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If x, y, and z are integers, is xyz a multiple of 6?

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Bunuel
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If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   29 May 2023, 09:45
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A
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65% (01:16) correct 35% (01:08) wrong based on 20 sessions
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If x, y, and z are integers, is xyz a multiple of 6?

(1) x + y + z is a multiple of 6
(2) x, y, and z are consecutive integers
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B
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divyadna
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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   29 May 2023, 10:47
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Statement 1) x + y + z is a multiple of 6
Let x=0,y=1, and z=11

0+1+11=12 is a multiple of 6
xyz=0 and 0 is not a multiple of 6.

Let x= 3, y=4, z=5
x+y+z= 3+4+5=12
xyz =3*4*5= 60 is a multiple of 6.
Statement I alone is insufficient.

(2) x, y, and z are consecutive integers

0*1*2=0 and 0 is not a multiple of 6.
1*2*3=6 and 6 is a multiple of6.

Statement II alone is insufficient.

Combining both statements
x=1, y=2, z=3
1+2+3=6 and 1*2*3=6

OR
x=3,y=4,z=5
3+4+5=12
xyz= 3*4*5=60 is a multiple of 6.

We are getting a YES everytime.

C is the answer

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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   31 May 2023, 03:24
IMO - answer is B

Thats because (x-1)(x)(x+1) (considering all are integers) has to be divisible by 6. Even 0 is divisible by 6.

Correct Bunuel ?
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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   01 Jun 2023, 03:55
zero is a multiple of every number. So, answer is B
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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   04 Jun 2023, 08:10
Bunuel

I have a question:

Should the answer not be C?

If we allow B, we have to assume that the integers are positive - however this is not indicated in the stem.
For example, in B we can have:
-3,-2,-1

Which multiples to -6, which is not a multiple of 6.

Or you can have 1,2,3 multiples to 6, which is M6.
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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink] New post   04 Jun 2023, 09:00
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mysterymanrog wrote:
Bunuel

I have a question:

Should the answer not be C?

If we allow B, we have to assume that the integers are positive - however this is not indicated in the stem.
For example, in B we can have:
-3,-2,-1

Which multiples to -6, which is not a multiple of 6.

Or you can have 1,2,3 multiples to 6, which is M6.


-6 is a multiple of 6.

When we say "integer 'a' is a multiple of integer 'b'," it means 'a' can be written as 'x*b', where 'x' is some integer: -6 = 1*6.
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Re: If x, y, and z are integers, is xyz a multiple of 6? [#permalink]
04 Jun 2023, 09:00
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Bunuel
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