There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is: A. 2 B. 3 C. 4 D. 8

GATE 2012 · General Aptitude · Logical Reasoning · medium

Answer: The minimum number of weighings required is 2.

1. Weighing 1: place 3 bags on each pan, set 2 aside: Weigh {1,2,3} vs {4,5,6}, bags {7,8} set aside. Case A: left pan heavier -> heavy bag is among {1,2,3}. Case B: right pan heavier -> heavy bag is among {4,5,6}. Case C: equal -> heavy bag is among {7,8}.
2. Weighing 2: identify the heavy bag within the candidate group: If candidates are {1,2,3}: weigh bag 1 vs bag 2. If left heavy: bag 1 is odd. If right heavy: bag 2 is odd. If equal: bag 3 is odd. If candidates are {4,5,6}: same strategy with those bags. If candidates are {7,8}: weigh 7 vs 8; the heavier side is the odd bag.