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JusTLucK04
GMAT 1: 730 Q51 V38
Posts: 270
20 Dec 2014, 07:06
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (03:12) correct
59%
(03:15)
wrong
based on 372
sessions
History
Date
Time
Result
Not Attempted Yet
Energy Usage Units - 11, 10, 8, 7
Number of Days of the respective unit- 4, 5, n, 3
The table above shows daily energy usage for an office building and the number of days that amount of energy was used. If the average (arithmetic mean) daily energy usage was greater than the median daily energy usage, what is the smallest possible value for n?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Number of Days of the respective unit- 4, 5, n, 3
The table above shows daily energy usage for an office building and the number of days that amount of energy was used. If the average (arithmetic mean) daily energy usage was greater than the median daily energy usage, what is the smallest possible value for n?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
20 Dec 2014, 19:13
Kudos
Bookmarks
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
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
General Discussion
20 Dec 2014, 21:10
Kudos
Bookmarks
I think testing the values is one of the convenient ways. Initially I wasted time thinking on strategy, but later found hit and trial much promising.
I got E, but spent approx 4-5 min on this.
I got E, but spent approx 4-5 min on this.
