Reverse calculation through a sequence of coin distributions
Question
A has some coins. He gives half of the coins and 2 more to B. B gives half of the coins and 2 more to C. C gives half of the coins and 2 more to D. The number of coins D has now, is the smallest two-digit number. How many coins does A have in the beginning?
Options
76
68
60
52
Explanation
Solve by reverse engineering the transaction chain.
The smallest two-digit number is 10. Therefore, D receives exactly 10 coins.
Step 1: C gives half his coins + 2 to D. C/2 + 2 = 10 \implies C/2 = 8 \implies C = 16.
Step 2: B gives half his coins + 2 to C. B/2 + 2 = 16 \implies B/2 = 14 \implies B = 28.
Step 3: A gives half his coins + 2 to B. A/2 + 2 = 28 \implies A/2 = 26 \implies A = 52.
A started with exactly 52 coins.
Answer: (d).
Question details
Year
2022
Paper
CSAT
Question
Q28
Section
Numerical Ability
Sub-topic
Algebra & Equations
Type
Factual single
Difficulty
Hard
Source hint
A gives half of the coins and 2 more
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