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.

These kinds of questions can be solved taking suitable examples.

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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