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Q2728/80Q29
Q28·CSAT · Prelims 2022

Reverse calculation through a sequence of coin distributions

NumericalAlgebra & EquationsFactual singleHard

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

a

76

b

68

c

60

d

52

Answer

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.

For sequential transaction chains where the final remnant is known, work backwards from the target value, inverting all mathematical operations (e.g., subtract 2, then multiply by 2).

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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