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19 Oct 2018, 07:17
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
33% (01:56) correct
67%
(01:09)
wrong
based on 89
sessions
History
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Time
Result
Not Attempted Yet
Is n/14 an Integer?
1) 3n/14 is an Integer
2) 2n/14 is an Integer
Source: www.GMATinsight.com
1) 3n/14 is an Integer
2) 2n/14 is an Integer
Source: www.GMATinsight.com
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
Updated on: 19 Oct 2018, 07:56
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.
Last edited by DavidTutorexamPAL on 19 Oct 2018, 07:56, edited 2 times in total.
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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
19 Oct 2018, 07:32
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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
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
