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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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If x,y,z are positive integers and x>y>z, is the product x*y*z odd? 1) pz =t , where p is a prime number and t is odd 2) x+1 = Prime
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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
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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 2z = +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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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!



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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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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. anaik100 can you please provide more info about the problem! thanks!!



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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
Answer is D.
What is the OA?



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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.



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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 > 2Z = 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
Answer B



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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.
Answer should be B.



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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=> odd1=> 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
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21 Nov 2016, 03:22






