Project ForgeThere are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is
Explanation
If every bag were 10gm, total = (1+2+4+8+16)×10 = 310gm. The actual excess, 323−310=13gm, equals 1 extra gram per coin for every coin drawn from an 11gm bag — so the coin-counts of the 11gm bags must sum to exactly 13. Since the counts are powers of two (1,2,4,8,16), and 13 = 8+4+1 in binary, the 11gm bags are exactly bags 4, 3, and 1 (with counts 8, 4, 1). Product of labels = 1×3×4 = 12.
Source: GATE CS 2014 (Session 1) (2014)
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