First Match and Jump
GMAT glossary · Playbook
Definition
Finding the first integer that satisfies all remainder rules, then jumping by the LCM of the moduli to list the whole arithmetic progression.
First Match and Jump in plain English
Pull First Match and Jump on remainder / congruence conditions with a repeating cycle. Clues include leaves remainder, congruent to, every nth, or LCM of cycles. Find the first integer that satisfies all remainder rules, then jump by the LCM of the moduli. Checking every integer is endless; first match + LCM jump inventories the whole arithmetic progression in two moves. If the moduli are not coprime, the LCM still works provided a solution exists. Micro-example: n leaves remainder 2 when divided by 3 and remainder 3 when divided by 5. First match might be 8; jump by mathrmLCM(3,5) = 15 to get 8, 23, 38, and so on.
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