A dealer sells half of the eggs that he has plus another half an egg to…
2019
A dealer sells half of the eggs that he has plus another half an egg to Anurag. Then he sells half of the balance plus another half an egg to Deepak. Then he sells half of the balance plus another half an egg to Sivani. In the end he is left with just 7 eggs, and he claims that he never broke an egg. How many eggs did he start with?
Answer: B. 63 — The trick is that selling "half the eggs plus another half an egg" always removes a whole number of eggs and leaves a whole number, so no egg is ever broken.…
- A.
65
- B.
63
- C.
67
- D.
69
Show answer & explanation
Correct answer: B
The trick is that selling "half the eggs plus another half an egg" always removes a whole number of eggs and leaves a whole number, so no egg is ever broken. If a person starts a step with N eggs, the sale is N/2 + 1/2 = (N + 1)/2 eggs, and the balance left is N − (N + 1)/2 = (N − 1)/2.
Work backwards from the 7 eggs left at the end. Reversing balance = (N − 1)/2 gives N = 2 × balance + 1.
Before Sivani's purchase: 2 × 7 + 1 = 15. Before Deepak's: 2 × 15 + 1 = 31. Before Anurag's (the start): 2 × 31 + 1 = 63.
Check forward from 63: Anurag buys (63 + 1)/2 = 32, leaving 31; Deepak buys (31 + 1)/2 = 16, leaving 15; Sivani buys (15 + 1)/2 = 8, leaving 7. Every sale is a whole number of eggs and exactly 7 remain, so the dealer started with 63 eggs.