12 Days of Christmas GMAT Competition - Day 10: Is m+10 positive?

Is m+10 positive?

Rephrasing the question:
m+10>0?
m>-10?

(1) On the number line, m+10 is closer to 0 than to m.
Let's consider the cases:
Case 1: If m > 0 , then m+10 will move us further from zero, and the result will be closer to m than to 0. (So, this case is invalid as it does not satisfy the statement)
Case 2: m = 0 , this case is not valid, since the statement says that m+10 is closer to 0 than to m and this cannot be unless m did not equal zero.
Case 3: m<0 , then m+10 will move us to numbers that are larger than m. And those will not be closer to zero unless m was approximately > -20. For example: if m= -9 then m+10 will be 1, which is closer to zero than to m. if m= -19 then m+10 will be -9, which is also closer to zero than it is to m. However, if m = -100, then m+10 will be -90, which does not satisfy the statement.
The problem is we cannot determine if m>-10 because we have negative numbers that are more or less than -10 and still satisfy the statement. (Consider m= -9 , and m=-19 )
Insufficient.

(2) On the number line, m -10 is closer to 0 than to m.
This statement alone is insufficient.
Consider the case in which m=12, then m-10= 2. m>-10
The case in which m<-10 will not satisfy the statement in any case.
Sufficinet, and m>-10

Answer B

Is m+10 positive?
or Is m+10>0 ?

Statement 1 - On the number line, m+10 is closer to 0 than to m.

Consider m= -8 so m+10 is 2 which is >0. So yes
now consider m = -11 so m+10 is -1 which is <0. So no.
Hence insufficient!

Statement 2 - On the number line, m -10 is closer to 0 than to m.

Consider m= 11 so m-10 is 1 which is >0. So yes
now We can't consider m as '-ve' to meet the condition " m -10 is closer to 0 than to m" . And thus m+10 will always be>0
Hence Sufficient!

In my opinion, answer is Option B

The distance between m and (m + 10) is always 10 units
So,
The distance between (m + 10) and 0 is always less than 10 which is possible if and only if m is less than -5
Similarly,
The distance between (m - 10) and 0 is also less than 10 which is possible if and only if m is greater than 5
So,
m + 10 is not always positive

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