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

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The table above shows daily energy usage for an office building and th  [#permalink]

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New post 20 Dec 2014, 06:06
2
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A
B
C
D
E

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Question Stats:

48% (03:03) correct 52% (03:17) wrong based on 147 sessions

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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

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Re: The table above shows daily energy usage for an office building and th  [#permalink]

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New post 20 Dec 2014, 18:13
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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.

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Re: The table above shows daily energy usage for an office building and th  [#permalink]

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New post 20 Dec 2014, 20:10
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.
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Re: The table above shows daily energy usage for an office building and th  [#permalink]

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New post 21 Dec 2014, 18:50
Hi PiyushK,

Most of the GMAT questions that you'll see on Test Day can be solved in a variety of ways, so beyond learning the "math approach" that the OG13/GMAT2015 usually emphasizes, it's important to practice the various tactical approaches too. Here, the question itself gives you a HUGE clue as to how to solve it...."what is the smallest possible value for N?" AND the answers are 5 numbers. Part of maximizing your performance on Test Day is in finding all the little clues that the GMAT writers leave for you...and then taking advantage of those clues.

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Re: The table above shows daily energy usage for an office building and th  [#permalink]

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New post 29 Mar 2015, 04:09
Please help me to understand this.
I got the below equation;

(115+8n/12+n)>9
here even 2(smallest value in answer choice) satisfies the equation


(115+16/14)>9
131>14*9
131>126

Then why 6 is the smallest value?
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Re: The table above shows daily energy usage for an office building and th  [#permalink]

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New post 29 Mar 2015, 04:28
ssriva2 wrote:
Please help me to understand this.
I got the below equation;

(115+8n/12+n)>9
here even 2(smallest value in answer choice) satisfies the equation


(115+16/14)>9
131>14*9
131>126

Then why 6 is the smallest value?


hi ssriva2,
the median value would depend on the value of n and would not be 9 in every case...
lets look at the table
units-days
11 -- 4
10 -- 5
8 -- n
7 -- 3...
or to find median , we can write it as
11,11,11,11,10,10,10,10,10,8..n times,7,7,7..
so if n+3<4+5... median is 10.. n can take values of 2,3,4,5....
but when n+3=4+5.. median will be(8+10)/2=9..
now substitue in your eqn to find answer...
eq 1 : (115 + 8N)/(12 + N) > 10, if n=2,3,4,5
eq 2: (115 + 8N)/(12 + N) > 9, if n=6..
only n=6 satisfies the eq..
hope it helped
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The table above shows daily energy usage for an office building and th  [#permalink]

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New post 15 Apr 2018, 13:47
chetan2u wrote:
ssriva2 wrote:
Please help me to understand this.
I got the below equation;

(115+8n/12+n)>9
here even 2(smallest value in answer choice) satisfies the equation


(115+16/14)>9
131>14*9
131>126

Then why 6 is the smallest value?


hi ssriva2,
the median value would depend on the value of n and would not be 9 in every case...
lets look at the table
units-days
11 -- 4
10 -- 5
8 -- n
7 -- 3...
or to find median , we can write it as
11,11,11,11,10,10,10,10,10,8..n times,7,7,7..
so if n+3<4+5... median is 10.. n can take values of 2,3,4,5....
but when n+3=4+5.. median will be(8+10)/2=9..
now substitue in your eqn to find answer...
eq 1 : (115 + 8N)/(12 + N) > 10, if n=2,3,4,5
eq 2: (115 + 8N)/(12 + N) > 9, if n=6..
only n=6 satisfies the eq..
hope it helped


Hi,
Can you explain how to find the median if have two related sets as in this case? And what if we had odd number of digits in the sets? Thanks
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The table above shows daily energy usage for an office building and th &nbs [#permalink] 15 Apr 2018, 13:47
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