Scenario A: At noon, you get some great news but you need to keep it a secret. I
ID: 3124072 • Letter: S
Question
Scenario A: At noon, you get some great news but you need to keep it a secret. It’s just too good to keep to yourself; so 5 minutes after you get the news you call 2 friends and tell them, but swear them to secrecy. They understand how important it is to keep a secret, so they don’t tell anybody. After 5 more minutes you call 2 more friends, and again they keep your secret. You are just so excited that after 5 more minutes you make your third set of calls and tell two more friends.
1. Complete the table below to show how many people are told and how many other people know the secret after each 5-minute interval.
Time
5 minute interval (n)
Number of other people told
Total number of other people know
12:05
1
2
2
12:10
2
2
4
12:15
3
2
12:20
4
12:25
5
12:30
6
12:35
7
12:40
8
12:45
9
12:50
10
12:55
11
1:00
12
2. How many other people know your secret at 12:40 PM?
3. After how many minutes would at least 100 other people know your secret?
4. According to the 2013 US Census, the population of NC is 9,848,060. After how many minutes could all the residents of NC know your secret?
Scenario B: Suppose you call the first two friends at 12:05 and you are satisfied because you’ve shared your secret, so you don’t tell anybody else. Unfortunately, none of your friends can keep a secret. Like you, they just need to tell two friends, but then each of those friends needs to tell two friends, and so on.
5. Complete the table below to show how many people are told and how many other people know the secret after each 5-minute interval.
Time
5 minute interval (n)
Number of other people told
Total number of other people know
12:05
1
2
2
12:10
2
4
6
12:15
3
8
12:20
4
12:25
5
12:30
6
12:35
7
12:40
8
12:45
9
12:50
10
12:55
11
1:00
12
6. How many other people know your secret at 12:40 PM?
7. After how many minutes would at least 100 other people know your secret?
8. According to the 2013 US Census, the population of NC is 9,848,060. After how many minutes could all the residents of NC know your secret?
Time
5 minute interval (n)
Number of other people told
Total number of other people know
12:05
1
2
2
12:10
2
2
4
12:15
3
2
12:20
4
12:25
5
12:30
6
12:35
7
12:40
8
12:45
9
12:50
10
12:55
11
1:00
12
Explanation / Answer
Scenario I)
1) Here it is said that after an interval of each 5 minutes, you call your two friends and tell the news that do not propogate it further. Based on this concept, the given table can be filled as :
2) By the table, it is cleared that till 12:40 p.m., total numbers of other people, that will know the secret will be 16.
3) By table, it is cleared that in each 10 minutes interval, total 4 new people, know the secret. Thus in this way, total 100 people will know this secret in 25 x 10 = 250 minutes, starting from 12:00 p.m. So its correct answer is 250 minutes.
4)
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