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If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7

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Bunuel
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If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  03 Oct 2018, 04:02
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If n is an integer, is n/7 an integer?

(1) 3n/7 is an integer.
(2) 5n/7 is an integer
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  03 Oct 2018, 04:05
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Bunuel wrote:
If n is an integer, is n/7 an integer?

(1) 3n/7 is an integer.
(2) 5n/7 is an integer


Question: is n/7 an integer?

Statement 1: 3n/7 is an integer
Since n is an Integer therefore n must be a multiple of 7 for 3n/7 to be an integer hence
SUFFICIENT

Statement 2: 5n/7 is an integer
Since n is an Integer therefore n must be a multiple of 7 for 3n/7 to be an integer hence
SUFFICIENT

Answer: Option D
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  03 Oct 2018, 04:08
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From statement 1:

3/7 is not an integer. If 3n/7 is an integer, then n is a factor of 7 and it's divisible by 7. Works even if n = 0.

Sufficient.

From statement 2:

5/7 is not an integer. If 5n/7 is an integer, then n is a factor of 7 and it's divisible by 7. Works even if n = 0.

Sufficient.

D is the answer.
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  03 Oct 2018, 04:41
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Bunuel wrote:
If n is an integer, is n/7 an integer?

(1) 3n/7 is an integer.
(2) 5n/7 is an integer



Given that n is an integer

Then 3n/7 = integer. 3 and 7 have no common factor and for 3n to be divisble by 7. N must be a multiple of 7

Sufficient.

Same applies to 5n/7

Sufficient.

Answer choice D.

This question follows the same as this one the only difference in here is that we are given n to be an integer. While the other is asking if n/18 is an integer

https://gmatclub.com/forum/is-n-18-an-i ... 34415.html

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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  20 May 2020, 04:14
Can confirm my process is correct, please.

From the prompt we know 7/n is an integer and r is =0 so we can write n=7q+0

1)3n/7 is an integer so 3n=7q+0 n=7q/3 =0 n=7q +0

2)5n/7 is an integer so 5n=7q +0 SO n=7q/5 +0 and n=7q +0

Answer D
is the process correct?
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  23 Jun 2021, 04:30
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Since n is an integer, for n/7 to be an integer, n has to be a multiple of 7; the question stem can therefore be rephrased as “Is n a multiple of 7?”

From statement I alone, 3n/7 is an integer.

This is possible only if n is a multiple of 7, since 3 is not divisible by 7.
Statement I alone is sufficient to give a YES to the question. Answer options B, C and E can be eliminated.

From statement II alone, 5n/7 is an integer.

This is possible only if n is a multiple of 7, since 5 is not divisible by 7.
Statement II alone is sufficient to give a YES to the question. Answer option A can be eliminated.

The correct answer option is D

Hope that helps!
Aravind B T
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  23 Jun 2021, 04:41
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Eduardo86 wrote:
Can confirm my process is correct, please.

From the prompt we know 7/n is an integer and r is =0 so we can write n=7q+0

1)3n/7 is an integer so 3n=7q+0 n=7q/3 =0 n=7q +0

2)5n/7 is an integer so 5n=7q +0 SO n=7q/5 +0 and n=7q +0

Answer D
is the process correct?


Hello Eduardo,

The prompt does not mention that 7/n is an integer; it ASKS whether n/7 is an integer. You need to be vigilant in reading the question statement, lest such errors cost you in more challenging questions.

Your analysis of the statements are also based on assumptions.

IN statement 1, you have assumed that q is a multiple of 3 in arriving at the conclusion that n is a multiple of 7. What happens if q = 1. Since the question is about n, we need to focus on n instead of 3n.

In statement 2, you have made a similar assumption.

Hope this answers your query!
Cheers
Aravind BT
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  31 Jul 2023, 06:36
In statement 1: 3n/7 is an integer. n could be 8 so that 24/7 is 3 (therefore an integer), but then n/7 which is 8/7 is not an integer. so it is indufficient

Statement 2: sufficient

So my answer would be B.

Does this make sense? Where is the error in my answer?
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Bunuel
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink] New post  31 Jul 2023, 06:47
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scengg wrote:
In statement 1: 3n/7 is an integer. n could be 8 so that 24/7 is 3 (therefore an integer), but then n/7 which is 8/7 is not an integer. so it is indufficient

Statement 2: sufficient

So my answer would be B.

Does this make sense? Where is the error in my answer?

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21/7 = 3
24/7 = 3.42...
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Re: If n is an integer, is n/7 an integer? (1) 3n/7 is an integer (2) 5n/7 [#permalink]
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