Hi All,

We're told that List L contains a total of N numbers, NOT necessarily DISTINCT, that are arranged in INCREASING order and L1 is the list consisting of the first N1 numbers in L and L2 is the list consisting of the last N2 numbers in L. We're asked if 17 is a MODE for L. It's worth noting that the two sub-lists (L1 and L2 could potentially "overlap", meaning that some numbers of List L appear in BOTH groups). Every number in List L is accounted for though (again though, it's possible that some values appear in both sub-lists).

To start, it's worth noting that a "mode" is a number that shows up the most often in a group of numbers (for example, the group 1, 2, 2, 3, 4 has a mode of 2). There can actually be more than one mode in a group though (for example, the group 1, 1, 2, 2, 3, 4 has two modes: 1 and 2).

(1) 17 is a mode for L1 and 17 is a mode for L2.

Fact1 tells us that 17 is a mode for both sub-lists. Note that the prompt did tell us that the list is arranged in INCREASING order...
IF....
-there is NO 'overlap', then some of the 17s appear in L1 and some appear in L2. Totaling all of those individual 17s would make the mode even larger than it is in the two individual sub-lists, meaning that no other value could appear more often in List L.
-there IS an 'overlap' - meaning one (or more) of the 17s appears in BOTH sub-lists, then that total number of 17s will still be a mode. There might be other values that are also modes, but those values could not show up more often than the 17s do, so none of them could "out-number" the 17s.
Fact 1 is SUFFICIENT

(2) N1 + N2 = N

Fact 2 tells us that the two sub-lists have no terms in common (meaning that there is no 'overlap'), but it does not tell us anything about the individual terms or what the mode(s) might be.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich