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MMLU-Pro / 8286 / The n^(th) term of a certain geometric series is given by …

Problem

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

question

The nthn^{\text{th}} term of a certain geometric series is given by a⋅rn−1a\cdot r^{n-1}, where aa and rr are positive integers and rr is greater than 1. Bill picks out kk different numbers in this sequence, all of which have the same number of digits. What is the largest possible value of kk?
Plain-text mathematical notation (without MathML)
The n^(th) term of a certain geometric series is given by a⋅r^(n−1), where a and r are positive integers and r is greater than 1. Bill picks out k different numbers in this sequence, all of which have the same number of digits. What is the largest possible value of k?
Original LaTeX notation
The $n^{\text{th}}$ term of a certain geometric series is given by $a\cdot r^{n-1}$, where $a$ and $r$ are positive integers and $r$ is greater than 1. Bill picks out $k$ different numbers in this sequence, all of which have the same number of digits. What is the largest possible value of $k$?

category

math

options

  1. 12
  2. 8
  3. 5
  4. 16
  5. 15
  6. 4
  7. 10
  8. 9
  9. 6
  10. 7

src

ori_mmlu-high_school_mathematics

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Source and history

upstream_id / Original problem ID
8286
task_id
9c19428c-d030-503a-9bee-471083ae2eed
task_key
default--test--8286
task_revision_id
1
config / split
default / test

Official source

initial import