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If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of

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Bunuel
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If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of [#permalink] New post   28 Apr 2022, 02:35
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Question Stats:

81% (01:09) correct 19% (01:10) wrong based on 54 sessions
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If N is an integer, is 2N a multiple of 7?

(1) N - 7 is a multiple of 7.
(2) 3N is a multiple of 7.
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D
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JerryAtDreamScore
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Re: If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of [#permalink] New post   01 May 2022, 07:25
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Bunuel wrote:
If N is an integer, is 2N a multiple of 7?

(1) N - 7 is a multiple of 7.
(2) 3N is a multiple of 7.


Number Properties:

We need N to be a multiple of 7 for 2N to be a multiple of 7.

Statement 1 Alone:

If N - 7 is a multiple of 7, then N is also a multiple of 7. Thus 2N is also a multiple of 7. Sufficient.

Statement 2 Alone:

The factor of 7 cannot come from 3, so it must come from N. Then N is a multiple of 7, and 2N is also a multiple of 7. Sufficient.

Answer: D
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Re: If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of [#permalink] New post   01 May 2022, 20:26
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Bunuel wrote:
If N is an integer, is 2N a multiple of 7?

(1) N - 7 is a multiple of 7.
(2) 3N is a multiple of 7.


2N can be a multiple of 7 only if N is a multiple of 7 as 2 is not a factor of 7.

So the question essentially asks us if N is a multiple of 7.

Statement 1: N - 7 is a multiple of 7.
N - 7 can be a multiple of 7 only if N is a multiple of 7.

Let's take 2 examples:
If n = 14
n-7 = 7 -> this can be a multiple of 7 only and only if n is a multiple of 7.

Sufficient.

Statement 2: 3N is a multiple of 7.

3N can be a multiple of 7 only if N is a multiple of 7.

Sufficient.

Option D
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Re: If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of [#permalink] New post   15 Nov 2022, 04:56
Bunuel wrote:
If N is an integer, is 2N a multiple of 7?

(1) N - 7 is a multiple of 7.
(2) 3N is a multiple of 7.


2N will be amultiple of 7 only if N is a multiple of 7.
Therefore, the question is: Is N the multiple of 7?

Stat1- N-7 =7I (I= any integer, I can be 0,1,2)
N= 7I+7
N= 7 (I+1)
Hence stat 1 is suff.


Stat2- 3N/7= I
Therfore, N must be a multiple of 7 for 3N/7 to be an Intger.
Sufficient.
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Re: If N is an integer, is 2N a multiple of 7? (1) N - 7 is a multiple of [#permalink]
15 Nov 2022, 04:56
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Bunuel
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