Statement (1): x > 10
This statement tells us that x is greater than 10. However, it does not provide any specific information about x's relationship with 30. Therefore, it is not sufficient to answer the question.
Statement (2): x > 25
This statement tells us that x is greater than 25. Similarly to statement (1), it does not provide any specific information about x's relationship with 30. Therefore, it is also not sufficient to answer the question.
When we consider each statement alone:
Statement (1) alone does not provide enough information to determine the relationship between |x - 10| and |x - 30|.
Statement (2) alone does not provide enough information to determine the relationship between |x - 10| and |x - 30|.
When we consider both statements together:
By combining the two statements, we have x > 10 and x > 25. Since x has to be greater than both 10 and 25, we can conclude that x > 25.
Now, let's compare |x - 10| and |x - 30|:
When x > 25, we can simplify |x - 10| and |x - 30| as follows:
|x - 10| = x - 10 (since x - 10 is positive when x > 10)
|x - 30| = x - 30 (since x - 30 is positive when x > 30)
Now we can rewrite the original inequality:
x - 10 > x - 30
By subtracting x from both sides of the inequality, we get:
-10 > -30
This statement is true. Therefore, |x - 10| is greater than |x - 30|.
Hence, when considered together, statement (2) alone is sufficient to answer the question asked. The answer is B: Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.