CRT Lattice Jump
GMAT glossary · Playbook
Definition
Solving simultaneous remainder conditions via successive substitutions or CRT, then jumping by lcm(m,n) to list every solution.
CRT Lattice Jump in plain English
Use CRT Lattice Jump for simultaneous remainder conditions with coprime (or LCM-friendly) moduli. Clues include leaves remainders a and b when divided by m and n. Solve the system via successive substitutions or the Chinese Remainder Theorem; jump by lcm(m,n). Searching by hand misses the period; the lattice jump lists every solution once the first match is known. If no first match exists, the system is inconsistent and you stop. Micro-example: n equiv 2 pmod3 and n equiv 3 pmod5. One solution is 8; thereafter add mathrmLCM(3,5) = 15 forever: 8, 23, 38, and so on. When moduli share a factor, first check that the remainders agree modulo that shared factor, or else no lattice exists.
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