BTGmoderatorDC wrote: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 two digits is 8
Given: m is a two-digit number.
To find out: The remainder when m is divided by 3.
Let's take each statement one by one.
(1) m+1 is divisible by 3.
Since m+1 is divisible by 3, m is not divisible by 3, leaving a remainder of 3 - 1 = 2. Sufficient.
You may take a few examples. Say the set of (m + 1) is: {12, 15, 18, 21, ... 96, 99}; thus, the set of m is: {11, 14, 17, 20, ..., 95, 98}. I each case, m divided by 3 leaves a remainder of 2.
Another way: Say m + 1 = 3x; where x is any integer
Thus, m = 3x - 1
=> m/3 = (3x - 1)/3 = x - 1/3
=> Remainder = -1; since remainder cannot be negative, the remainder = 3 - 1 = 2.
(2) m is positive, and the sum of its two digits is 8.
We know that if a number is divisible by 3, the sum of its two digits is divisible by 3; thus, the remainder when m is divided by 3 is given by when the sum is divided by 3. Thus, the remainder = remainder when 8 is divided by 3 = 2. Sufficient.
On the same line, we can conclude that since the sum of the two digits of m is 8, the sum of the two digits of (m+1) is 9, which is divisible by 3. Thus, the situation is the same as that in Statement 1. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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