Is x divisible by y?1) (x – 1) is divisible by y2) x > ya)Exa...
1. Statement (1): (x - 1) is divisible by y
This means there exists an integer k such that:
x - 1 = ky (for some integer k)
Rearranging this, we have:
x = ky + 1
From this equation, we can see that x is equal to ky + 1. Therefore, x cannot be divisible by y unless k is such that 1 is also divisible by y, which can only happen if y = 1. Thus, this statement alone is not sufficient to determine if x is divisible by y.
2. Statement (2): x > y
This statement only tells us that x is greater than y but provides no information about the divisibility of x by 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 = ky + 1.
- From statement (2), we know x > y.
We can substitute ky + 1 into the inequality from statement (2):
ky + 1 > y
This simplifies to:
ky > y - 1
or
k > (y - 1)/(y)
However, this still doesn't provide any information about the divisibility of x by y.