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Manhattan GMAT Archive
06/24/02
Question
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.
Answer
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).