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

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Retired Moderator
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When the positive integer x is divided by 6, the remainder i [#permalink]  12 Aug 2018, 15:35
Expert's post
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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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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4804
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 169

Kudos [?]: 2833 [0], given: 394

Re: When the positive integer x is divided by 6, the remainder i [#permalink]  15 Aug 2018, 05:24
Expert's post
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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Senior Manager
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Re: When the positive integer x is divided by 6, the remainder i [#permalink]  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]  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
Joined: 17 Aug 2019
Posts: 257
Followers: 2

Kudos [?]: 32 [0], given: 64

Re: When the positive integer x is divided by 6, the remainder i [#permalink]  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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