The correct answer is option (B):
Statement (2) alone is sufficient to answer the question
Let's analyze the question and the statements to determine if we can tell if (a/6 + b/5) is an integer.
The core idea here revolves around whether the fractional parts of a/6 and b/5 cancel out or combine in a way that results in an integer.
Statement 1: 'a' is divisible by 5 and 'b' is divisible by 6.
If 'a' is divisible by 5, we can write a = 5k, where k is an integer. Then a/6 = 5k/6. This is not necessarily an integer.
If 'b' is divisible by 6, we can write b = 6m, where m is an integer. Then b/5 = 6m/5. This is not necessarily an integer.
Now consider (a/6 + b/5) = (5k/6 + 6m/5). The denominators are different, and there's no guarantee the fractional parts will cancel. For example, if k=1 and m=1, the expression is (5/6 + 6/5) = (25 + 36)/30 = 61/30, which isn't an integer. Thus, statement 1 alone is insufficient.
Statement 2: 'a' is a multiple of 6 which is one-tenth the value of 'b'.
This statement gives us two key pieces of information.
1. 'a' is a multiple of 6. This means a = 6n, where n is an integer.
2. 'a' is one-tenth of 'b'. This means a = b/10, or b = 10a.
Now, we can substitute into the original expression:
a/6 + b/5 = (6n)/6 + (10a)/5 = n + 2a.
Since a = 6n, we can further substitute: n + 2(6n) = n + 12n = 13n.
Since n is an integer, 13n is always an integer. Therefore, (a/6 + b/5) is an integer. Thus, statement 2 alone is sufficient.
Final Answer: The final answer is Statement (2) alone is sufficient to answer the question.