A small firm launched a computer software update that employees of the company had to download on Tuesday last week. For each of the 15 employees who downloaded the update on that day, the table shows the employee’s length of employment (in number of months), the time in the morning (hour and minute) at which the employee began the download, and the length of time it took the update to download completely (rounded to the nearest minute).
| Length of employment | Time of update | Length of download |
|---|
| 73 | 08:45 | 3 |
| 60 | 09:01 | 3 |
| 1 | 09:20 | 9 |
| 41 | 09:21 | 9 |
| 321 | 09:21 | 9 |
| 8 | 09:40 | 3 |
| 289 | 09:45 | 3 |
| 23 | 09:49 | 6 |
| 72 | 09:50 | 6 |
| 68 | 10:01 | 3 |
| 210 | 10:06 | 3 |
| 52 | 10:12 | 6 |
| 106 | 10:12 | 6 |
| 42 | 10:22 | 6 |
| 11 | 10:23 | 6 |
For each of the following statements about the 15 employees, select Yes if the statement is supported by the information provided. Otherwise, select No.
For any two employees, if an employee had a greater length of employment, then the employee had an earlier time of update.For this statement to be true, it must be that, in every case, the greater an employee's length of employment, the earlier was the time of update the employee had. If even one Length of employment/Time of update pair is out of order, then this statement won't be true.
So, to see whether the pattern holds for every length of employment and time of update, we can
sort the Length of employment column from least to greatest and see whether the Time of update column is sorted from latest to earliest in every case.

Doing so, we see that, with Length of employment sorted from least to greatest, Time of update is mixed up, with earlier times at the top of the column, then later times, then some more earlier and later times mixed as we go down the columns and Length of employment becomes greater.
So, it's clear that greater length of employment is not always associated with earlier time of update.
Select
No.
For any two employees, if an employee had an earlier time of update, then the length of time it took that employee to completely download the update was shorter.For this statement to be true, it must be that, in every case, the earlier an employee's time of update, the shorter was the length of time it took the employee to download the upate. If even one Time of update/Length of download pair is out of order, then this statement won't be true.
So, to see whether the pattern holds for every time of update and length of download, we can
sort the Time of update column from earliest to latest and see whether the Length of download is sorted from shorter to longer in every case.

Doing so, we see that, with Time of update sorted from earliest to latest, Length of update is mixed up, with shorter times, 3, at the top of the column, then longer times, 9, then some more shorter times and longer times mixed as we go down the columns and Time of update becomes later.
So, it's clear that earlier time of update is not always associated with shorter length of update.
Select
No.
Each employee who had a time of update within three minutes of another employee had longer download lengths than any employee who did not.Since this statement is about employees having "longer download lengths," we can
sort by Length of download to be able to compare download lengths.

Having sorted Length of download from least to greatest, we can then go through the Time of update column to see whether it's true that "Each employee who had a time of update within three minutes of another employee had longer download lengths than any employee who did not."
Doing so, we see that, toward the top of the Time of update column, the times are spread out by at least five minutes until we get through all the 3s in the Length of download column.
Then, the times of update become less spread out so that each is "within three minutes of another," starting with 9:49 to 9:50, then 10:12 to 10:12 and so on. At the same time, the lengths of update also increase to 6 and 9.
So, we see that it is indeed the case that each employee who had a time of update within three minutes of another employee had longer download lengths (6 or 9) than any employee who did not (3).
Select
Yes.
Correct answer: No,
No,
Yes