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MATH / The UPC code, made up of numbers and dashes, on a video tape is…

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problem

The UPC code, made up of numbers and dashes, on a video tape is 9-78094-11006-xx. The digit xx is in the 12th12^{\mathrm{th}} position. Let nn be the value obtained by adding the digits in the odd positions, tripling that sum, and then adding the digits in the even positions. A valid UPC code is such that nn is divisible by 10. For what value of xx will this UPC code be valid?
Plain-text mathematical notation (without MathML)
The UPC code, made up of numbers and dashes, on a video tape is 9-78094-11006-x. The digit x is in the 12^(th) position. Let n be the value obtained by adding the digits in the odd positions, tripling that sum, and then adding the digits in the even positions. A valid UPC code is such that n is divisible by 10. For what value of x will this UPC code be valid?
Original LaTeX notation
The UPC code, made up of numbers and dashes, on a video tape is 9-78094-11006-$x$. The digit $x$ is in the $12^{\mathrm{th}}$ position. Let $n$ be the value obtained by adding the digits in the odd positions, tripling that sum, and then adding the digits in the even positions. A valid UPC code is such that $n$ is divisible by 10. For what value of $x$ will this UPC code be valid?

level

Level 4

type

Number Theory

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Source and history

task_id
1e0c34ed-8f58-537e-94f9-ecdb689619f9
task_key
number~5ftheory--test--1e0c34ed-8f58-537e-94f9-ecdb689619f9
task_revision_id
1
config / split
number_theory / test

Official source

initial import