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17 Oct 2025, 02:25
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:54) correct
35%
(02:06)
wrong
based on 133
sessions
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For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above
17 Oct 2025, 02:50
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Let the three numbers be
a, b, and c
Expression to compare:
(a+b+c)/3
I. Ordering the numbers from highest to lowest and selecting the middle number:
This is selecting the median of the three numbers.
The median is the middle value, but it is not always equal to the average, especially if the three numbers are not evenly spaced.
So statement I is not always equivalent to the average.
II. Dividing each of the numbers by 3 and then adding the results:
a/3 + b/3 + c/3 = (a+b+c)/3
This matches the average formula exactly.
Therefore, statement II is always equivalent.
III. Multiplying each number by 6, adding the result, then dividing the sum by 9:
(6a+6b+6c)/9 = 2(a+b+c)/3
This is 2/3 times the sum, not the average (unless the sum happens to be zero or other special cases).
Therefore, statement III is not equivalent to the average.
The correct answer is B: II only.
a, b, and c
Expression to compare:
(a+b+c)/3
I. Ordering the numbers from highest to lowest and selecting the middle number:
This is selecting the median of the three numbers.
The median is the middle value, but it is not always equal to the average, especially if the three numbers are not evenly spaced.
So statement I is not always equivalent to the average.
II. Dividing each of the numbers by 3 and then adding the results:
a/3 + b/3 + c/3 = (a+b+c)/3
This matches the average formula exactly.
Therefore, statement II is always equivalent.
III. Multiplying each number by 6, adding the result, then dividing the sum by 9:
(6a+6b+6c)/9 = 2(a+b+c)/3
This is 2/3 times the sum, not the average (unless the sum happens to be zero or other special cases).
Therefore, statement III is not equivalent to the average.
The correct answer is B: II only.
17 Oct 2025, 22:53
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We are given, three numbers:
Suppose these three numbers are a, b and c.
Now as per the question, we will add the three numbers and will divide it by 3,
So the expression will be like this:-
(a+b+c)/3
Now check each statement as per the question:-
Statement I:
Ordering the three numbers and choosing the middle number gives the median, not the mean.
Example:
If the numbers are 2, 5, and 10,
Mean = (2+5+10)/3 = 17/3 = 5.67
Median = 5
These are not the same, so Statement I is not always equivalent.
Statement II:
Dividing each number by 3 and then adding the results gives:
a/3+b/3+c/3 = (a+b+c)/3
This is exactly the same as the given operation.
So Statement II is equivalent.
Statement III:
Multiplying each number by 6 and then dividing the total by 9 gives:
(6a+6b+6c)/9 = 6(a+b+c)/9 = 2/3*(a+b+c)
This is not equal to (a+b+c)/3
So Statement III is not equivalent.
Final Answer:
Only Statement II is equivalent.
Answer: B. II only
Suppose these three numbers are a, b and c.
Now as per the question, we will add the three numbers and will divide it by 3,
So the expression will be like this:-
(a+b+c)/3
Now check each statement as per the question:-
Statement I:
Ordering the three numbers and choosing the middle number gives the median, not the mean.
Example:
If the numbers are 2, 5, and 10,
Mean = (2+5+10)/3 = 17/3 = 5.67
Median = 5
These are not the same, so Statement I is not always equivalent.
Statement II:
Dividing each number by 3 and then adding the results gives:
a/3+b/3+c/3 = (a+b+c)/3
This is exactly the same as the given operation.
So Statement II is equivalent.
Statement III:
Multiplying each number by 6 and then dividing the total by 9 gives:
(6a+6b+6c)/9 = 6(a+b+c)/9 = 2/3*(a+b+c)
This is not equal to (a+b+c)/3
So Statement III is not equivalent.
Final Answer:
Only Statement II is equivalent.
Answer: B. II only
