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Directions: Select one of the following answer choices.
Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.
Quantity A: The median of the 24 integers
Quantity B: 50
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
- d)The relationship cannot be determined from the information given.
Correct answer is option 'D'. Can you explain this answer?
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Directions: Select one of the following answer choices.Q. In a set of...
Understanding the problem:
We are given a set of 24 positive integers. Out of these, 12 integers are less than 50, and the rest are greater than 50. We need to determine the relationship between the median of the 24 integers and the number 50.
Solution:
To begin solving this problem, let's first understand what the median of a set of numbers is. The median is the middle value in a set of numbers when they are arranged in ascending or descending order. If the number of elements in the set is odd, the median is the middle value. If the number of elements is even, the median is the average of the two middle values.
Case 1: 12 integers less than 50 and 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have 12 numbers less than 50 followed by 12 numbers greater than 50. The median will be the average of the 12th and 13th numbers, which will be greater than 50. So, in this case, Quantity A (the median of the 24 integers) will be greater than Quantity B (50).
Case 2: More than 12 integers less than 50 and less than 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have more than 12 numbers less than 50 followed by less than 12 numbers greater than 50. The median will be the middle value, which will be less than 50. So, in this case, Quantity A (the median of the 24 integers) will be less than Quantity B (50).
Case 3: Less than 12 integers less than 50 and more than 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have less than 12 numbers less than 50 followed by more than 12 numbers greater than 50. The median will be the middle value, which will be greater than 50. So, in this case, Quantity A (the median of the 24 integers) will be greater than Quantity B (50).
Case 4: Exactly 12 integers less than 50 and exactly 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have exactly 12 numbers less than 50 followed by exactly 12 numbers greater than 50. The median will be the average of the 12th and 13th numbers, which could be equal to 50. So, in this case, Quantity A (the median of the 24 integers) could be equal to Quantity B (50).
Conclusion:
Based on the analysis of different cases, the relationship between Quantity A (the median of the 24 integers) and Quantity B (50) cannot be determined from the given information. Therefore, the correct answer is option 'D'.
We are given a set of 24 positive integers. Out of these, 12 integers are less than 50, and the rest are greater than 50. We need to determine the relationship between the median of the 24 integers and the number 50.
Solution:
To begin solving this problem, let's first understand what the median of a set of numbers is. The median is the middle value in a set of numbers when they are arranged in ascending or descending order. If the number of elements in the set is odd, the median is the middle value. If the number of elements is even, the median is the average of the two middle values.
Case 1: 12 integers less than 50 and 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have 12 numbers less than 50 followed by 12 numbers greater than 50. The median will be the average of the 12th and 13th numbers, which will be greater than 50. So, in this case, Quantity A (the median of the 24 integers) will be greater than Quantity B (50).
Case 2: More than 12 integers less than 50 and less than 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have more than 12 numbers less than 50 followed by less than 12 numbers greater than 50. The median will be the middle value, which will be less than 50. So, in this case, Quantity A (the median of the 24 integers) will be less than Quantity B (50).
Case 3: Less than 12 integers less than 50 and more than 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have less than 12 numbers less than 50 followed by more than 12 numbers greater than 50. The median will be the middle value, which will be greater than 50. So, in this case, Quantity A (the median of the 24 integers) will be greater than Quantity B (50).
Case 4: Exactly 12 integers less than 50 and exactly 12 integers greater than 50:
In this case, if we arrange the numbers in ascending order, we will have exactly 12 numbers less than 50 followed by exactly 12 numbers greater than 50. The median will be the average of the 12th and 13th numbers, which could be equal to 50. So, in this case, Quantity A (the median of the 24 integers) could be equal to Quantity B (50).
Conclusion:
Based on the analysis of different cases, the relationship between Quantity A (the median of the 24 integers) and Quantity B (50) cannot be determined from the given information. Therefore, the correct answer is option 'D'.
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Directions: Select one of the following answer choices.Q. In a set of...
In general, the median of a set of n positive integers, where n is even, is obtained by ordering the integers from least to greatest and then calculating the average (arithmetic mean) of the two middle integers. For this set of 24 integers, you do not know the values of the two middle integers; you know only that half of the integers are less than 50 and the other half are greater than 50. If the two middle integers in the list are 49 and 51, the median is 50; and if the two middle integers are 49 and 53, the median is 51. Thus the relationship cannot be determined from the information given, and the correct answer is Choice D.
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Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer?
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Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer?.
Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer? for GRE 2024 is part of GRE preparation. The Question and answers have been prepared according to the GRE exam syllabus. Information about Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GRE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Directions: Select one of the following answer choices.Q. In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.Quantity A: The median of the 24 integersQuantity B: 50a)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GRE.
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