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## 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

### 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. #### Juhi Gupta

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