Remainder after subtraction

Number Theory Level 2

If the integer $N$ leaves a remainder of 12 when divided by 345, what remainder does the integer $N-67$ leave when divided by 345?

The answer is 290.

1 solution

Arron Kau Staff
May 13, 2014

$N = q \times 345 + 12$ , where $q$ is the quotient.
Hence $N- 67 = (q-1) \times 345 + 12 + 345-67 = (q-1) \times 345 + 290$ .
Hence, the remainder is 290.

Remainder after subtraction

The answer is 290.

1 solution

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