**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 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?

- 17 is a mode for L
_{1}and 17 is a mode for L_{2}. - n
_{1}+ n_{2}= 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__

__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.
- L
_{1}is the list consisting of the first n_{1}numbers in L. - L
_{2}is the list consisting of the last n_{2}numbers in L.

We need to determine

- Whether 17 is a mode for L or not.

__Step 3: Analyse Statement 1__

__Step 3: Analyse Statement 1__

As per the information given in statement 1, 17 is a mode for L_{1} and 17 is a mode for L_{2}.

Therefore, we can infer that

- 17 must occur in L
_{1}, either same or a greater number of times as any other number in L_{1}^{.} - 17 must occur in L
_{2}, either same or a greater number of times as any other number in L_{2}^{.}

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

- Each number between last occurrence of 17 in L
_{1}and the first occurrence of 17 in L_{2}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__

__Step 4: Analyse Statement 2__

As per the information given in statement 2, n_{1} + n_{2} = n.

- However, from this statement, we cannot conclude anything about the mode of L
_{1}, L_{2}, or L.

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

__Step 5: Combine Both Statements Together (If Needed)__

__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:

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

- If 17 is the mode for L