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I'm not sure why you're saying "Why can't statement 2 be a fraction?" when the question stem says "integer Z".
if \(\frac{Z}{3}\) is odd, then this means the result is an integer because decimials are neither even nor odd. If we take values for Z that when divided by 3 give us integers, we can use (3, 6, 9, 12, 15, 18, 21...}
The resulting value when each is divided by 3 is {1, 2, 3, 4, 5, 6, 7...}. Lets look at which values for Z give us the odd value...that would be 3, 9, 15, 21..etc. These are also odd. So Z is odd from statement 1.
With statement 2, we have to remember number properties. Odd * Odd = Odd [always!]. So if 3*Z is odd, Z must be odd. Just as simple as that.
vishy007 wrote:
Is integer \(Z\) odd?
1. \(\frac{Z}{3}\) is odd 2. \(3Z\) is odd
Here OA is D with explanation S2 also implies that \(Z\) is odd.
Why can't S2 be a fraction? For example 5/3.
I think answer to this question needs to be changed.
_________________
------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.
The email that comes as GMAT question of the day, says -- 2. 49 is odd. This seemed odd, but looking at the actuals question on this webpage makes it clear about answer being D.
Went for A when I received it as question of the day since 2. 49 is odd seemed quite irrelevant to solve the question. But when I saw the actual question I knew it had to be D
Here we go: z/3 is odd, hence z is odd, it could be 3 or any odd number multiplied by 3. - keep A 3*z - is odd, it could be look above, hence the answer is (D) each answer choices is sufficient. Did not delve deep since it is data sufficiency quesiton Correct me, if I went awry.
Here are a few equations that one needs to absolutely remember. One would be surprised at the number of questions in which these concepts can be applied.
[*]ODD x ODD = ODD The only way to get an odd integer as a result when 2 integers are multiplied is when BOTH the integers are ODD.
As a consequence of the above rule, the division rule also applies [*]ODD/ODD = ODD
ODD x EVEN = EVEN ODD + ODD = EVEN ODD - ODD = EVEN ODD + EVEN = ODD ODD - EVEN = ODD
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Z cannot be a fraction. when GMAT question says 3Z is odd. It is a true statement. For 3Z (or Z/3) to be odd, 3Z (or Z/3) should be an integer. For 3Z (or Z/3) to be an integer, Z should be an integer. From my point of view answer to this question is B. For Z/3 to be odd Z should be a multiple of 3 (like 3,6, 9, 12....) if Z is 3,9,15... result will be odd. otherwise, it is even. So, this statement is not sufficient to answer if Z is odd or not. Correct me if I am wrong.
Z cannot be a fraction. when GMAT question says 3Z is odd. It is a true statement. For 3Z (or Z/3) to be odd, 3Z (or Z/3) should be an integer. For 3Z (or Z/3) to be an integer, Z should be an integer. From my point of view answer to this question is B. For Z/3 to be odd Z should be a multiple of 3 (like 3,6, 9, 12....) if Z is 3,9,15... result will be odd. otherwise, it is even. So, this statement is not sufficient to answer if Z is odd or not. Correct me if I am wrong.
z cannot be a fraction because the stem says that z IS an integer: "is integer z odd?".
Next, if we were not told that z is an integer, then the answer would be A:
(1) \(\frac{z}{3}\) is odd --> \(\frac{z}{3}=odd\) --> \(z=3*odd=odd\). Sufficient.
(2) \(3z\) is odd --> \(3z=odd\). Now, if z IS an integer, then it must be odd but if z is say 1/3 (in this case 3z=3*1/3=1=odd), then z is not an odd integer. Not sufficient.
Z cannot be a fraction. when GMAT question says 3Z is odd. It is a true statement. For 3Z (or Z/3) to be odd, 3Z (or Z/3) should be an integer. For 3Z (or Z/3) to be an integer, Z should be an integer. From my point of view answer to this question is B. For Z/3 to be odd Z should be a multiple of 3 (like 3,6, 9, 12....) if Z is 3,9,15... result will be odd. otherwise, it is even. So, this statement is not sufficient to answer if Z is odd or not. Correct me if I am wrong.
z cannot be an integer because the stem says that z IS an integer: "is integer z odd?".
Next, if we were not told that z is an integer, then the answer would be B:
(1) \(\frac{z}{3}\) is odd --> \(\frac{z}{3}=odd\) --> \(z=3*odd=odd\). Sufficient.
(2) \(3z\) is odd --> \(3z=odd\). Now, if z IS an integer, then it must be odd but if z is say 1/3 (in this case 3z=3*1/3=1=odd), then z is not an odd integer. Not sufficient.
Hope it's clear.
"Is integer Z odd?" means Z is integer (means not a fraction). Even/Odd applies to only integers. What was is thinking about Z/3. When Z/3 is odd Z should be odd multiple of 3. So, Z is Odd. Sorry for that. Answer is D. Both (I) & (II) alone are sufficient