A code reads 2, 9, 6, x, 3, with the fourth…

A code reads 2, 9, 6, x, 3, with the fourth digit smudged.

Question 38

MediumOriginal 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.

A code reads 2, 9, 6, $x$ , 3, with the fourth digit smudged. What is $x$ ?

3

Correct answerYour answer

4

Correct answerYour answer

6

Correct answerYour answer

7

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$2 + 9 + 6 + x \equiv 3 \pmod{10}$ , that is $17 + x \equiv 3$ .
$x \equiv 3 - 17 = -14 \equiv 6$ , and the only digit that works is 6.

Worth noting

4 drops the minus sign of $-14$ and takes its last digit.

Concept: Solving for a missing digit
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsModular addition, subtraction and multiplication

Practise this chapter →

Ten questions from Modulo Arithmetic & Congruence, at your own pace.

Practise this chapter →

Ten questions from Modulo Arithmetic & Congruence, at your own pace.

A code reads 2, 9, 6, x, 3, with the fourth digit smudged.

Question 38

Explanation