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

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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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?

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

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

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...