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Modulo Arithmetic & Congruence · Question 10 of 97

Question 10

MediumOriginal question

When a number aa is divided by 8, the remainder is 5. Which of these can aa be?

Options for question 10

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. a mod 8=5a \bmod 8 = 5 means a=8q+5a = 8q + 5: 5, 13, 21, 29, 37, 45, …

  2. 37=8×4+537 = 8 \times 4 + 5. The others leave 3, 2 and 3.

Worth noting

43 is 5 more than 38, but 38 is not a multiple of 8.

Concept
Numbers with a given remainder
Typical time
90 s
Your time
—
The rule this testsThe modulo operation
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.