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MMLU-Pro / 8826 / Suppose x−3 and y+3 are multiples of 7. What is the smallest positive…

Problem

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

question

Suppose x−3x-3 and y+3y+3 are multiples of 77. What is the smallest positive integer, n,n, for which x2+xy+y2+nx^2+xy+y^2+n is a multiple of 77?
Plain-text mathematical notation (without MathML)
Suppose x−3 and y+3 are multiples of 7. What is the smallest positive integer, n, for which x²+xy+y²+n is a multiple of 7?
Original LaTeX notation
Suppose $x-3$ and $y+3$ are multiples of $7$. What is the smallest positive integer, $n,$ for which $x^2+xy+y^2+n$ is a multiple of $7$?

category

math

options

  1. 9
  2. 8
  3. 5
  4. 6
  5. 3
  6. 2
  7. 4
  8. 7
  9. 10
  10. 1

src

ori_mmlu-high_school_mathematics

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Source and history

upstream_id / Original problem ID
8826
task_id
edcacfcb-96e4-5b91-8407-e81f9cc625bb
task_key
default--test--8826
task_revision_id
1
config / split
default / test

Official source

initial import