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

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Director
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Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd [#permalink]

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01 May 2007, 00:09
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is Z an odd integer?

(1) Z/3 is odd.
(2) 3Z is odd.
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01 May 2007, 00:41
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.

Javed.

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01 May 2007, 01:18
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

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

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

Last edited by Fig on 01 May 2007, 02:05, edited 1 time in total.
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01 May 2007, 02:07
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
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01 May 2007, 02:10
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
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01 May 2007, 02:23
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
Director
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01 May 2007, 03:00
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
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01 May 2007, 06:30
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.

Last edited by Mishari on 01 May 2007, 11:27, edited 1 time in total.
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01 May 2007, 07:09
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!
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01 May 2007, 08:12
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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01 May 2007, 08:34
[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
Director
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01 May 2007, 10:02
OA is A.
Thanks guys!!
01 May 2007, 10:02
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