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Set X consists of 10 integers and has median of 20 and a range of 20. What is the value of the greatest possible integer that can be present in the set?
- a)32
- b)37
- c)40
- d)43
- e)50
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Set X consists of 10 integers and has median of 20 and a range of 20. ...
Given: Median and Range
To Find: The greatest possible number
Let the lowest number be P and the greatest number be Q
Given:
- Range = 20
- Q – P = 20
- Q = 20 + P
Here we expressed Q (the highest value) in terms of P (the lowest value).
Therefore by finding the max value of P, we can find the max value of Q.
Now we know that the median = 20
- So, the greatest value which P can take = 20
- This means that at least 6 numbers in the given set of 10 numbers will have the same value of 20. This ways, when the 10 numbers are arranged in an ascending order, the median will be equal to half the sum of the 5th and 6th term. And so, will be equal to 20. The 7th, 8th and 9th terms (when the 10 numbers are arranged in an ascending order) can take any value between 20 and 40. The 10th term will be 40.
- That is, Q = 40
- Thus, the greatest integer that can be present in this set is 40.
Remember -The difference between any two numbers in a set cannot be greater than the range.
Answer: Option (C)
Most Upvoted Answer
Set X consists of 10 integers and has median of 20 and a range of 20. ...
Given information:
- Set X consists of 10 integers
- Median of X is 20
- Range of X is 20
To find:
- The greatest possible integer that can be present in the set X
Approach:
- Since the median of X is 20, there are 5 integers in the set that are less than or equal to 20, and 5 integers that are greater than or equal to 20.
- Let the smallest integer in the set be 'a'. Then, the largest integer in the set will be 'a+20'.
- We need to find the greatest possible integer that can be present in the set. Therefore, we need to find the maximum value of 'a+20' that satisfies the given conditions.
Calculation:
- Since there are 5 integers less than or equal to 20, the 5th integer will be 20.
- Similarly, since there are 5 integers greater than or equal to 20, the 6th integer will be 20.
- Therefore, the set can be represented as: {a, a+1, a+2, a+3, 20, 20, a+17, a+18, a+19, a+20}
- Since the range of the set is 20, we have: a+20 - a = 20
- Solving for 'a', we get: a = 1
- Therefore, the set can be represented as: {1, 2, 3, 4, 20, 20, 18, 19, 20, 21}
- The greatest possible integer in the set is 21.
Answer:
The greatest possible integer that can be present in the set is 21, which is not given in the options. However, the closest option is 'C' (40), which is incorrect. Therefore, the given question is flawed.
- Set X consists of 10 integers
- Median of X is 20
- Range of X is 20
To find:
- The greatest possible integer that can be present in the set X
Approach:
- Since the median of X is 20, there are 5 integers in the set that are less than or equal to 20, and 5 integers that are greater than or equal to 20.
- Let the smallest integer in the set be 'a'. Then, the largest integer in the set will be 'a+20'.
- We need to find the greatest possible integer that can be present in the set. Therefore, we need to find the maximum value of 'a+20' that satisfies the given conditions.
Calculation:
- Since there are 5 integers less than or equal to 20, the 5th integer will be 20.
- Similarly, since there are 5 integers greater than or equal to 20, the 6th integer will be 20.
- Therefore, the set can be represented as: {a, a+1, a+2, a+3, 20, 20, a+17, a+18, a+19, a+20}
- Since the range of the set is 20, we have: a+20 - a = 20
- Solving for 'a', we get: a = 1
- Therefore, the set can be represented as: {1, 2, 3, 4, 20, 20, 18, 19, 20, 21}
- The greatest possible integer in the set is 21.
Answer:
The greatest possible integer that can be present in the set is 21, which is not given in the options. However, the closest option is 'C' (40), which is incorrect. Therefore, the given question is flawed.
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