A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.
The OA is C.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
A is a set containing 7 different numbers...
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- Jay@ManhattanReview
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These kinds of questions can be solved taking suitable examples.swerve wrote:A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.
The OA is C.
Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
Let's take each statement one by one.
A. The range of A is equal to the range of B.
Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 7, 9, 13}; Range of Set A = Range of Set B = 13 - 1 = 12. Can be true.
B. The mean of A is greater than the mean of B.
Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 7, 9, 11}; Mean of Set A = 7; Mean of Set B = (5 + 7)/2 = 6. Can be true.
C. The range of A is less than the range of B.
This is not possible since all the numbers in Set B are there in Set A, thus, it is possible that the range of Set B is less than the range of Set A, but visa-versa is not possible. This is the correct answer.
For the sake of understanding, let's discuss other options too.
D. The mean of A is equal to the mean of B.
Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 9, 11, 13}; Mean of Set A = 7; Mean of Set B = (5 + 9)/2 = 7. Can be true.
E. The median of A is equal to the median of B.
Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 9, 11, 13}; Median of Set A = 7; Median of Set B = (5 + 9)/2 = 7. Can be true.
The correct answer: C
Hope this helps!
-Jay
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Let B = {1, 3, 5, 7, 9, 11}A is a set containing 7 different numbers. B is a set containing 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
A) The range of A is equal to the range of B
B) The mean of A is greater than the mean of B
C) The range of A is less than the range of B
D) The mean of A is equal to the mean of B
E) The median of A is equal to the median of B
All of the members of B are also members of A.
Since A must include all of the values contained in B, its range cannot be smaller than B's range.
The correct answer is C.
A) The range of A is equal to the range of B
D) The mean of A is equal to the mean of B
E) The median of A is equal to the median of B
These options are possible if A = {1, 3, 5, 6, 7, 9, 11}
B) The mean of A is greater than the mean of B
This option is possible if A = {1, 3, 5, 7, 9, 11, 100}
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Since all of the number in set B are in set A, and A has 1 more number than set B, it would be impossible for the range of set A to be any less than set B.swerve wrote:A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?
A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.
Answer: C
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