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# If x, y, and z are positive integers, where x > y > z, is x*y*z an odd

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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
2
Kudos
IMO, B

1) Not suf
- Case p = 2, z needs to be odd (e.g., 1)
- Case p=3, z needs to be even (e.g., 2)

2) if x+1=prime, the only prime number that by adding another prime results in another prime is 2. So x = 2. Having this, whatever numbers are y and z, x*y*z will always be even due to having x= 2. Hence, Sufficient

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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
yashikaaggarwal I have one question.
Statement 2 states that x+1 is a prime number, based on your approach you concluded that x has to be even which I agree with but the question I have is the smallest prime number is the digit 2, so if the value of x is 1 then 1+1 is also a prime number then shouldn't statement B also be insufficient ?
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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
kntombat wrote:
yashikaaggarwal I have one question.
Statement 2 states that x+1 is a prime number, based on your approach you concluded that x has to be even which I agree with but the question I have is the smallest prime number is the digit 2, so if the value of x is 1 then 1+1 is also a prime number then shouldn't statement B also be insufficient ?

See, X can't be 1 and 2
why?
Simply because X, Y, and Z are positive integers.
the smallest positive integer is 1
and Z is the smallest among X, Y, and Z.
so taking the least value of X, Y, and Z
Z is 1, Y is 2, and X is 3
Now we know, X+1 is a prime.
and the least value of X = 3+1 = 4 is not a prime.
so we know, every prime no. - 1 is even no. (except 1, which can't be the value of X because of given constraint)
so X will be an even no.
and any multiple of even is even.
so X*Y*Z is even.
hope its clear.
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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
Yes now it's clear. Thank you yashikaaggarwal.
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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
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Re: If x, y, and z are positive integers, where x > y > z, is x*y*z an odd [#permalink]
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