A number when divided by a certain divisor left remainder 245, when twice the number was divided by the same divisor, the remainder was 112. Find the divisor?  Choose the correct choice from the following answers:
A) 378
B) 365
C) 380
D) 456
E) 460

Rationale: "easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a"
Answer: A