Question

What is the remainder when the positive integer x is divided by 6? (1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0. (2) When x is divided by 12, the remainder is 3.

Answer 1

Step-by-step explanation:

As

When x is divided by 2, the remainder is 1. It means x being an odd number.

When x is divided by 3, the remainder is 0. It means x being the odd multiple of 3. i.e. 3, 9, 15,..

So, observing the pattern, we can determine that any such number divided by 6 would bring the remainder of 3.

As also,

When x is divided by 12, the remainder is 3.

Meaning,

$x = 12t + 3 = 6(2t) + 3$

As any such number divided by 6 yields remainder of 3 and we can observe that $12t$ is divisible by 6 and 3 divided by 6 yields the remainder of 3.

Keywords: remainder, integer, divisibility

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