A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If \(L_1\) is the list consisting of the first \(n_1\) numbers in L and \(L_2\) is the list consisting of the last \(n_2\) numbers in L, is 17 a mode for L ?
Say the list is a, b, c, c, d, e, f, h, h, h, k, l..
\(L_1\) could be just a, and \(L_2\) could be h,h,k,l OR
\(L_1\) could be a,b,c,c,d and \(L_2\) could be c,c,d..h,h,k,l
(1) 17 is a mode for \(L_1\) and 17 is a mode for \(L_2\).
Since the list is in increasing order and mode is 17 in both cases, the list L1 and L2 either have all numbers within themselves OR only some other 17 are left.
For example 1,3,5,17,17,17,17,17,20,25....L1 could be 1,3,5,17,17 and L2 could be 3,5,17,17,17,17,17,20,25
OR L1 could be 1,3,5,17,17 and L2 could be 17,17,20,25
So the mode of L will be 17 in each case.
Suff
(2) \(n_1 + n_2 = n\)
We do not know the numbers.
Insuff
A
_________________