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PQID: DS08091.01 

GMAT Quant OG 2020 Solution: Question No. 377

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?

1. 17 is a mode for L₁ and 17 is a mode for L₂.
2. n₁ + n₂ = n

Source	OG 2020
Type	Data Sufficiency
Topic	Number Properties
Sub-Topic	Statistics
Difficulty	Very Hard
PQID	DS08091.01

Solution to GMAT Quant OG Question no 377

Steps 1 & 2: Understand Question and Draw Inferences

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.

We need to determine

• Whether 17 is a mode for L or not.

Step 3: Analyse Statement 1

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 L₂, 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.

Hence, statement 1 is sufficient to answer the question.

Step 4: Analyse Statement 2

As per the information given in statement 2, n₁ + n₂ = n.

• 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.

Step 5: Combine Both Statements Together (If Needed)

Since we can determine the answer from statement 1 individually, this step is not required.

Hence, the correct answer choice is option A.

Takeaways from solution to GMAT Quant OG 2020 Question No 377:

1. Mode is the most frequently observed element in a data set.  
   1. If 17 is the mode for L₁, 17 occurs either the same or a greater number of times as any other number in L₁.
   2. Similarly, if 17 is the mode for L₂, 17 occurs either the same or a greater number of times as any other number in L₂.