Discussion Forum

A man has a certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 in a parcel, he is left with one over; if he packs 7 in a parcel, none is left over. what is the number of boxes, he may have to pack?

Answer:

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. (60x+ 1) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So, the number is 301.