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Difficulty:
25%
(medium)
Question Stats:
72% (01:08) correct
28%
(01:16)
wrong
based on 107
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If m is an integer, is 14 a factor of m ?
(1) 14 is a factor of 15 m.
(2) 14 is a factor of 16 m.
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(1) 14 is a factor of 15 m.
(2) 14 is a factor of 16 m.
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
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Posts: 175
(1) 14 is a factor of 15 m. :
Factors of 14: 7*2,
Factors of 15 m : 3*5* m
No same factors. Therefore for 14 to be factor of 15m it must have 7 and 2 as factors also.
On checking you can get 15*14 =210 :
14 is least number to satisfy the condition: Sufficient
(2) 14 is a factor of 16 m :
Factors of 14: 7*2,
Factors of 16 m : 2^4* m
Same factor :2
Yes and no both possible answers.
Nearest integer than can give NO answer is 112 :
16*8 : 112 : of which 14 is also a factor
but 14 is not a factor of 8
Yes : 16*14 :
Hence both possible: Insufficient
Answer :A
Factors of 14: 7*2,
Factors of 15 m : 3*5* m
No same factors. Therefore for 14 to be factor of 15m it must have 7 and 2 as factors also.
On checking you can get 15*14 =210 :
14 is least number to satisfy the condition: Sufficient
(2) 14 is a factor of 16 m :
Factors of 14: 7*2,
Factors of 16 m : 2^4* m
Same factor :2
Yes and no both possible answers.
Nearest integer than can give NO answer is 112 :
16*8 : 112 : of which 14 is also a factor
but 14 is not a factor of 8
Yes : 16*14 :
Hence both possible: Insufficient
Answer :A
Posts: 82
St1: 14 is a factor of 15m. i.e. 15m / 14 will give an integer value.
Since 15 is not divisible by 14. We can say that m must be divisible by 14 so that 14 becomes a factor of 15m. Since m is divisible by 14 = > 14 is a factor of m
St1 is sufficient
St2: 16m is a factor of 14 => 16m/14 = integer => 8m/7 = integer
Since 8 is not divisible by 7. So, m must be divisible by 7. => m is a multiple of 7
m = 7, 14 , 21... but m is not divisible by 14 for every value. Hence, St2 is insufficient.
Since 15 is not divisible by 14. We can say that m must be divisible by 14 so that 14 becomes a factor of 15m. Since m is divisible by 14 = > 14 is a factor of m
St1 is sufficient
St2: 16m is a factor of 14 => 16m/14 = integer => 8m/7 = integer
Since 8 is not divisible by 7. So, m must be divisible by 7. => m is a multiple of 7
m = 7, 14 , 21... but m is not divisible by 14 for every value. Hence, St2 is insufficient.
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