The table above shows daily energy usage for an office building and th

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