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If \(m\) is a two-digit number, what is the remainder when

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by AAPL » Thu Aug 15, 2019 7:00 am

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Economist GMAT

If \(m\) is a two-digit number, what is the remainder when \(m\) is divided by 3?

1) \(m+1\) is divisible by 3.
2) \(m\) is positive, and the sum of its digits is 8.

OA D
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Source: — Data Sufficiency |

by Jay@ManhattanReview » Fri Aug 16, 2019 12:29 am
AAPL wrote:Economist GMAT

If \(m\) is a two-digit number, what is the remainder when \(m\) is divided by 3?

1) \(m+1\) is divisible by 3.
2) \(m\) is positive, and the sum of its digits is 8.

OA D
Let's take each statement one by one.

1) \(m+1\) is divisible by 3.

=> \(m-2+3\) is divisible by 3 => \(m-2\) is divisible by 3; thus, the remainder when \(m\) is divided by 3 = 2. Sufficient.

2) \(m\) is positive, and the sum of its digits is 8.

We know that a number is divisible by 3 if its sum of digits is divisible by 3.

Since it is given that the sum of \(m\) is 8, the sum of \(m+1\) is 9. Thus, \(m+1\) is divisible by 9. If a number is divisible y 9, it is divisible by 3, too. So, we have \(m+1\) is divisible by 3. It is the same statement as Statement 1. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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