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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # x, y, and z are consecutive integers, where x < y < z. Whic  Question banks Downloads My Bookmarks Reviews Important topics
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Moderator  Joined: 18 Apr 2015
Posts: 5917
Followers: 96

Kudos [?]: 1158 , given: 5488

x, y, and z are consecutive integers, where x < y < z. Whic [#permalink]
Expert's post 00:00

Question Stats: 53% (01:22) correct 46% (00:48) wrong based on 26 sessions

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

_________________
Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink]
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)? Moderator  Joined: 18 Apr 2015
Posts: 5917
Followers: 96

Kudos [?]: 1158  , given: 5488

Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink]
1
KUDOS
Expert's post
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
_________________
Intern Joined: 07 Jul 2018
Posts: 9
Followers: 0

Kudos [?]: 5 , given: 1

Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink]
Why not B & C? Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7  , given: 100

Re: x, y, and z are consecutive integers, where x < y < z. Whic [#permalink]
1
KUDOS
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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# x, y, and z are consecutive integers, where x < y < z. Whic  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.