Question

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.

Answer 1

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.