Question

A man distributed 43 chocolates to his children. How many of his children are more than five years old?

Statements:
I. A child older than five years gets 5 chocolates. 
II. A child 5 years or younger in age gets 6 chocolates. 

• A. The question can be answered with the help of statement I alone.
• B. The question can be answered with the help of statement II alone.
• C. Both statements I and II are needed to answer the question.
• D. The question cannot be answered even with the help of both the statements.

Hint:

In DS problems with distributions, define variables for each group and use the total. Modular checks often confirm uniqueness of integer solutions.

Answer 1

The Correct Option is C

1. Statement I alone: Only fixes the rate for older children (5 each); with no information on younger children, the total 43 cannot be split into a unique count.
2. Statement II alone: Only fixes the rate for younger children (6 each); same issue in reverse — insufficient alone.
3. Both together: Solving \(5x+6y=43\) by testing integer values of \(x\) from 0 to 8 gives a divisible-by-6 remainder only at \(x=5\) (\(y=3\)), a unique solution.

\[ \boxed{\text{Both statements needed; older children}=5} \]