GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 25 Mar 2019, 11:25

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2848
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

19 Oct 2018, 07:17
00:00

Difficulty:

95% (hard)

Question Stats:

15% (01:40) correct 85% (01:02) wrong based on 33 sessions

HideShow timer Statistics

Is n/14 an Integer?

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

Source: www.GMATinsight.com

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
examPAL Representative
Joined: 07 Dec 2017
Posts: 912
Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

Updated on: 19 Oct 2018, 07:56
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.

_________________

Originally posted by DavidTutorexamPAL on 19 Oct 2018, 07:26.
Last edited by DavidTutorexamPAL on 19 Oct 2018, 07:56, edited 2 times in total.
Intern
Joined: 12 Dec 2010
Posts: 42
Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

19 Oct 2018, 07:32
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.

Posted from my mobile device
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2848
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

Updated on: 19 Oct 2018, 07:47
rahulkashyap wrote:

Posted from my mobile device

rahulkashyap

No, It is NOT A

Please check the video solution of similar question

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 19 Oct 2018, 07:42.
Last edited by GMATinsight on 19 Oct 2018, 07:47, edited 1 time in total.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2848
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

19 Oct 2018, 07:43
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.

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
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
examPAL Representative
Joined: 07 Dec 2017
Posts: 912
Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So  [#permalink]

Show Tags

19 Oct 2018, 09:06
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!
_________________
Re: Is n/14 an Integer? 1) 3n/14 is an Integer 2) 2n/14 is an Integer So   [#permalink] 19 Oct 2018, 09:06
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.