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Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd [#permalink]
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30 Apr 2007, 23:09
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Is Z an odd integer?
(1) Z/3 is odd.
(2) 3Z is odd.



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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.
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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
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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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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



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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.
Last edited by Fig on 01 May 2007, 01:05, edited 1 time in total.



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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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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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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
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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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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
Last edited by Mishari on 01 May 2007, 10:27, edited 1 time in total.



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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!



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Re: Fractions [#permalink]
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01 May 2007, 07:12
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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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



Director
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OA is A.
Thanks guys!!



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