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Manager  Joined: 20 Mar 2008
Posts: 125
Location: USA

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Is integer $$Z$$ odd?

1. $$\frac{Z}{3}$$ is odd
2. $$3Z$$ is odd

Spoiler: :: OA
D

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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Joined: 30 Apr 2008
Posts: 1696
Location: Oklahoma City
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Re: m04 Q23  [#permalink]

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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.

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Math Expert V
Joined: 02 Sep 2009
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Re: m04 Q23  [#permalink]

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3
vishy007 wrote:
Is integer $$Z$$ odd?

1. $$\frac{Z}{3}$$ is odd
2. $$3Z$$ is odd

Spoiler: :: OA
D

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.

Is integer $$z$$ odd?

(1) $$\frac{z}{3}$$ is odd --> $$\frac{z}{3}=odd$$ --> $$z=3*odd=odd$$. Sufficient.

(2) $$3z$$ is odd --> $$3z=odd$$ --> in order the product of two integers 3 and $$z$$ to be odd both must be odd. So, $$z=odd$$. Sufficient.

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Manager  Joined: 20 Jun 2008
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Re: m04 Q23  [#permalink]

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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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(i) z/3=odd
z=oddx3
z=oddXodd
always odd-sufficient

(ii) 3z=odd
if z is odd then 3z is odd, if z is even then 3z is even - sufficient

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Re: m04 Q23  [#permalink]

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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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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

Spoiler: :: OA
D

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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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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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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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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Intern  Joined: 29 Sep 2013
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Re: m04 Q23  [#permalink]

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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.
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Re: m04 Q23  [#permalink]

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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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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 Re: m04 Q23   [#permalink] 07 Nov 2013, 06:53
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