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# If x, y, z are integers, is xyz a multiple of 3?

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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
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Lastlap2016 wrote:
Vyshak wrote:
St1: x+y+z is a multiple of 3.
If x = 1, y = 1, z = 1 then xyz is not a multiple of 3.
If x = 3, y = 3, z = 3 then xyz is a multiple of 3
Not Sufficient

St2: x, y, z are consecutive --> Product of three consecutive integers will always be a multiple of 3.
Sufficient

i think answer should be D . coz XYZ appears to be a three digit number rather than product of three digits IMO.

Hi,
whenever xyz is written, it means product of x, y and z..
If xyz is 3-digit nnumber, it will be mentioned..

In that the case would be-
If x, y, z are integers and xyz is a 3-digit number, is xyz a multiple of 3?
OR If x, y, z are integers, is xyz, a 3-digit number, a multiple of 3?
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If x, y, z are integers, is xyz a multiple of 3? [#permalink]
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I was confused for a moment, I missed that 0 is a multiple of any number.
I chose (C) thinking we needed Stmnt 1 to tell us that X,Y,Z is positive (which it in fact does not).

Take-away for me is to differentiate between multiple (which can be 0, -3, -6 etc too) and positive multiple (3,6,9)
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
If we multiply the consecutive 3 integers, the outcome is always a multiple of 6. The condition 2) gives an answer that is always yes and the condition is sufficient. Hence, the correct answer is B. The condition is not sufficient because it gives 2 answers, 1+2+3 yes and 2+2+2 no.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
Let x,y,z => 1,1,1 and x,y,z => 3,3,3 => statement 1 is insuff
now using the rule => "THE PRODUCT OF N CONSECUTIVES IS ALWAYS DIVISIBLE BY N! " => xyz=> divisible by 6.
((((Hence using the factor foundation rule => its clearly divisible by 3)))

Smash that B
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
Not sure if this makes sense. The problem doesn't state the xyz are positive integers. So if x = -1, y = 0, z = 1 they would be considered consecutive but statement 2 would be insufficient. So the answer should be C
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
Akuthiala wrote:
Not sure if this makes sense. The problem doesn't state the xyz are positive integers. So if x = -1, y = 0, z = 1 they would be considered consecutive but statement 2 would be insufficient. So the answer should be C

You sure mate?
Here the product = -1*0*1=0
=> ZERO is divisible By every Integer hence xyz is divisble by 3 here too
Suff
The generalised rule => PRODUCT of n consecutive integers is always divisible by n! (which is n factorial)

I hope it helps with your query
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]

1) 1 + 1 +1 = 3 then 111 is also a multiple of 3 111 = 37 * 3
2 + 2 + 2 = 6 then 222 is a multiple of 3 222 = 74 * 3

2) since x y z are consecutive then cuz will be multiple of 3
7 8 9
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
if x, y , z were three distinct positive integers, what would have been the answer ?

in this case, option would have been D.
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
stonecold - I'm just a few years late on this but I have a burning query. I see that zero is divisible by 3 but wouldn't that make zero a factor of 3 and not a multiple of 3??
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
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LaurenGol wrote:
stonecold - I'm just a few years late on this but I have a burning query. I see that zero is divisible by 3 but wouldn't that make zero a factor of 3 and not a multiple of 3??

0=3*0, so 0 is a multiple of 3, same way as 6 is because 6=3*2.

OR

Does 3 come in 0s table ...No, so 3 is not a multiple of 0.
Does 0 come in 3s table if we include negative integers too... ...-6,-3,0,3,6..
Yes, 0 is a multiple of 3 and every number.
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
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Re: If x, y, z are integers, is xyz a multiple of 3? [#permalink]
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