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Intern
Joined: 15 Oct 2009
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If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)
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06 Sep 2010, 06:39
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If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) z is even OA: C
Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?
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Manager
Joined: 09 Jun 2010
Posts: 101

Re: Odd or not
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06 Sep 2010, 06:47
The answer should be E
Q: is XY(Z+1) odd??
(1) y is odd => value of XY(Z+1) depends on Y & (Z+1). Y may be even or (Z+1) may be even. Insufficient (2) z is even => value of XY(Z+1) depends on Y & X either of them can be even. Insufficient
Combine: We don't know whether X is odd or even. If X = odd then product is odd & if X = even then product is even. Insufficient
Answer  E



Math Expert
Joined: 02 Sep 2009
Posts: 52296

Re: Odd or not
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06 Sep 2010, 06:49
anticipation wrote: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) z is even OA: C
Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ? Hi, and welcome to Gmat Club. Below is a solution for your problem. The product of two integers (in our case \(y\) and \(z+1\)) to be odd both of them must be odd. Question: is \(y*(z + 1)=odd\) > so basically the question asks is \(y=odd\) and \(z+1=odd\), or \(z=even\)? (1) \(y\) is odd, we don't know whether \(z=even\). Not sufficient. (2) \(z\) is even, we don't know whether \(y=odd\). Not sufficient. (1)+(2) \(y=odd\) and \(z=even\), so both necessary conditions are satisfied. Sufficient. Answer: C. As for your question: first of all, \(y\) can not be zero as \(y=odd\) and zero is an even integer, next if \(z=0=even\), then \(z+1=0+1=even+odd=odd\) and as from (1) \(y=odd\) we still have the product of two odd numbers which is odd. For more on this issues please check Number Theory chapter of Math Book (link in my signature). Hope it helps.
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Manager
Joined: 14 Jun 2010
Posts: 202

Re: Odd or not
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06 Sep 2010, 20:05
The answer should be C... the Q asks if y(z+1) is odd , in other words it asks if Y is odd and Z is even ( Z+1) is odd ONLY when Z is even. Thus we have C, points 1 and 2 give the info required!



Intern
Joined: 06 Sep 2010
Posts: 10

Re: Odd or not
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06 Sep 2010, 21:08
Answer  C
For y*(z + 1) to be Odd..the product of y and (z+1) has to be odd..It could happen in only one way when both the terms are odd(like 3*3=9). 1.) When y is odd  This will only give us one part of the answer since nature of z is unknown.Hence,INSUFFICIENT 2.) When z is even  This is also INSUFFICIENT coz nature of y is unknown.
On combining both cases,we can conclude that that when z is added to 1,it will become an odd number and when multiplied by an odd number y,it will always give an odd value.
Hence,answer should be C



Manager
Joined: 04 Aug 2010
Posts: 98

Re: Odd or not
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07 Sep 2010, 09:33
If y and z are integers, is y*(z + 1) odd?
(1) y is odd (2) z is even
Basically there are two conditions where you can answer if a product is odd: either (a) both terms are odd  THEN product would be odd or (b) one of the terms are even  THEN product would be even
Evaluate (1) y is odd  According to condition (a), we don't know if (z + 1) is odd too.  INSUFFICIENT
Evaluate (2) z is even  Which means term (z + 1) is odd  According to condition (a), we don't know if y is odd too.  INSUFFICIENT
Evaluate (1) + (2)  (z + 1) is odd AND y is odd  SUFFICIENT to conclude that the product of the 2 terms is odd
Ans C



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Joined: 15 Oct 2009
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Re: Odd or not
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07 Sep 2010, 21:07
anticipation wrote: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) z is even OA: C
Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ? Thanks everyone for the solution. The key here is to know that zero is even. Pays to know the parity of zero.



Manager
Joined: 17 Nov 2009
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Re: Odd or not
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08 Sep 2010, 09:15
anticipation wrote: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) z is even OA: C
Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ? Rephrase as: Is Y odd and Z even? Logic: O*O=Odd. since z+1 should be odd Z should be even. st 1: answers only 1 part of what is needed the Y part st 2: answers only 1 part of what is needed the Z part Together I have all I need on Y and Z



Manager
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Re: Odd or not
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08 Sep 2010, 09:16
Could this be a 700 level? Does not seem like the regular 700 questions



Manager
Joined: 19 Sep 2010
Posts: 139

Re: Odd or not
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15 Oct 2010, 09:01
No..even i don't rate it as a 700 level question . I gave few MGMAT tests . The 700 level there was pretty tough , more calculation oriented and time consuming.



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Re: Odd or not
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15 Oct 2010, 09:19
agnok wrote: Could this be a 700 level? Does not seem like the regular 700 questions no way. It is max of 600 level. To solve just plug in even numbers including 0 {0;2} and few odd {1;1;3} you will see that in any of cases the result will be odd. No chances for us after Bunuel's excellent explanations.
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)
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29 Nov 2014, 22:20
With DS always spend 10 second stop and write down what is being asked. Here we are asked y*(z + 1) odd? Only way we can say this is by know whether y and z are odd/even. 1. NS  we don't know about z. 2. NS  we don't know about y. 1&2: S  have all the info to answer. Answer: C anticipation wrote: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) z is even OA: C
Why can't i plugin either of them as zero ? In that case, OA should be E. Any inputs to correct my thought process would be great ?
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2)
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30 Sep 2018, 08:57
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Re: If y and z are integers, is y*(z + 1) odd? (1) y is odd (2) &nbs
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