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GMAT/Data Sufficiency - The Middle Member
The Middle Member
Set A, Set B, and Set C each contain only positive integers. If Set A is composed entirely of all the members of Set B plus all the members of Set C, is the median of Set B greater than the median of Set A?
(1) The mean of Set A is greater than the median of Set B.
(2) The median of Set A is greater than the median of Set C.
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
ОТВЕТЫ И КОММЕНТАРИИ
Решение
From the question stem, we know that Set A is composed entirely of all the members of Set B plus all the members of Set C.
The question asks us to compare the median of Set A (the combined set) and the median of Set B (one of the smaller sets).
Statement (1) tells us that the mean of Set A is greater than the median of Set B. This gives us no useful information to compare the medians of the two sets. To see this, consider the following:
Set B: { 1, 1, 2 }
Set C: { 4, 7 }
Set A: { 1, 1, 2, 4, 7 }
In the example above, the mean of Set A (3) is greater than the median of Set B (1) and the median of Set A (2) is GREATER than the median of Set B (1).
However, consider the following example:
Set B: { 4, 5, 6 }
Set C: { 1, 2, 3, 21 }
Set A: { 1, 2, 3, 4, 5, 6, 21 }
Here the mean of Set A (6) is greater than the median of Set B (5) and the median of Set A (4) is LESS than the median of Set B (5).
This demonstrates that Statement (1) alone does is not sufficient toanswer the question.
Let's consider Statement (2) alone: The median of Set A is greater than the median of Set C.
By definition, the median of the combined set (A) must be any value at or between the medians of the two smaller sets (B and C).
Test this out and you'll see that it is always true. Thus, before considering Statement (2), we have three possibilities
Possibility 1: The median of Set A is greater than the median of Set B but less than the median of Set C.
Possibility 2: The median of Set A is greater than the median of Set C but less than the median of Set B.
Possibility 3: The median of Set A is equal to the median of Set B or the median of Set C.
Statement (2) tells us that the median of Set A is greater than the median of Set C. This eliminates Possibility 1, but we are still left with Possibility 2 and Possibility 3. The median of Set B may be greater than OR equal to the median of Set A.
Thus, using Statement (2) we cannot determine whether the median of Set B is greater than the median of Set A.
Combining Statements (1) and (2) still does not yield an answer to the question, since Statement (1) gives no relevant information that compares the two medians and Statement (2) leaves open more than one possibility.
Therefore, the correct answer is Choice (E): Statements (1) and (2) TOGETHER are NOT sufficient.
Some philosophers have argued that there exist certain human or natural rights
that belong to all human beings by virtue of their humanity. But a review of
the laws of different societies shows that the rights accorded a person vary
from society to society and even within a society over time. Since there is no
right that is universally
protected, there are no natural rights.
A defender of the theory that natural rights do exist might respond to this
objection by arguing that
A) some human beings do not have any natural rights
B) some human rights are natural, whereas others derive from a source such as a
constitution
C) people in one society may have natural rights that people in another society
lack
D) all societies have some institution that protects the rights of an
individual in that society
E) natural rights may exist even though they are not protected by some
societies
Вверх 
