When a number is divided by 36, the remainder is 19. What will be the…
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When a number is divided by 36, the remainder is 19. What will be the remainder when the number is divided by 12 ?
- A.
7
- B.
5
- C.
3
- D.
0
Attempted by 11 students.
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Correct answer: A
Key idea: the remainder upon division by 12 depends only on the remainder modulo 12 of the number.
Let the number be n = 36k + 19 for some integer k.
Since 36k = 12*(3k), rewrite n as n = 12*(3k) + 19. The multiple of 12 does not affect the remainder on division by 12.
Reduce 19 modulo 12: 19 = 12 + 7, so the remainder contributed by 19 is 7.
Therefore, the remainder when the number is divided by 12 is 7.