Question

If Y is a prime number greater than 10000 and it leaves a remainder of 2 when divided by 3, then what remainder does Y leave on division by 6?
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Answer 1

The number is of the form 3y+ 2 and as it is a prime number, it is odd.
$\therefore$ y is odd and is of the form 2k+1.
$\therefore$ 3y+ 2 = 3(2k+ 1) + 2 = 6k+5

$\therefore$ The number leaves a remainder of 5 when divided by 6.