1.2K

Cost$0.0042

Latency16.7s

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 = 60% of 1000 = 600", "Initial paid users = 40% of 1000 = 400", "Converted users = 8% of 600 = 48", "Free users after conversion = 600 - 48 = 552", "Paid users after conversion = 400 + 48 = 448", "Churn applies only to original paid users (converted users are exempt this month)", "Churned users = 4% of 400 = 16", "Paid users after churn = 448 - 16 = 432" ], "assumptions": [ "The 4% churn rate applies only to the 400 original paid users, since the 48 newly converted users cannot churn in the same month they convert.", "No new users join the system, so total user count only decreases due to churn.", "Conversion is calculated on the starting free user count at the beginning of the month." ] }