Is x divisible by y?1) x is a multiple of (y + 1)2) y > 1a)Exactly ...
To determine whether x is divisible by y, let's analyze the statements provided:
1. Statement (1): x is a multiple of (y + 1)
This means there exists an integer k such that:
x = k(y + 1) (for some integer k)
To see if x is divisible by y, we can rewrite this as:
x = ky + k
For x to be divisible by y, the term k (which is equal to &frac{x}{y + 1}) must also ensure that when you take ky + k, k alone is divisible by y. However, this is not guaranteed. Therefore, this statement alone is not sufficient to determine if x is divisible by y.
2. Statement (2): y > 1
This statement tells us that y is greater than 1, but it does not provide any information about the relationship between x and y. Therefore, this statement alone is also not sufficient to determine if x is divisible by y.
Combining the Statements:
Now, let's analyze both statements together:
- From statement (1), we know x = k(y + 1).
- From statement (2), we know y > 1.
Even when we combine the two statements, we still only have information about x being a multiple of (y + 1) while y is simply greater than 1. This still does not help in determining if x is divisible by y because the fact that x is a multiple of (y + 1) does not imply anything about divisibility by y.
Conclusion:
Neither statement alone is sufficient to determine if x is divisible by y, and combining the two statements does not lead to a definitive answer. Thus, the answer is:
The statements together are not sufficient to determine if x is divisible by y.