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When the positive integer x is divided by 6, the remainder i

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When the positive integer x is divided by 6, the remainder i [#permalink] New post 12 Aug 2018, 15:35
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Question Stats:

44% (01:09) correct 55% (01:45) wrong based on 36 sessions
When the positive integer x is divided by 6, the remainder is 4. Each of the following could also be an integer EXCEPT

(A) \(\frac{x}{2}\)
(B) \(\frac{x}{3}\)
(C) \(\frac{x}{7}\)
(D) \(\frac{x}{11}\)
(E) \(\frac{x}{17}\)
[Reveal] Spoiler: OA

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Retired Moderator
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Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 2839 [0], given: 394

Re: When the positive integer x is divided by 6, the remainder i [#permalink] New post 15 Aug 2018, 05:24
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Explanation

When dealing with remainder questions on the GRE, the best thing to do is test a few real numbers:

Multiples of 6 are 0, 6, 12, 18, 24, 30, 36, etc.

Numbers with a remainder of 4 when divided by 6 are those 4 greater than the multiples of 6:

x could be 4, 10, 16, 22, 28, 34, 40, etc.

You could keep listing numbers, but this is probably enough to establish a pattern.

(A) \(\frac{x}{2}\) → ALL of the listed x values are divisible by 2. Eliminate (A).

(B) \(\frac{x}{3}\) → NONE of the listed x values are divisible by 3, but continue checking.

(C) \(\frac{x}{7}\) → 28 is divisible by 7.

(D) \(\frac{x}{11}\) → 22 is divisible by 11.

(E) \(\frac{x}{18}\) → 34 is divisible by 17.

The question is “Each of the following could also be an integer EXCEPT.” Since four of the choices could be integers, (B) must be the answer.
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Re: When the positive integer x is divided by 6, the remainder i [#permalink] New post 27 Jul 2020, 10:30
I was confused here with the question, x should be the same number in the question and divisible by " All" the choices except the answer. What was the clue of concluding Sandy answer?
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Re: When the positive integer x is divided by 6, the remainder i [#permalink] New post 27 Jul 2020, 10:33
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x could be 4, 10, 16, 22, 28, 34, 40

All answer choices but B are divisible for these numbers
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Senior Manager
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Joined: 17 Aug 2019
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Kudos [?]: 32 [0], given: 64

Re: When the positive integer x is divided by 6, the remainder i [#permalink] New post 27 Jul 2020, 10:37
I mean that if X=22
It mus be divisible by all the answer choices except B.
How did you conclude that we can take all the possibilities?
Re: When the positive integer x is divided by 6, the remainder i   [#permalink] 27 Jul 2020, 10:37
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When the positive integer x is divided by 6, the remainder i

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