Bunuel wrote:
If x and y are different prime numbers, each greater than 2, which of the following must be true?
I. x+y is an even integer
II. xy is an odd integer
III. (x/y) is not an integer
A. II only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
Kudos for correct solution.
\(x\) and \(y\) are different prime numbers, each greater than 2.
As 2 is the only even prime number, both \(x\) and \(y\) must be odd.
So, we have three properties that will be useful in solving this question:
1. \(x\) and \(y\) are prime numbers
2. \(x\) and \(y\) are odd numbers
3. \(x\) and \(y\) are
different numbers
Now, let us consider each statement.
Statement I: \(x + y\) is an even integer
We know that both \(x\) and \(y\) are odd. We also know that odd + odd = even
hence, \(x + y\) is an even integer.
So, statement I must be true.
Statement II: \(xy\) is an odd integer
We know that both \(x\) and \(y\) are odd. We also know that odd x odd = odd
hence, \(xy\) is an odd integer.
So, statement II must also be true.
Statement III: \(x/y\) is not an integer
This could have been tricky. But we know that \(x\) and \(y\) are different numbers. So, \(x/y\) cannot be 1. We also know that \(x\) and \(y\) are prime numbers. So, \(x\) is definitely not divisible by \(y\).
Hence, \(x/y\) cannot be an integer.
So, statement III must also be true.
Therefore, the correct answer is
E.
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83% (00:33) correct 
