KurilooStudy·Practice·Succeed
Aptitude Topics

Word Problems

Real-world word problems don't always say 'HCF' or 'LCM' directly. Success relies on identifying key words in the problem that trigger the correct method.

Fundamental Principles

Synchronized Cycle Problems (LCM Trigger)

Scenarios involving events that repeat at regular intervals—like traffic lights changing, bells tolling, or runners on a track—where you need to find when they will line up or trigger at the same time again.

Maximized Distribution Problems (HCF Trigger)

Scenarios where you need to divide different quantities into equal, maximum-sized groups, containers, or rows without mixing the items or leaving any behind.

Essential Formulation Tips

  • When you see phrases like 'minimum time to meet again', 'repeating patterns', or 'intervals', think LCM.
  • When you see phrases like 'maximum possible size', 'largest equal capacity', or 'greatest length', think HCF.

Shortcut Execution Techniques

  • Time Sync Adjustment: For interval problems where events toll together, if a question asks how many times they ring together in an hour, calculate: $\text{Occurrences} = (\text{Total Time} / \text{LCM}) + 1$. The $+1$ accounts for the very first synchronized toll at time zero.

Contextual Inquiries (FAQs)

Q: Why do we add 1 to the final result in repeating bell-ringing problems?

A: Because the division tells you how many intervals passed. You have to add 1 to include the initial synchronized ring at the starting line.