Which cannot be true?

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Which cannot be true?

by LulaBrazilia » Fri Mar 07, 2014 10:55 am
S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements cannot be true?

A) The mean of S is equal to the mean of T.

B) The median of S is equal to the median of T.

C) The range of S is equal to the range of T.

D) The mean of S is greater than the mean of T.

E) The range of S is less than the range of T.

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by Patrick_GMATFix » Fri Mar 07, 2014 11:04 am
Good question; a good understanding of the concepts of mean median and range can allow us to solve it without having to plug-in multiple times. Since we're asked what cannot be true, we should do our best to think of scenarios that make each answer choice true. The answer is E. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by GMATGuruNY » Fri Mar 07, 2014 1:15 pm
LulaBrazilia wrote:S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements cannot be true?

A) The mean of S is equal to the mean of T.

B) The median of S is equal to the median of T.

C) The range of S is equal to the range of T.

D) The mean of S is greater than the mean of T.

E) The range of S is less than the range of T.
Let T = [1, 2, 3, 4, 5, 6, 7, 8}.
Let x = the value added to T to form S.

Try to prove that one of the answer choices CANNOT be true.
Answer choices C and E compare the range of S to the range of T.
Range = biggest - smallest.
The range of T = 8-1 = 7.

If 1<x<8, then S and T will have SAME RANGE, as in the following cases:
If x=1.5, then S = {1, 1.5, 2, 3, 4, 5, 6, 7, 8}, in which case the range of S = 8-1 = 7.
If x=7.5, then S = {1, 2, 3, 4, 5, 6, 7, 7.5, 8}, in which case the range of S = 8-1 = 7.
Since S and T can have the same range, eliminate C.

If x<1 or x>8, then S will have a GREATER range than T, as in the following cases:
If x=0, then S = {0, 1, 2, 3, 4, 5, 6, 7, 8}, in which case the range of S = 8-0 = 8.
If x=9, then S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, in which case the range of S = 9-1 = 8.

The cases above illustrate that there is no way for S to have a smaller range than T.
Thus, answer choice E cannot be true.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Mar 07, 2014 1:53 pm
LulaBrazilia wrote:S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements cannot be true?

A) The mean of S is equal to the mean of T.
B) The median of S is equal to the median of T.
C) The range of S is equal to the range of T.
D) The mean of S is greater than the mean of T.
E) The range of S is less than the range of T.
This is a "cannot be true", so if a statement CAN be true, we'll eliminate it.

A) The mean of S is equal to the mean of T.
How about...
S = {-4, -3, -2, -1, 0, 1, 2, 3, 4} Mean = 0
T = {-4, -3, -2, -1, 1, 2, 3, 4} Mean = 0
Since the mean of S CAN equal the mean of T, we can ELIMINATE A


B) The median of S is equal to the median of T.
How about...
S = {-4, -3, -2, -1, 0, 1, 2, 3, 4} Median = 0
T = {-4, -3, -2, -1, 1, 2, 3, 4} Median = 0
Since the median of S CAN equal the median of T, we can ELIMINATE B


C) The range of S is equal to the range of T.
How about...
S = {-4, -3, -2, -1, 0, 1, 2, 3, 4} Range = 8
T = {-4, -3, -2, -1, 1, 2, 3, 4} Range = 8
Since the range of S CAN equal the range of T, we can ELIMINATE C


D) The mean of S is greater than the mean of T.
How about...
S = {1, 2, 3, 4, 5, 6, 7, 8, 9} Mean = some positive value
T = {-8, -7, -6, -5, -4, -3, -2, -1} Mean = some negative value
Since the mean of S CAN be greater than the mean of T, we can ELIMINATE D


E) The range of S is less than the range of T.
No need to check E, since we've already eliminated A, B, C, and D

Answer: E

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