In a school, there are three sections A, B, and C having 120, 144, and 192 students respectively. These students are to be divide…

Question

In a school, there are three sections A, B, and C having 120, 144, and 192 students respectively. These students are to be divided into groups of equal strength, such that each group consists of students from only one section.

What is the least possible number of groups that can be formed?

1. A. 24
2. B. 48
3. C. 19 (Correct answer)
4. D. 23

Correct Answer

Option C — 19

Detailed Solution & Explanation

The correct answer is 19.

Key Points

• Each group must be of equal size and drawn from a single section, so the group size must divide 120, 144 and 192 — and to minimise the number of groups, take the largest such size, the HCF.
• 120 = 2³ × 3 × 5; 144 = 2⁴ × 3²; 192 = 2⁶ × 3. The common part is 2³ × 3 = 24.
• Groups = 120/24 + 144/24 + 192/24 = 5 + 6 + 8 = 19.

Additional Information

• Largest group size ⇒ fewest groups, which is why the HCF (not the LCM) is the right tool.
• The distractor 24 is the HCF itself — the group *size*, not the number of groups.

*Ministry of Papers worked solution. The Commission has not yet published the official key for this paper; this answer will be reconciled with it on release.*