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Is integer \(Z\) odd? 1. \(\frac{Z}{3}\) is odd 2. \(3Z\) is odd Source: GMAT Club Tests  hardest GMAT questions 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.



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Re: m04 Q23 [#permalink]
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14 Sep 2008, 06:48
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.
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Re: m04 Q23 [#permalink]
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18 Oct 2012, 05:18



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Re: m04 Q23 [#permalink]
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18 Oct 2012, 05:23
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.



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Re: m04 Q23 [#permalink]
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18 Oct 2012, 05:30
(i) z/3=odd z=oddx3 z=oddXodd always oddsufficient (ii) 3z=odd if z is odd then 3z is odd, if z is even then 3z is even  sufficient Answer :D
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Re: m04 Q23 [#permalink]
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18 Oct 2012, 07:43
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



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Re: m04 Q23 [#permalink]
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18 Oct 2012, 11:42
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. vishy007 wrote: Is integer \(Z\) odd? 1. \(\frac{Z}{3}\) is odd 2. \(3Z\) is odd Source: GMAT Club Tests  hardest GMAT questions 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.
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Re: m04 Q23 [#permalink]
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19 Oct 2012, 12:50
I concur. Both the options 1 & 2 are based on the rule odd * odd = odd. Kind of easy to crack.



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Re: m04 Q23 [#permalink]
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17 Oct 2013, 10:47
D.
Apply the following rules when evaluating this question.
Even integer x any integer (Even OR odd) = Even integer (example: 2 x 2 = 4, 2 x 3 = 6) Odd integer x Odd integer = Odd integer. (example: 3 x 3 = 9)
On to the question:
Given: You can't rephrase the question, just note that Z is an integer  and we're answering a "Yes/No" question type.
Statement 1: z/3 = some odd number. So z = 3xodd number (which is odd x odd). Sufficient. ("yes", z is odd)
Statement 2: 3z = some odd number. So, z must be odd. If z were even, then 3z would be even (refer to rule 1 above). Sufficient. ("yes", z is odd)
Both statements are sufficient, so D.



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Re: m04 Q23 [#permalink]
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19 Oct 2013, 07:08
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 = ODDThe 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 = ODDODD x EVEN = EVEN ODD + ODD = EVEN ODD  ODD = EVEN ODD + EVEN = ODD ODD  EVEN = ODD
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Re: m04 Q23 [#permalink]
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07 Nov 2013, 05:13
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.



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Re: m04 Q23 [#permalink]
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07 Nov 2013, 05:42
winwin02 wrote: 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. Hope it's clear.
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Re: m04 Q23 [#permalink]
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07 Nov 2013, 06:53
Bunuel wrote: winwin02 wrote: 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











