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Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd.

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Juaz
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Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   01 May 2007, 00:09
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Is Z an odd integer?

(1) Z/3 is odd.
(2) 3Z is odd.

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kevincan
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   01 May 2007, 02:02
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Juaz wrote:
Is Z an odd integer?

(1) Z/3 is odd.
(2) 3Z is odd.


(1) z/3 is an odd integer, so we can write z/3=k for some odd integer k
Thus z=3k, which is an odd integer. SUFF

(2) 3z is an odd integer m. Thus z=m/3. If m is a multiple of 3, z is an odd integer. However, if m is not a multiple of 3, z will not be an integer.

NOT SUFF

A
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   Updated on: 01 May 2007, 02:05
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(A) for me :)

From 1
z/3 = 2*k+1 where k is an integer
<=> z = 3*(2*k + 1) = ODD*ODD = ODD

SUFF.

From 2
3*z = 2*k+1
<=> z= (2*k+1)/3

So,
o If 2*k+1 = 3*n (n an ODD integer), then:
z = 3*n / 3 and z is an ODD

o If 2*k+1 is not a multiple of 3, then:
z is even not an integer.

INSUFF.

Originally posted by Fig on 01 May 2007, 02:02.
Last edited by Fig on 01 May 2007, 02:05, edited 1 time in total.
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   Updated on: 01 May 2007, 11:27
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No, odds and evens are only for integers. While the question asks about whether Z is odd, statements 1 and 2 gives clue some fractions that contain z.

Statemnet 1 confirms that Z is indeed an integer, while statement 2 does not neccessarily indicate that Z is an integer, regardless whether odd or even.

My updated Answer: A

Originally posted by Mishari on 01 May 2007, 06:30.
Last edited by Mishari on 01 May 2007, 11:27, edited 1 time in total.
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   01 May 2007, 08:12
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Juaz wrote:
Is Z an odd integer?

(1) Z/3 is odd.
(2) 3Z is odd.


Crazy...it's like playing word games. Is Z odd AND integer?

(1) Z/3=Odd -> Z=3*Odd -> Z=Odd*Odd, so Z must be Odd. SUFF.

(2) 3Z=Odd -> Z=Odd/3. So Z could be 7/3 or 15/3, one is integer another one isn't. Or you can look at it as 3*(5)=Odd (yes, Z is an odd integer); but 3*(1/3) = Odd (no, Z is neither odd nor an integer). -___-

So the answer is A I guess.
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   26 Apr 2019, 12:20
The Alternative approach to this question is to try to find specific numbers that would eliminate certain answers because they lead to more than one option.
Statement (1) works for 3,9,15,21... all odd. Since z/3 equals odd, z = 3 times odd, so it must be odd. Statement (1) is sufficient, so (B), (C) and (E) are eliminated.
Statement (2) works for 1,3,5,7... but also for 1/3, so there's more than one option. Answer choice (D) is eliminated. The correct answer is (A).

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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   08 Jul 2020, 00:15
Is z an odd integer?

a) z/3 is odd integer
z=3*odd = odd*odd = odd {sufficient, cancel (BCE)}

b)3z= odd integer
z= odd integer /3
it may or may not be integer. Not sufficient

Answer A
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink] New post   05 Dec 2022, 11:37
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd. [#permalink]
05 Dec 2022, 11:37
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