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Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So

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Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post 19 Oct 2018, 06:17
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A
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C
D
E

Difficulty:

  95% (hard)

Question Stats:

19% (01:07) correct 81% (00:53) wrong based on 31 sessions

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Is n/14 an Integer?

1) 3n/14 is an Integer
2) 2n/14 is an Integer

Source: www.GMATinsight.com

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Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post Updated on: 19 Oct 2018, 06:56
GMATinsight wrote:
Is n/14 an Integer?

1) 3n/14 is an Integer
2) 2n/14 is an Integer

Source: http://www.GMATinsight.com


EDIT: corrected explanation.

Questions dealing with number properties can almost always be solved logically, with very little calculation.
We'll look for such an answer, a Logical approach.

(1) If we were told that n were an integer, than this would be sufficient, as 3 and 14 are mutually prime. Since it is not, we can manipulate things however we like. For example, choosing 3n/14 = 1, would give n/14 = 1/3, which is not an integer while choosing 3n/14 = 3 would give n/14 = 1, which is
Insufficient.

(2) this implies that n/7 is an integer which in turn implies that n is an integer divisible by 7. If n has 2 in its prime factors, then n/14 is an integer and if it does not, it is not.
Insufficient.

Combined.
From (2) we learn that n is an integer. Therefore, based on the observation that 3 and 14 are mutually prime, (1) implies that n/14 must be an integer.
Sufficient.

(C) is our answer
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Originally posted by DavidTutorexamPAL on 19 Oct 2018, 06:26.
Last edited by DavidTutorexamPAL on 19 Oct 2018, 06:56, edited 2 times in total.
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Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post 19 Oct 2018, 06:32
1
Hi David,

Here n is not given to be an integer.

Pls assume n can take the value 14/3 which makes 3 x n/14 an integer but n/14 is not an integer.

Hence statement 1 is not sufficient.

Statement 2 states that 2n/14 is an integer and hence n/7 is an integer.
n has 7 for sure but may or may not have 2. Not sufficient.

Combining, statement 1 says n has a 2 and statement 2 says n/7 is an integer and hence n/14 is an integer.

Ans: Option C.

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Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post Updated on: 19 Oct 2018, 06:47
rahulkashyap wrote:
Shouldn't the answer be a?

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rahulkashyap

No, It is NOT A

Please check the video solution of similar question


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Originally posted by GMATinsight on 19 Oct 2018, 06:42.
Last edited by GMATinsight on 19 Oct 2018, 06:47, edited 1 time in total.
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Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post 19 Oct 2018, 06:43
DavidTutorexamPAL wrote:
GMATinsight wrote:
Is n/14 an Integer?

1) 3n/14 is an Integer
2) 2n/14 is an Integer

Source: http://www.GMATinsight.com


Questions dealing with number properties can almost always be solved logically, with very little calculation.
We'll look for such an answer, a Logical approach.

(1) Since 3n/14 is an integer, then 3n divides 14. But since 3 and 14 are mutually prime (meaning they have no common prime factors) then n must divide 14 without remainder. Put differently, all of the prime factors of 14 must 'fit into' the prime factors of n because none of them overlap with 3.
Sufficient.

(2) this implies that n/7 is an integer. If n has 2 in its prime factors, then n/14 is an integer and if it does not, it is not.
Insufficient.

(A) is our answer


CLUE: n is not given an Integer. so n may be 14/3 as per first statement and n/14 is NOT an integer for this value of n
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Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

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New post 19 Oct 2018, 08:06
1
mcmoorthy wrote:
Hi David,

Here n is not given to be an integer.

Pls assume n can take the value 14/3 which makes 3 x n/14 an integer but n/14 is not an integer.

Hence statement 1 is not sufficient.

Statement 2 states that 2n/14 is an integer and hence n/7 is an integer.
n has 7 for sure but may or may not have 2. Not sufficient.

Combining, statement 1 says n has a 2 and statement 2 says n/7 is an integer and hence n/14 is an integer.

Ans: Option C.

Posted from my mobile device



Oops, went too fast there.
Fixed,thanks!
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Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So &nbs [#permalink] 19 Oct 2018, 08:06
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