Hi JusTLucK04,
This question can be solved by TESTing THE ANSWERS. Before we get to that though, I'm going to re-create a real basic version of the "table" that you're describing:
En Used - # of Days:
11 --> 4
10 --> 5
8 --> N
7 --> 3
We're told that the AVERAGE daily use > MEDIAN daily use. We're then asked for the SMALLEST possible value of N.
The value of N will impact both the average and the median, but there is a pattern/shortcut worth noting:
If N = 2, 3, 4, or 5, then the MEDIAN = 10
If N = 6, then the Median = 9
The average of the numbers will be:
(115 + 8N)/(12 + N)
So we're really just looking for the SMALLEST relative value of N that will give us an average that is greater than 10 (in 4 of the options) or 9 (in the fifth option).
From here, we can either "brute force" the options to find the match or do some algebra to disprove the wrong answers.
Since 4 of the answers have the same median (10), I'm going to focus on THAT group. For the average to be > the median, we'd have...
(115 + 8N)/12 + N) > 10
115 + 8N > 10(12 + N)
115 + 8N > 120 + 10N
-2N > 5
N < -5/2
This tells us that N would have to be a NEGATIVE number, which is not possible. This eliminates answers A through D (since they're all POSITIVE and they all have the same median of 10).
Final Answer:
Here's the proof that it's the correct answer:
Since that answer would gives us a median of 9, we'd have...
(115 + 8N)/(12 + N) > 9
115 + 8N > 9(12 + N)
115 + 8N > 108 + 9N
7 > N
This is the only answer that gives us a range for N that includes the actual answer choice that generated the range.
GMAT assassins aren't born, they're made,
Rich