Question

If twenty sweets are distributed among some boys and girls such that each girl gets two sweets and each boy gets three sweets, what is the number of boys and girls?
I. The number of girls is not more than five.
II. If each girl gets 3 sweets and each boy gets 2 sweets, the number of sweets required for the children will still be the same.

• A. Statement I alone sufficient
• B. Both statements needed
• C. Statement II alone sufficient
• D. Cannot be answered even with both

Hint:

Write the sweet count as an equation in the number of girls and boys; check how many whole-number solutions each statement leaves.

Answer 1

The Correct Option is C

Step 1: Basic equation:
Let there be \(g\) girls and \(b\) boys. Then \(2g + 3b = 20\).

Step 2: Statement I alone:
Whole-number solutions with \(g \ge 1\): \((g,b) = (1,6), (4,4), (7,2), (10,0)\). With \(g \le 5\), both \((1,6)\) and \((4,4)\) remain. Not unique.

Step 3: Statement II alone:
The new distribution needs the same 20 sweets: \(3g + 2b = 20\). Together with \(2g+3b = 20\), subtract: \(g - b = 0\), so \(g = b\), and \(5g = 20\) gives \(g = b = 4\). A unique answer: 4 boys and 4 girls.

Final Answer:
Statement II alone is enough. The correct option is (3): Statement II alone sufficient.