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sparkles3144
- Master | Next Rank: 500 Posts
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Yes, you can assume that x is an integer. It says so in the question ("...integer x ...")sparkles3144 wrote:Is the integer x even?
(1) x^2 is an even integer.
(2) x/4 is an odd integer.
For (1) can I safely assume that x has to be an integer?
Can't x be (2)^(1/2)?
Target question: Is the integer x even?
Statement 1: x^2 is an even integer.
If (x)(x) is even, then it must be the case that x is even
To demonstrate this, consider the following rules:
(odd)(odd) = odd
(odd)(even) = even
(even)(even) = even
So, if the product of two integers is even, then it must be the case that either both numbers are even or one is odd and one is even.
Since, x^2 requires us to multiply x by itself, we can rule out the possibility of one number being odd and the other number being even. This means that both numbers (x and x) are even.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x/4 is an odd integer.
We need only focus on the part that says, x/4 is an integer.
Let's say that x/4 = k (where k is an integer)
This means that x = 4k
In other words, x = (2)(2)k, which means x is a multiple of 2, which means x is definitely even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
