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x, y, and z are consecutive integers, where x < y < z. Whic

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x, y, and z are consecutive integers, where x < y < z. Whic [#permalink] New post 12 Aug 2017, 09:59
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x, y, and z are consecutive integers, where x < y < z. Which of the following must be divisible by 3 ?

Indicate all that apply.

❑ xyz

❑ (x + 1)yz

❑ (x + 2)yz

❑ (x + 3)yz

❑ (x + 1)(y + 1)(z + 1)

❑ (x + 1)(y + 2)(z + 3)

[Reveal] Spoiler: OA
A,D,E,F
[Reveal] Spoiler: OA

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Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink] New post 08 Jul 2018, 06:36
Carcass wrote:


x, y, and z are consecutive integers, where x < y < z. Which of the following must be divisible by 3 ?

Indicate all that apply.

❑ xyz

❑ (x + 1)yz

❑ (x + 2)yz

❑ (x + 3)yz

❑ (x + 1)(y + 1)(z + 1)

❑ (x + 1)(y + 2)(z + 3)

[Reveal] Spoiler: OA
A,D,E,F


Any explanation please, especially for the last one (F) and (D)?
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Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink] New post 08 Jul 2018, 10:30
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The stem is pretty straight: 3 consecutive numbers and integers.

Pick 1,2,3

D) \((x + 3)yz\) \(= 4*6=24\) divisible by 3

F) \((x + 1)(y + 2)(z + 3) = 2*4*6= 48\) divisible by 3

Each number above has a number divisible by 3 inside. So they must be divisible by 3

Hope this helps

PS: more often than not is useful picking number strategy instead to think theoretically, especially when you are not at that level.

Regards
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Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink] New post 13 Jul 2018, 17:32
Why not B & C?
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Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink] New post 13 Jul 2018, 22:47
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Akash03jain wrote:
Why not B & C?



Thanks Carcass. Back to your question, the reason simply because 3,4,5 in B are 4 * 4 * 5 does not have 3 prime factor, so it's not divisible. Same with C.
Re: x, y, and z are consecutive integers, where x < y < z. Whic   [#permalink] 13 Jul 2018, 22:47
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