BTGmoderatorDC wrote:Each of the five divisions of a certain company sent representatives to a conference. If the numbers of representatives sent by four of the divisions were 3, 4, 5, and 5, was the range of the numbers of representatives sent by the five divisions greater than 2 ?
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
(2) The median of the numbers of representatives sent by the five divisions was 4.
OA C
Source: Official Guide
Let's take each statement one by one.
(1) The median of the numbers of representatives sent by the five divisions was greater than the average (arithmetic mean) of these numbers.
Assuming that the range is greater than 2; say, the number of representatives sent by the fifth division is x.
Case 1: Say x ≥ 6
So, the numbers of representatives sent by the five divisions in ascending order: 3, 4, 5, 5, x
Median = 5.
Thus, 5 > (3 + 4+ 5+ 5 + x)/5 => x < 8. It is a valid case.
Case 2: Say x ≤ 2
So, the numbers of representatives sent by the five divisions in ascending order: x, 3, 4, 5, 5
Median = 4.
Thus, 4 > (x + 3 + 4+ 5+ 5)/5 => x < 3. It is a valid case.
Case 3: Say x = 5
So, the numbers of representatives sent by the five divisions in ascending order: 3, 4, 5, 5, 5
Median = 5.
Thus, 5 > (3 + 4+ 5+ 5 + 5)/5 => 5 > 4.4. It is a valid case.
With case 3, the range is 5 - 3 = 2, not greater than 2.
No unique answer. Insufficient.
(2) The median of the number of representatives sent by the five divisions was 4.
Case 4: Say x = 3
So, the numbers of representatives sent by the five divisions in ascending order: 3, 3, 4, 5, 5
Median = 4. And range = 5 - 3 = 2, not greater than 2.
Case 4: Say x = 2
So, the numbers of representatives sent by the five divisions in ascending order: 2, 3, 4, 5, 5
Median = 4. And range = 5 - 2 = 3, greater than 2.
No unique answer. Insufficient.
(1) and (2) together
Only Case 2 is valid; thus, the range is greater than 2. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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