Here is a tough one from GMAT CLUB

by **rhoeta** Tue Sep 25, 2007 11:34 am

If g(n) represented the product of every even integer from 2 to n, then g(80) + 1 is divisible by the lowest prime number p. P is:

A. Between 1 and 10
B. Between 11 and 20
C. Between 21 and 30
D. Between 31 and 40
E. Greater than 40

by **StaceyKoprince** Thu Sep 27, 2007 8:17 pm

Moved to the GMAT Math section; please note, this section is only for problems found on MGMAT CATs.

Please note: this question was authored by Manhattan Review.

by **RonPurewal** Sat Sep 29, 2007 5:21 am

Well, g(80) is divisible by all of 2, 4, 6, 8, ..., 80, which means it's divisible by all of 1, 2, 3, 4, 5, ..., 40 (and, specifically, by all of the prime numbers in that list).

Which means that g(80) + 1 is divisible by NONE of the prime numbers in that list.

So it's E.

This problem reminds me of OG #153 (the one in which one of the statement reads 13! <= k <= 13! + 13), a problem that we occasionally use in lectures. The underlying principle is the same.