Limited Product Divisibility Trap
GMAT glossary · Playbook
Definition
A product of consecutive integers must be divisible by a composite whose primes are scarce in the window.
Limited Product Divisibility Trap in plain English
Pull Limited Product Divisibility Trap when a product of consecutive integers must be divisible by a composite whose primes are scarce in the window. Clues include Product of k consecutive, divisible by a composite. Blueprint: Factor the composite into primes. Check each prime power against the consecutive window. The scarcest prime is the bottleneck. Why it beats the long way: Checking the composite as a blob hides which prime fails. Micro-example: Is some product of 3 consecutive integers always divisible by 6? Factor 6=2· 3. Among any three consecutive integers you always get an even and a multiple of 3, so yes. For 8=2^3, three consecutive may supply only one factor of 2, so the claim fails.
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