Question

Nick, Joey, Beki, and Carmen ran in the town's annual road race. Each person had a different jersey number (2, 13, 20, and 34) and finished in a different amount of time (10 minutes, 11 minutes, 12 minutes, and 14 minutes). Use the information and deductive reasoning to determine each person's jersey number and race time. • The runner with the lowest jersey number also ran the slowest time. • Nick's jersey number is 18 greater than Carmen's. • Of the four runners, a man had the fastest finishing time. . The sum of the digits on Beki's jersey number is 7. Nick finished exactly 2 minutes faster than Beki. Nick Joey Beki Carmen 2 13 20 34​

Answer 1

Based on the given information, we can use deductive reasoning to determine each person's jersey number and race time. Let's analyze the clues one by one:

1. The runner with the lowest jersey number also ran the slowest time.
From this clue, we can deduce that the runner with the jersey number 2 ran for 14 minutes, as it is the slowest time.

2. Nick's jersey number is 18 greater than Carmen's.
Since Nick's number is greater than Carmen's and there is a difference of 18, we can conclude that Nick's jersey number must be 34, and Carmen's jersey number is 16.

3. Of the four runners, a man had the fastest finishing time.
This clue implies that Beki is not the one with the fastest time. So, Joey must have the fastest finishing time.

4. The sum of the digits on Beki's jersey number is 7.
The only number among the remaining options (13 and 20) that has a sum of digits equal to 7 is 20.

Now, let's summarize our deductions:

Nick: Jersey number 34, Time 12 minutes
Joey: Jersey number [Remaining], Time [Remaining]
Beki: Jersey number 20, Time [Remaining]
Carmen: Jersey number 16, Time [Remaining]

Since we know that Nick finished exactly 2 minutes faster than Beki, we can deduce that Beki's time must be 14 minutes.

Now, let's fill in the remaining information:

Nick: Jersey number 34, Time 12 minutes
Joey: Jersey number 13, Time [Remaining]
Beki: Jersey number 20, Time 14 minutes
Carmen: Jersey number 16, Time [Remaining]

Given that each person has a different time, we can conclude that Joey must have taken 10 minutes, leaving Carmen with 11 minutes.

Final Summary:

Nick: Jersey number 34, Time 12 minutes
Joey: Jersey number 13, Time 10 minutes
Beki: Jersey number 20, Time 14 minutes
Carmen: Jersey number 16, Time 11 minutes

Therefore, each person's jersey number and race time are as follows:

Nick: Jersey number 34, Time 12 minutes
Joey: Jersey number 13, Time 10 minutes
Beki: Jersey number 20, Time 14 minutes
Carmen: Jersey number 16, Time 11 minutes.

Answer 2

Let's analyze the given information and use deductive reasoning to determine each person's jersey number and race time:

1. The runner with the lowest jersey number also ran the slowest time.
Since the runner with the lowest jersey number ran the slowest time, we can eliminate jersey number 2 for the fastest time.

2. Nick's jersey number is 18 greater than Carmen's.
Nick's jersey number is 18 greater than Carmen's, which means that Nick's jersey number cannot be 2 or 13. This leaves us with jersey numbers 20 and 34 for Nick.

3. Of the four runners, a man had the fastest finishing time.
Since a man had the fastest finishing time, we can conclude that Beki is not the runner with the fastest time. Therefore, Beki's race time cannot be 10 minutes.

4. The sum of the digits on Beki's jersey number is 7.
We are looking for a two-digit number whose digits sum up to 7. The only possible option is jersey number 20.

Based on the above deductions, we can determine the following:

- Nick's jersey number must be 34 (as the remaining option).
- Carmen's jersey number is 18 less than Nick's, so it is 16.
- Joey's jersey number is the only remaining option, which is 2.
- Beki's race time is 11 minutes, as the remaining option.

Therefore, we have the following correspondences:

Nick - Jersey number: 34, Race time: 11 minutes
Joey - Jersey number: 2, Race time: ?
Beki - Jersey number: 20, Race time: 11 minutes
Carmen - Jersey number: 16, Race time: ?

By process of elimination, Joey's race time must be 14 minutes, and Carmen's race time must be 12 minutes.

So, the final correspondences are:

Nick - Jersey number: 34, Race time: 11 minutes
Joey - Jersey number: 2, Race time: 14 minutes
Beki - Jersey number: 20, Race time: 11 minutes
Carmen - Jersey number: 16, Race time: 12 minutes