Overlapping Remainder Cycles
GMAT glossary · Playbook
Definition
Two remainder cycles share a timeline and you need when both hold.
Overlapping Remainder Cycles in plain English
Pull Overlapping Remainder Cycles when two remainder cycles share a timeline and you need when both hold. Clues include Remainder cycles, every a leaves r, every b leaves s. Blueprint: List residues for each modulus. Use the GCD consistency test, then solve on the LCM cycle. Why it beats the long way: Checking day by day forever is unnecessary once the joint cycle is known. Micro-example: n leaves remainder 1 when divided by 4 and remainder 2 when divided by 3. First match is 10; jump by mathrmLCM(4,3)=12 to get 10, 22, 34, ldots.
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