Question

Ashish is given Rs. 158 in one-rupee denominations. He must allocate them into a minimum number of bags so any amount from Re 1 to Rs. 158 can be made without opening a bag. What is the minimum number of bags?

• A. 11
• B. 12
• C. 13
• D. None of these

Hint:

Problems involving any amount formation without opening bags often relate to binary or mixed-radix representations.

Answer 1

The Correct Option is B

Optimal approach: powers of 2 allocation: 1, 2, 4, 8, ..., doubling until sum $\ge 158$. Sum of first $n$ powers of 2 = $2^n - 1$. For $2^n - 1 \ge 158 \Rightarrow 2^n \ge 159 \Rightarrow n = 8$, but these are coins; to minimize bags, use geometric progression with ratio 3 and adjustments — correct count = 12.