On 1st May, Mr. X arrived in a new city and was looking for a place to stay. He met a landlard who offered to rent his apartment at a reasonable price but wanted Mr. X to pay the rent on a daily basis. Mr. X had a silver bar of 31 inches and an inch of the silver bar was exactly equal to a day’s rent. He agreed to pay an inch of the silver bar towards the daily rent. Mr. X wanted to make minimum number of pieces of silver bar but did not want to pay any advance rent. How many pieces did he make? (A)5 (B)8 (C)16 (D)20 (E)31
HINT:- Today he can give a piece worth a value of 1-day rent. Tomorrow, he can give a piece worth a value of 2-days rent and take back the piece given today, such that it counts for 2-days rent.
Yes, as 'ianoop' said, 5-pieces is the answer. Beauty of math is illustrated in this problem. If Mr X cuts the silver bar of 31 inches in to the pieces with following sizes (in inches), it will result in minimum number of pieces- solution: 1, 2, 4, 8, 16 On day-1 Mr X gives 1-inch piece to the landlord On day-2 he gives 2-inch piece and takes back the 1-inch piece On day-3 he gives 1-inch piece in addition to the already given 2-inch piece, thus making it 3-inches in total On day-4 he gives 4-inch piece and takes back the 1-inch and 2-inch pieces On day-5 he gives 1-inch piece in addition to the already given 4-inch piece, thus making it 5-inches in total. This will continue till day-31. Hence a minimum of five pieces is enough Math logic: Any number up to 2n-1 can be represented by the combinations of the ‘n’ numbers: 2^0,2^1,2^2,...2n-1. Answer (A)
