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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
54% (01:28) correct
46%
(01:33)
wrong
based on 110
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Which of the following can be the median of four positive integers a, b, c, and d?
I. \(\frac{a + d}{2}\)
II. \(\frac{a+b+c}{3}\)
III. \(a+b+c\)
IV. \(a+b+c+d\)
A. I only
B. II only
C. I and II only
D. I and III only
E. II, III, and IV only
I. \(\frac{a + d}{2}\)
II. \(\frac{a+b+c}{3}\)
III. \(a+b+c\)
IV. \(a+b+c+d\)
A. I only
B. II only
C. I and II only
D. I and III only
E. II, III, and IV only
01 Sep 2024, 01:24
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To solve this problem, we need to understand the concept of the median for a set of four numbers
a, b, c, and d.
When the numbers are ordered in ascending order as a≤b≤c≤d, the median is defined as the average of the two middle numbers. Therefore, the median of the four numbers is given by:
Median = b+c/2
Option I:
[a+d][/2]
This expression is the average of the smallest and the largest numbers. It can only be the median if
b=a and c=d, meaning that the middle two numbers are equal to the smallest and largest numbers. While this situation is possible, it is quite specific. Therefore, this option can be the median in certain cases.
Option II:
[a+b+c ]/[/3]
This expression represents the average of the first three numbers. For this to be the median,
b+c must be equal to 2× [a+b+c[/3] which is not generally possible, but under certain conditions where a=b=c, this could be equal to
b or c. Therefore, this option can also be the median under specific conditions.
Option III:
a+b+c
This expression is a sum of the first three numbers. There is no scenario where the sum of three numbers could represent the median of four numbers. Therefore, this option cannot be the median.
Option IV:
a+b+c+d
This expression is the sum of all four numbers. There is no scenario where the sum of all four numbers could represent the median of four numbers. Therefore, this option cannot be the median.
Answer: C. I and II only
a, b, c, and d.
When the numbers are ordered in ascending order as a≤b≤c≤d, the median is defined as the average of the two middle numbers. Therefore, the median of the four numbers is given by:
Median = b+c/2
Option I:
[a+d][/2]
This expression is the average of the smallest and the largest numbers. It can only be the median if
b=a and c=d, meaning that the middle two numbers are equal to the smallest and largest numbers. While this situation is possible, it is quite specific. Therefore, this option can be the median in certain cases.
Option II:
[a+b+c ]/[/3]
This expression represents the average of the first three numbers. For this to be the median,
b+c must be equal to 2× [a+b+c[/3] which is not generally possible, but under certain conditions where a=b=c, this could be equal to
b or c. Therefore, this option can also be the median under specific conditions.
Option III:
a+b+c
This expression is a sum of the first three numbers. There is no scenario where the sum of three numbers could represent the median of four numbers. Therefore, this option cannot be the median.
Option IV:
a+b+c+d
This expression is the sum of all four numbers. There is no scenario where the sum of all four numbers could represent the median of four numbers. Therefore, this option cannot be the median.
Answer: C. I and II only
01 Sep 2024, 01:43
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The question says can be, so
If a,b,c,d are consecutive integers (ex-1,2,3,4)
Then (a+d)/2 is possible
If a,b,c or a,b,c,d are equal then option b is possible (ex- 1,1,1,4 or 1,1,1,1)
Option 3&4 are impossible.
Hence, answer is C
Posted from my mobile device
If a,b,c,d are consecutive integers (ex-1,2,3,4)
Then (a+d)/2 is possible
If a,b,c or a,b,c,d are equal then option b is possible (ex- 1,1,1,4 or 1,1,1,1)
Option 3&4 are impossible.
Hence, answer is C
Posted from my mobile device
