# Thread: Set abc and positive integers

1. ## Set abc and positive integers

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.  Reply With Quote

2. Tricky!

Target question: Is the median of Set B greater than the median of Set A?

Once we have a hunch that the statements might not be sufficient, we can start looking for conflicting cases.

Let's jump right to . . .

Statements 1 + 2 combined:
Given the information, many different cases are possible. Here are two:

case a:
Set A: 1, 2, 5, 100 (mean = 27, median = 3.5)
Set B: (median = 5)
Set C: 1, 2, 100 (median = 2)
In this case, the median of Set B IS greater than the median of Set A?

case b:
Set A: 1, 3, 7, 7, 100 (mean = 24, median = 7)
Set B: 7, 7 (median = 7)
Set C: 1, 3, 100 (median = 3)
In this case, the median of Set B IS NOT greater than the median of Set A?

Since we can't answer the target question with certainty, the combined statements are NOT SUFFICIENT, so the answer is E

Cheers,
Brent  Reply With Quote