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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If x, y, z are positive integers, is xyz divisible by 6? 1) x, y, z ar  [#permalink]

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If x, y, z are positive integers, is xyz divisible by 6?

1) x, y, z are consecutive.
2) x+y+z is a multiple of 3.

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If x, y, z are positive integers, is xyz divisible by 6? 1) x, y, z ar  [#permalink]

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MathRevolution wrote:
If x, y, z are positive integers, is xyz divisible by 6?

1) x, y, z are consecutive.
2) x+y+z is a multiple of 3.

1) $$x, y, z$$ are consecutive.

Rule : Product of $$3$$ consecutive numbers are always divisible by $$6$$.

Lets check this rule.

Let $$x, y , z = 1,2,3$$

$$xyz = 1*2*3 = 6$$.

$$6$$ is divisible by $$6$$. Therefore $$xyz$$ is divisible by $$6$$.

Hence I is Sufficient.

2) $$x+y+z$$ is a multiple of $$3$$.

Multiples of $$3$$ are $$= 3,6,12,15,18$$ etc...

From above $$3, 15$$ are not divisible by $$6$$. Hence Not all multiples of $$3$$ are divisible by $$6$$.

Hence II is Not Sufficient.

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Re: If x, y, z are positive integers, is xyz divisible by 6? 1) x, y, z ar  [#permalink]

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1) x, y, z are consecutive
Since we are talking about positive integers,
lets assume the lowest set of consecutive positive integers(1,2 and 3) possible
The product of these numbers is divisible by 6.
Hence, the sum of all three positive consecutive numbers is always divisible by 6 (Sufficient)

2) x+y+z is a multiple of 3.
Consider x+y+z = 6( a multiple of 3) which is divisible by 6
Similarly x+y+z = 21(a multiple of 3) which is not divisible by 6. (Insufficient)(Option A)
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x, y, z are positive integers, is xyz divisible by 6? 1) x, y, z ar  [#permalink]

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==> The product of 3 consecutive integers is always a multiple of 6. For con 1), it is yes and sufficient, and for con 2), (x,y,z)=(1,2,3) yes but (x,y,z)=(2,2,2) no, hence it is not sufficient.

Therefore, the answer is A.
_________________ Re: If x, y, z are positive integers, is xyz divisible by 6? 1) x, y, z ar   [#permalink] 30 Jun 2017, 01:00
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