Which numbers among 0, 1, , 9 satisfy 2x ≡ 4 (mod 10)?

Modulo Arithmetic & Congruence · Question 70 of 97

Question 70

MediumOriginal question

Which numbers among $0, 1, \dots, 9$ satisfy $2x \equiv 4 \pmod{10}$ ?

2 onlyCorrect answerYour answer2 and 4Correct answerYour answer7 onlyCorrect answerYour answer2 and 7Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$2x$ must end in 4, so $2x$ is 4 or 14 for $x$ up to 9.
That gives $x = 2$ and $x = 7$ : two solutions, as $\gcd(2, 10) = 2$ promises.

Worth noting

Dividing both sides by 2 gives only $x = 2$ ; dividing a congruence also divides its modulus, to 5, and $x \equiv 2 \pmod{5}$ has two values below 10.

Concept: Listing every solution
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsSolving with congruences

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Which numbers among 0,1,…,90, 1, \dots, 90,1,…,9 satisfy 2x≡4(mod10)2x \equiv 4 \pmod{10}2x≡4(mod10)?

Explanation

Which numbers among $0, 1, \dots, 9$ satisfy $2x \equiv 4 \pmod{10}$ ?