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Modulo Arithmetic & Congruence · Question 44 of 97

Which mistake can this check digit NOT catch?

Question 44

HardOriginal question

A shop gives each product a 5-digit code. The first four digits name the product, and the fifth, the check digit, is the sum of the first four digits taken modulo 10.

Which mistake can this check digit NOT catch?

Writing one of the first four digits wronglyCorrect answerYour answerSwapping two of the first four digitsCorrect answerYour answerAdding 1 to one of the first four digitsCorrect answerYour answerWriting the check digit wronglyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

A swap leaves the sum of the first four digits unchanged, so the check digit still matches.
Changing a single digit changes the sum by 1 to 9, which always changes its last digit.

Worth noting

This is why many real codes weight the digits differently, so that a swap changes the sum.

Concept: What a check digit can detect
Typical timeTypical: 150 s
Your timeYours: —

The rule this testsModular addition, subtraction and multiplication

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