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

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Senior Manager
Joined: 18 Jul 2006
Posts: 482
Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd  [#permalink]

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30 Apr 2007, 23:09
1
Is Z an odd integer?

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

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Senior Manager
Joined: 01 Jan 2007
Posts: 299
Re: Fractions  [#permalink]

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30 Apr 2007, 23:41
Juaz wrote:
Is Z an odd integer?

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

1-> z/3 is odd i.e z=3(n) and z/n=3(n)/3=n and that is equal to odd . And hence Z=odd. So sufficient.

2-> 3z is odd only when z is odd (odd * odd= odd) and hence sufficient.

So answere is D.

Javed.

Cheers!
Manager
Joined: 04 Oct 2006
Posts: 69
Re: Fractions  [#permalink]

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01 May 2007, 00:18
Juaz wrote:
Is Z an odd integer?

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

(1) Sufficient
If Z=9 then 9/3 is odd
If Z=6 then 6/3 is even

(2) Sufficient
If Z=2 then 3*2 is even
If Z=3 then 3*3 is odd

Answer D.
Director
Joined: 30 Nov 2006
Posts: 573
Location: Kuwait

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01 May 2007, 00:46
1
I think the answer is E

Even with statements 1 and 2 together, we can never know if Z is actually an integer.
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1251
Location: Madrid
Re: Fractions  [#permalink]

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01 May 2007, 01:02
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
SVP
Joined: 01 May 2006
Posts: 1775

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Updated on: 01 May 2007, 01:05
1
(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, 01:02.
Last edited by Fig on 01 May 2007, 01:05, edited 1 time in total.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 4804
Location: Singapore

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01 May 2007, 01:07
St1:
Testing some values... z is 9, z/3 is odd. z is 15, z/3 is odd... etc
Sufficient.

St2:
odd * z = odd

z must be odd. Sufficient.

Ans D
SVP
Joined: 01 May 2006
Posts: 1775

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01 May 2007, 01:10
ywilfred wrote:
St1:
Testing some values... z is 9, z/3 is odd. z is 15, z/3 is odd... etc
Sufficient.

St2:
odd * z = odd

z must be odd. Sufficient.

Ans D

In 2, try z=1/3 ... We have 3*z = ODD
Intern
Joined: 01 May 2007
Posts: 1
Re: Fractions  [#permalink]

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01 May 2007, 01:23
Juaz wrote:
Is Z an odd integer?

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

if u simply appy 5/3 u can figure out d is not the answer
the answer is E
Director
Joined: 12 Jun 2006
Posts: 516

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01 May 2007, 02:00
Going for A
Quote:
Even with statements 1 and 2 together, we can never know if Z is actually an integer.

is there such a thing as an odd or even fraction? And if so, are there odd/even fractions at the level of math we're dealing with. If not, A must be suff
Director
Joined: 30 Nov 2006
Posts: 573
Location: Kuwait

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Updated on: 01 May 2007, 10:27
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, 05:30.
Last edited by Mishari on 01 May 2007, 10:27, edited 1 time in total.
Senior Manager
Joined: 01 Jan 2007
Posts: 299
Re: Fractions  [#permalink]

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01 May 2007, 06:09
kevincan wrote:
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

Hi kevin,

Can you elaborate on why statement 2 is insufficient..?

Javed.

Cheers!
Intern
Joined: 05 Jun 2003
Posts: 47
Re: Fractions  [#permalink]

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01 May 2007, 07:12
1
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.
Manager
Joined: 11 Nov 2006
Posts: 135
Re: Fractions  [#permalink]

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01 May 2007, 07:34
[quote="Juaz"]Is Z an odd integer?

(1) Z/3 is odd.
(2) 3Z is odd.[/quote]

A

stmt 1)
z must be ODD and multiple of 3 (it's not possible to have fractions because the condition would not be satisfied)
--> Sufficient

stmt 2)
if z=5/3 then 3*z=3*5/3=5 the condition is satisfied but z is not an integer

if z=5 then 3*z=3*5=15 the condition is satisfied and z is an odd integer

---> Insufficient
Senior Manager
Joined: 18 Jul 2006
Posts: 482

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01 May 2007, 09:02
OA is A.
Thanks guys!!
Non-Human User
Joined: 09 Sep 2013
Posts: 9420
Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd  [#permalink]

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08 Jan 2018, 01:13
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Re: Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd &nbs [#permalink] 08 Jan 2018, 01:13
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