A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. If 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, is 17 a mode for L ? 17 is a mode for L1 and 17 is a mode for L2.

In this question, we are given ,

A certain list, L, contains a total of n numbers, not necessarily distinct, that are arranged in increasing order. L1 is the list consisting of the first n1 numbers in L. L2 is the list consisting of the last n2 numbers in L.

Explanation:

As per the information given in statement 1, 17 is a mode for L1 and 17 is a mode for L2.

Therefore, we can infer that ,

17 must occur in L1, either same or a greater number of times as any other number in L1. 17 must occur in L1, either same or a greater number of times as any other number in L2.

As all elements in L are in ascending order, we can also conclude that

Each number between last occurrence of 17 in L1 and the first occurrence of 17 in L2 must be equal to 17 only. Therefore, 17 occurs either same or greater number of times as any other number in L. Thus, 17 is a mode for L.

However, from this statement, we cannot conclude anything about the mode of L1, L2, or L.

Hence, statement 2 is not sufficient to answer the question.

Therefore, 17 is a mode for L1 and 17 is a mode for L2.

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