NIMCET 2010
There are 6561 balls, out of which 1 is heavy. Find the minimum number of weighings required to find the heavy ball.
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option C — 8
Detailed Solution
Split the balls into three equal groups and weigh two of them; the heavier pan, or the group left out if they balance, holds the heavy ball. Each weighing cuts the count to one-third.
, so after weighings one ball is left.
✓ Check
, so 7 weighings cannot separate all the balls; 8 are needed.⚠ Common trap
(A) 12 comes from halving the balls each time, but is still less than 6561, and halving ignores the information from a balanced weighing.Quick tip
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Analytical Reasoning — Preparation
This question tests your understanding of Analytical Reasoning, a key topic in the Logical Reasoning section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Analytical reasoning questions give a set of conditions about people, objects or events and ask you to deduce facts from them. They include puzzles on scheduling (who does what on which day), distribution (who owns which item), floor-based puzzles, comparisons, and grouping or selection problems where certain people must or cannot be chosen together. The key is organising the information. Draw a table or grid with the categories as rows and columns, and fill in the definite clues first. Then use the conditional clues to eliminate possibilities, marking crosses for what is impossible and ticks for what is certain. When a clue leaves two possibilities, write both cases and test each against the remaining clues. Usually one case leads to a contradiction. Most puzzles have four or five questions, so time spent setting up a clear grid pays off. Practise the analytical reasoning puzzles below. Each solution shows the grid built step by step.