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# If x, y and z are integers then is the product of x, y, and z divisibl

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Joined: 22 May 2017
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If x, y and z are integers then is the product of x, y, and z divisibl  [#permalink]

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Updated on: 21 Jan 2018, 23:14
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35% (medium)

Question Stats:

83% (01:13) correct 17% (02:56) wrong based on 9 sessions

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If x, y and z are integers then is the product of x, y, and z divisible by 6?

(1) x = y - 1 and z = y + 1

(2) x, y, and z are successive multiples of 2

Hello please check the answer and explain the significance?

Does the sequence -2,0,2 violate the statement 2???

Attachment:

Doubt.png [ 68.12 KiB | Viewed 431 times ]

Originally posted by akgulhane on 21 Jan 2018, 21:49.
Last edited by Bunuel on 21 Jan 2018, 23:14, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x, y and z are integers then is the product of x, y, and z divisibl  [#permalink]

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21 Jan 2018, 22:40
Hi

In general, when we talk about 'multiples of 2', we mean positive multiples only. So 3 successive multiples of 2 could be (2,4,6) or (4,6,8) or (1002,1004,1006) etc.

But still even if you look at -2,0,2 their product is 0 which is divisible by 6 (0 is divisible by all numbers except 0, resulting in 0 only)
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Re: If x, y and z are integers then is the product of x, y, and z divisibl  [#permalink]

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21 Jan 2018, 23:21
I have a query here.

as per statement 1, we can conclude that x, y and z are successive numbers. like 1,2,3 or 4,5,6 or -77-,78,-79 and so on. but as per statement 2 they are consecutive multiples of 2, which means they are 2,4,6 or -88,-86,-84.

Doesn't st1 and st2 contradicts each other and they are against the general rule of DS questions?

Need some expert reply
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If x, y and z are integers then is the product of x, y, and z divisibl  [#permalink]

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21 Jan 2018, 23:28
akgulhane wrote:
If x, y and z are integers then is the product of x, y, and z divisible by 6?

(1) x = y - 1 and z = y + 1

(2) x, y, and z are successive multiples of 2

Hello please check the answer and explain the significance?

Does the sequence -2,0,2 violate the statement 2???

Attachment:
Doubt.png

If x, y and z are integers then is the product of x, y, and z divisible by 6?

(1) x = y - 1 and z = y + 1. In this case xyz = (y - 1)y(y + 1) = the product of three consecutive integers, so at least one of them must be even and one of them must be a multiple of 3, so the product for sure will be a multiple of 6. Sufficient.

Or you can recall following property: The product of n consecutive integers is always divisible by n!. Thus, the product of three consecutive integers, must be divisible by 3! = 6.

(2) x, y, and z are successive multiples of 2 --> xyz = (2k - 2)2k(2k + 2) = 8*(k - 1)k(k + 1). The same here: (k - 1)k(k + 1) = the product of three consecutive integers, so the product for sure will be a multiple of 6. Sufficient.

Technically the answer should be D, as EACH statement ALONE is sufficient to answer the question.

But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. (1) says that x, y and z are consecutive integers, while (2) says that x, y and z are EVEN consecutive integers. The statement clearly contradict each other, which cannot happen.

So, the question is flawed. You won't see such a question on the test.

As for you question: 0 is a multiple of every integer, so 0 IS a multiple of both 2 (0 is even) and 6.

Finally, you tagged this question as GMAT Prep, which is NOT true.

Please, read carefully and follow our rules of posting: https://gmatclub.com/forum/rules-for-po ... 33935.html Thank you.

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If x, y and z are integers then is the product of x, y, and z divisibl   [#permalink] 21 Jan 2018, 23:28
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# If x, y and z are integers then is the product of x, y, and z divisibl

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