Concept: The question tests on Number properties

Solution:
 
Is n a multiple of 140. i.e is n = 140, 280, 420 ....

Statement 1: n is a multiple of 10

n = 10 is a multiple of 10, but 10 is not a multiple of 140 (it is a factor of 140)

Answer options could be B, C or E Therefore Statement 1 Alone is Insufficient
 

Statement 2: n is a multiple of 14.

n = 14 is a multiple of 14, but not a multiple of 140.

Answer Options could be C or E Therefore Statement 2 Alone is Insufficient.
 

Combining Both Statements: n is a multiple of 10 and 14 i.e LCM of 10 and 14 = 70

n = 70 is a multiple of 10 and 14, but is not a multiple of 140

Therefore Both Statements together are Insufficient.

Option E