Question

A woman sells to the first customer half her stock and half an apple, to the second customer half her remaining stock and half an apple, and so on to a third and fourth customer. She finds she has 15 apples left. How many apples did she have originally?

• A. 250
• B. 255
• C. 252
• D. 260
• E. 270

Hint:

For "half plus half" problems, working backward by adding 0.5 and doubling at each step is much faster than setting up a forward equation.

Answer 1

The Correct Option is B

Step 1: Analyse options.
- Let the total apples be $x$. - After the 1st customer: $x - (\frac{x}{2} + 0.5) = \frac{x-1}{2}$. - This pattern continues for four customers. - Working backward: If she has 15 left after the 4th, before the 4th she had $(15 + 0.5) \times 2 = 31$. - Before the 3rd: $(31 + 0.5) \times 2 = 63$. - Before the 2nd: $(63 + 0.5) \times 2 = 127$. - Before the 1st: $(127 + 0.5) \times 2 = 255$.
Step 2: Conclusion.
The original number of apples was 255. Final Answer: (b) 255