GATE 2014 CS (CS1) – Question 47

Engineering Mathematics · Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) · 2 marks · Numerical answer

Five bags labelled 1–5 each contain equal-weight coins within the bag; some bags have 10 g coins and others 11 g coins. Taking 1,2,4,8,16 coins respectively from bags 1–5 gives total 323 g. Find the product of labels of bags with 11 g coins.

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Correct answer: 12 to 12

Explanation

If every selected coin weighed10g, the total would be10(1+2+4+8+16)=310g. The excess is13g, whose binary decomposition is1+4+8. Thus bags1,3,4 have11g coins and their label product is **12**.