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Modulo Arithmetic & Congruence · Question 29 of 97

Question 29

MediumOriginal question

What is the additive inverse of 5 modulo 12, written as one of 0,1,…,110, 1, \dots, 11?

Options for question 29

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. The additive inverse of aa is the number bb with a+b≡0(mod12)a + b \equiv 0 \pmod{12}.

  2. 5+7=12≡05 + 7 = 12 \equiv 0, so it is 7.

Worth noting

5 is the number itself: 5+5=105 + 5 = 10, not a multiple of 12.

Concept
The additive inverse modulo n
Typical time
90 s
Your time
—
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.