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Director
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Is Z an odd integer? (1) Z/3 is odd. (2) 3Z is odd [#permalink]
 01 May 2007, 00:09
Is Z an odd integer?
(1) Z/3 is odd.
(2) 3Z is odd.
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Senior Manager
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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!
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Manager
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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.
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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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GMAT Instructor
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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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SVP
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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, 02:05, edited 1 time in total.
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GMAT Club Legend
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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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SVP
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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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Intern
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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
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Director
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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
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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, 11:27, edited 1 time in total.
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Senior Manager
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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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Intern
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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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Manager
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[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
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Director
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OA is A.
Thanks guys!!
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