A man has a certain number of small boxes to pack into parcles. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcle, none is left over. What is the number of boxes, he may have to pack? Choose the correct choice from the following options:
A) 106 B) 301 C) 309 D) 400 E) 450

Rationale: explanation : clearly , the required number would be such that it leaves a remainder of 1 when divided by 3 , 4 , 5 , or 6 and no remainder when divided by 7 . thus , the number must be of the form ( l . c . m of 3 , 4 , 5 , 6 ) x + 1 i . e . , ( 60 x + 1 ) and a multiple of 7 . clearly , for x = 5 , the number is a multiple of 7 . so the number is 301 . answer : b ) 301
Answer: B