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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