UPSC CSE Prelims
Numerical Reasoning Previous Year Questions (PYQs)
Practice solved questions for Numerical Reasoning with detailed step-by-step solutions, key insights, and trend analysis for UPSC CSE PRELIMS.
Solved Previous Year Questions
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Seven cubes are identical in shape. Out of these, the weight of each of the six cubes is equal and the weight of the remaining cube is less than the weight of any other cube. A balance is used to identify the lightest cube. What is the minimum number of attempts required to distinguish the odd cube with certainty?
Detailed Explanation:
Divide the 7 cubes into groups of 3, 3, and 1. In the first weighing, place 3 cubes on each pan. If balanced, the lightest cube is the one left aside (identified in 1 attempt). If unbalanced, the lightest is among the 3 cubes on the lighter pan.
In the second weighing, take the 3 cubes from the lighter pan and weigh any 2 (one on each side), leaving the third aside. If balanced, the lightest is the one left aside. If unbalanced, the lightest is on the lighter pan.
Therefore, a maximum of 2 weighings guarantees identification of the lightest cube with certainty, making Option 1 the correct answer.
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