Is the integer x even?
(1) x2 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)?
Integer
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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
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Hello Brent,
I understand all this.
I just wanted to know about (1).
Can't I assume that x can be square root of 2?
square of (2)^1/2 is 2.
Then, x does not have to be even integer.
Do I need to assume that x is an integer?
I understand all this.
I just wanted to know about (1).
Can't I assume that x can be square root of 2?
square of (2)^1/2 is 2.
Then, x does not have to be even integer.
Do I need to assume that x is an integer?
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The question tells us that x is an integer.sparkles3144 wrote: Can't I assume that x can be square root of 2?
The square root of 2 is approximately 1.4
Since 1.4 is not an integer, x cannot equal sqrt(2).
It's not an assumption. You are explicitly told that x is an integer.sparkles3144 wrote: Do I need to assume that x is an integer?
Cheers,
Brent
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Consider this analogous question:sparkles3144 wrote:Hello Brent,
I understand all this.
I just wanted to know about (1).
Can't I assume that x can be square root of 2?
square of (2)^1/2 is 2.
Then, x does not have to be even integer.
Do I need to assume that x is an integer?
X is a female tennis player. Who is X?
(1) X won the 2013 Wimbleton Singles title
(2) blah blah blah
Aside: There are two singles titles: one for the winning male and one for the winning female.
In 2013, Andy Murray won the men's title, and Marion Bartoli won the women's title.
So, is statement 1 sufficient?
Well, we cannot say that person X is either Andy Murray or Marion Bartoli, because Andy Murray is not a woman.
So, statement 1 is SUFFICIENT.
Cheers,
Brent
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Stmt 1: x^2 is even integer (Sufficient)
a) x is an integer,
b) square of odd integer is odd
c) square of even integer is even
all three above being true, based on stmt 1, we can conclude that x is even
Stmt 2: x/4 is an odd integer (Sufficient)
x/4 is an integer 2(x/4) and 4(x/4) i.e. x will always be even integers
So answer is D
Regards,
-----------
Trying for 750+
a) x is an integer,
b) square of odd integer is odd
c) square of even integer is even
all three above being true, based on stmt 1, we can conclude that x is even
Stmt 2: x/4 is an odd integer (Sufficient)
x/4 is an integer 2(x/4) and 4(x/4) i.e. x will always be even integers
So answer is D
Regards,
-----------
Trying for 750+