There are 1000 magical beanstalks planted in a row. Each stalk is 10 feet taller
There are 1000 magical beanstalks planted in a row. Each stalk is 10 feet taller than the one before it. The smallest stalk is 10 feet tall. What is the median height of the stalks?
- A. 5005 ft
- B. 5000 ft
- C. 750 ft
- D. No median can be calculated
Correct Answer: A. 5005 ft
Explanation
The first thing to do is figure out which stalk is in the middle. Since there are an even number of stalks, there is no exact middle; there are 500 on one side and 500 on the other. This means that the 500th and the 501st are the median. These will have to be averaged. Now, we need to determine the height of these two stalks. Consider the pattern given: 1st stalk: 10 feet 2nd stalk: 20 feet 3rd stalk: 30 feet 4th stalk: 40 feet You should see the pattern that emerges for this problem. Each stalk is 10 times that stalk's place in the row. This means that the 500th stalk will be: 500?10=5000 The 501st stalk will be: 501?10=5010 The average of these two numbers is: 5000+5010/2= 10010/2=5005 5005 feet is the median.