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A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?
Correct answer is '77'. Can you explain this answer?
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A set of 17 distinct integers has a range of 34 and the median of this...
Median of the set = 51
The set contains 8 integers smaller than 51 and 8 integers greater than 51.
Now, for the highest possible number to be contained in this set, the lowest number in the set has to be maximized.
Thus, all the numbers in the set that are less than 51 need to be consecutive integers.
The maximum value of the lowest integer in the set = 51 - 8 = 43
Thus, the largest possible integer is 43 + 34 = 77 ... (v Range = 34)
Answer: 77
The set contains 8 integers smaller than 51 and 8 integers greater than 51.
Now, for the highest possible number to be contained in this set, the lowest number in the set has to be maximized.
Thus, all the numbers in the set that are less than 51 need to be consecutive integers.
The maximum value of the lowest integer in the set = 51 - 8 = 43
Thus, the largest possible integer is 43 + 34 = 77 ... (v Range = 34)
Answer: 77
Most Upvoted Answer
A set of 17 distinct integers has a range of 34 and the median of this...
Given:
- A set of 17 distinct integers
- The range of the set is 34
- The median of the set is 51
To find:
- The largest possible integer that such a set can contain
Approach:
- The range of a set is the difference between the largest and smallest values in the set.
- Since the range is given as 34, we can determine the smallest possible integer in the set.
- We know the median is 51, so there are 8 integers smaller than 51 and 8 integers larger than 51 in the set.
- To maximize the largest integer in the set, we need to make the 8 integers larger than 51 as large as possible.
- We can do this by setting the smallest integer in the set as 51 - 17 = 34.
- Now, we have 8 integers smaller than 51 and 8 integers larger than 51, with a range of 34.
Solution:
- We know the smallest integer in the set is 34.
- The largest integer in the set is given by adding the range to the smallest integer: 34 + 34 = 68.
- However, we need to ensure that all integers in the set are distinct.
- To do this, we can set the largest integer in the set as 1 more than the largest integer obtained above.
- Therefore, the largest possible integer that such a set can contain is 68 + 1 = 69.
Correction:
- I apologize for the incorrect answer provided earlier.
- The correct largest possible integer that such a set can contain is 69, not 77.
- A set of 17 distinct integers
- The range of the set is 34
- The median of the set is 51
To find:
- The largest possible integer that such a set can contain
Approach:
- The range of a set is the difference between the largest and smallest values in the set.
- Since the range is given as 34, we can determine the smallest possible integer in the set.
- We know the median is 51, so there are 8 integers smaller than 51 and 8 integers larger than 51 in the set.
- To maximize the largest integer in the set, we need to make the 8 integers larger than 51 as large as possible.
- We can do this by setting the smallest integer in the set as 51 - 17 = 34.
- Now, we have 8 integers smaller than 51 and 8 integers larger than 51, with a range of 34.
Solution:
- We know the smallest integer in the set is 34.
- The largest integer in the set is given by adding the range to the smallest integer: 34 + 34 = 68.
- However, we need to ensure that all integers in the set are distinct.
- To do this, we can set the largest integer in the set as 1 more than the largest integer obtained above.
- Therefore, the largest possible integer that such a set can contain is 68 + 1 = 69.
Correction:
- I apologize for the incorrect answer provided earlier.
- The correct largest possible integer that such a set can contain is 69, not 77.
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A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer?
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A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer?.
A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A set of 17 distinct integers has a range of 34 and the median of this set is 51. What is the largest possible integer that such a set can contain?Correct answer is '77'. Can you explain this answer?.
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