Weighing 78g with specific silver coins combinations
Question
There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:
Which of the statements given above is/are correct?
Options
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Explanation
Evaluate the coin combination limits independently under both constraints:
Statement 1 focuses on buying exactly 78 gm, meaning the sum of the positive values must equal 78. To minimize the coin count, use the largest possible denominations:
Statement 2 covers weighing 78 gm. In a standard two-pan balance scale system, you can place coins on both sides of the balance pans (subtraction). Let's optimize using subtraction: Place 50 + 25 + 5 = 80 gm on one pan, and a single 2 gm coin on the opposite pan with the target material. Net balance weight = 80 - 2 = 78 gm. This requires a total of only 4 coins, which is strictly less than 7. Statement 2 is correct.
Answer: (c).
Question details
Year
2023
Paper
CSAT
Question
Q69
Section
Numerical Ability
Sub-topic
Optimization / Number Puzzles
Type
Number theory
Difficulty
Medium
Source hint
Number theory
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