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# Is XYZ an odd number? Where X, Y, Z are positive integers

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Manager
Joined: 11 Feb 2008
Posts: 90
Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 11:17
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Question Stats:

50% (01:36) correct 50% (01:12) wrong based on 4 sessions

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If x,y,z are positive integers and x>y>z, is the product x*y*z odd?

1) p-z =t , where p is a prime number and t is odd
2) x+1 = Prime
[Reveal] Spoiler: OA

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Amar
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Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 12:41
B ?
With the second you can know that x must be even
so any other two numbers x an even number = even number
With the first one you have two option I think: if the primer number is 2 or any other

What is the OA?
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 12:58
IMO E,

2nd statement just give information about X, we need to know primarily the Z.
thus not sufficient.

now in statement 1
Any prime number - Z = Positive Odd number

as prime number - any number can be equal to odd number only when:

case 1-- prime number is 2...then 2-z = +ve odd number only when z=1
case 2-- prime number other than 2.....say 7 -z = odd then z must be even....
thus this is also not sufficient.

even if you combine no success..thus E
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Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 15:31
Hi gurpreetsingh, can you please explain more why 2) is INSUF

Quote:
Is XYZ an odd number? Where X, Y, Z are positive integers
Such that XYZ is not divisible by 4 and X>Y>Z

1) Any prime number - Z = Positive Odd number
2) X +1 = Prime

Since X is the biggest numbers, x can be 2, in this case 2>1>0 and 2x1x0 = 0 = even
or if x is other number for example 10
10+1 = 11 prime number
xyz = 10yz = even*number = even

but x cannot be 1
because if x= 1 y must be 0 and z = -1 since x>y>z and all must be positive integers
so I think that xyz should be even

any ideas? something wrong in my way of thinking? thanks!
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2783
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 15:43
i took xyz as 3 digit number, not x*y*z
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Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 15:47
Ok. I can see your point now.
We are dealing with two different problems.
thanks!!
Manager
Joined: 29 Oct 2009
Posts: 200
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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08 Apr 2010, 20:16
I am considering XYZ as X*Y*Z.

From the question stem, X,Y,Z are positive integers and X>Y>Z.
Inference: XYZ is not divisible by 4 => XYZ do not have two even numbers, either it should be 1 even and two odd numbers or three odd numbers.
Statement 1: Any prime - Z = positive odd number, So it shows Z is an even number. ( we can exclude 2 as a prime number in this situation because,the statements says it is any prime, all other primes are odd except 2)

From inference,
Because Z is even, the only other possibility for XYZ is to have two odd numbers X, Y.
odd*odd*even = even
Sufficient

Statement 2: X +1 = Prime
Because X>Y>Z and all are +ve integers, X should be greater than 1.
X should be an even number to make X+1 as prime number (odd).

From inference, because X is even the only other possibility for XYZ is to have two odd numbers Y,Z.
even*odd*odd = even
Sufficient

What is the OA?
Manager
Joined: 26 Feb 2010
Posts: 79
Location: Argentina
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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09 Apr 2010, 01:23
Hi mads I didn't understood why you exclude 2 from statement 1.
Can you please provide more details.
Thanks.
Intern
Joined: 08 Apr 2010
Posts: 1
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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09 Apr 2010, 06:50
Hi,

I am also considering XYZ as X*Y*Z.

From the question stem:
1) X,Y,Z are positive integers so 1,2,3 .... 1000000
2) X>Y>Z so X>Y>Z>0
3) XYZ is not divisible by 4, so XYZ is not a multiple of 4 or XYZ do not have two even numbers (two 2)

The real question is whether XYZ contain a 2 or is even ?

Statement 2:
2) X + 1 = Prime
Prime: 2,3,5,7,11,...
X could be 1,2,6,10 but as we know that X>Y>Z>0 then X can not be equal to 1, then X is even
Sufficient

1) Any prime number - Z = Positive Odd number
Prime Odd number: 3,5,7,11,...
Prime number: 2,3,5,7,11,...

Z is positive from question stem.
If prime number = 2 -> 2-Z = positive odd number then Z = 1
If prime number = 3,5,7,11 -> 3 - Z = positive odd number then Z = 2 or a multiple of 2
Insufficient

Manager
Joined: 29 Oct 2009
Posts: 200
Concentration: General Management, Sustainability
WE: Consulting (Computer Software)
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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09 Apr 2010, 07:17
Sorry guys,
I think I was wrong in exclding 2 for statement 1.
If we consider 2 also then for the first statement will give us two answers and so it is Insufficient.

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185
Re: Is XYZ an odd number? Where X, Y, Z are positive integers [#permalink]

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21 Nov 2016, 03:22
Hi Everyone.
I just Formatted the Question to make it slightly more pleasing to the Eye

Heres my solution
here we are given that x,y,z are all >0 and integers with x>y>z
We need to check if xyz is odd or not

Statement 1
Here using test cases
Let z=1
x=10
y=9
hence xyz is even
let z=1
x=9
y=7
hence xyz sill be odd
Clearly not sufficient

Statement 2
Here the least value of x is 3 as x>y>z and all are positive integers
hence x+1=> prime number >4
Since all the prime number greater than 4 are odd
hence x+1=> odd
so x=> odd-1=> even
Hence xyz will always be even

hence B
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Re: Is XYZ an odd number? Where X, Y, Z are positive integers   [#permalink] 21 Nov 2016, 03:22
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