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

Question

If x, y, z are integers, is xyz a multiple of 3?
1) x+y+z is a multiple of 3
2) x, y, z are consecutive

*An answer will be posted in two days.

Kurtosis · Answer

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

Answer: B

Lastlap2016 · Answer

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

chetan2u · Answer

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?

etienneg · Answer

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)

MathRevolution · Answer

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.

stonecold · Answer

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

Akuthiala · Answer

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

stonecold · Answer

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 Stone Cold

anumeharai21090 · Answer

Answer should be D

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

brs1cob · Answer

if x, y , z were three distinct positive integers, what would have been the answer ?

in this case, option would have been D.

Logo · Answer

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??

chetan2u · Answer

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.

bumpbot · Answer

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

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