If \(m\) and \(n\) are positive integers and \(r\) is the

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GMAT Prep

If \(m\) and \(n\) are positive integers and \(r\) is the remained when \(5(10^n)+m\) is divided by \(3\), what is the value of \(r\)?

1. \(n=10\)
2. \(m=1\)

OA B

[Ian Stewart]

If you want a number's remainder when you divide it by 3, you can sum the digits of the number and take the remainder by 3 of that sum. The sum of the digits of (5)(10^n) is always going to be 5 no matter what n equals, so we only need the value of m. If m = 1, then the digits of (5)(10^n) + m will sum to 6, so the number will be a multiple of 3 and the remainder will be zero. So the answer is B.