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AIME 2024 / AIME 2024 train fdb72a89-60e5-5803-998a-5d2111009a54

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Let

N

be the greatest four-digit positive integer with the property that whenever one of its digits is changed to

1

, the resulting number is divisible by

7

. Let

Q

and

R

be the quotient and remainder, respectively, when

N

is divided by

1000

. Find

Q+R

Plain-text mathematical notation (without MathML)

Let N be the greatest four-digit positive integer with the property that whenever one of its digits is changed to 1, the resulting number is divisible by 7. Let Q and R be the quotient and remainder, respectively, when N is divided by 1000. Find Q+R.

Original LaTeX notation

Let $N$ be the greatest four-digit positive integer with the property that whenever one of its digits is changed to $1$, the resulting number is divisible by $7$. Let $Q$ and $R$ be the quotient and remainder, respectively, when $N$ is divided by $1000$. Find $Q+R$.

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Source and history

task_id: fdb72a89-60e5-5803-998a-5d2111009a54
task_key: default--train--fdb72a89-60e5-5803-998a-5d2111009a54
task_revision_id: 2
config / split: default / train

Official source

initial import