What was the median of the daily numbers of phone calls received at a

Question

What was the median of the daily numbers of phone calls received at a certain radio station for the last 5 days?

(1) 50 phone calls were received at the radio station on each of the last 3 days.

(2) The total number of phone calls received at the radio station during the last 5 days was 230.

gmatophobia · Accepted Answer

Statement 1

(1) 50 phone calls were received at the radio station on each of the last 3 days.

Case 1  : The number of calls on the other two days was less than 50

X \quad Y \quad 50 \quad 50 \quad 50

Median = 50

Case 2  : The number of calls on the other two days was greater than 50

50 \quad 50 \quad 50\quad X \quad Y

Median = 50

Case 3  : The number of calls on one day was less than 50 and on the other day was greater than 50

X \quad\ 50 \quad 50 \quad 50\quad Y

Median = 50

Hence, in all three cases, the median = 50.

Statement 1 alone is sufficient and we can eliminate B, C, and E.

Statement 2

(2) The total number of phone calls received at the radio station during the last 5 days was 230

Knowing the sum of the number of calls does not help as we can have multiple combinations to arrive at the sum. For example, let's assume in each of the first four days the number of calls received was 1 and on the fifth day the number of calls received was 226. In that case, the median will be equal to 1.
Alternatively, if no calls was received on the first four days and 230 calls were received on the fifth day, the median equals zero.

As we can have multiple possible answers, the statement alone is not sufficient.

Option A

JeffTargetTestPrep · Answer

n = 5

We need to answer the question:

median = ?

Statement One Alone:

=> 50 phone calls were received at the radio station on each of the last 3 days.

Since the number of data points is 5, which is an odd number, the median is the middle value (the 3rd value) in the list of daily numbers in ascending order.

We know that 3 data points are equal to 50.

The median takes its smallest possible value if the unknown data points also take their smallest possible values.

If the ordered data set is {0,0,50,50,50}, then the median is 50.

The median takes its greatest possible value if the unknown data points also take their greatest possible values.

If the ordered data set is {50,50,50,big number,big number}, then the median is again 50.

Therefore, the median must be 50. Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> The total number of phone calls received at the radio station during the last 5 days was 230.

If the ordered data set is {0,0,0,0,230}, then the median is 0.

Whereas, if the ordered data set is {5,5,5,5,210}, then the median is 5.

Statement two is not sufficient.

Answer: A

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What was the median of the daily numbers of phone calls received at a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

What was the median of the daily numbers of phone calls received at a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards