EduFarming
Your list · 0हिं

Type at least two letters. Press Esc to close.

↑↓ navigate↵ openTAB cycle filter

Modulo Arithmetic & Congruence · Question 88 of 97

Question 88

MediumOriginal question

Which of these numbers lies in the same residue class as 17 modulo 5?

Options for question 88

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. 17 leaves remainder 2, so its class is [2]={…,−8,−3,2,7,12,17,… }[2] = \{\dots, -8, -3, 2, 7, 12, 17, \dots\}.

  2. −3=5×(−1)+2-3 = 5 \times (-1) + 2, so −3-3 is in it. 8, 21 and 14 leave 3, 1 and 4.

Worth noting

−3-3 looks far from 17, but 17−(−3)=2017 - (-3) = 20 is a multiple of 5.

Concept
Members of a residue class
Typical time
90 s
Your time
—
The rule this testsResidue classes
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.