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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # The cost per unit of electricity during a 4 year period is a  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 24 Jan 2014 Posts: 10 Schools: SMU Singapore The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags Updated on: 08 Apr 2014, 00:31 2 10 00:00 Difficulty: 75% (hard) Question Stats: 62% (02:29) correct 38% (02:16) wrong based on 241 sessions ### HideShow timer Statistics The cost per unit of electricity during a 4 year period is as follows: Year 1,$1 per unit;
Year 2, $1.5 per unit; Year 3,$1.2 per unit;
Year 4, $2 per unit. If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period? A.$1.333
B. $1.250 C.$1.425
D. $1.175 E.$1.500

Originally posted by Safal on 07 Apr 2014, 21:18.
Last edited by Bunuel on 08 Apr 2014, 00:31, edited 4 times in total.
Edited the question
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Re: Try this out!  [#permalink]

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07 Apr 2014, 21:23
8
1
Let money spent each year = 6 Units bought first year = 6 Units bought second year = 4 Units bought third year = 5 Units bought fourth year = 3 Total number of units = 18 Total money spent = 6*4 = 24 Average = 24/18 = 4/3 = 1.33 Answer is A _________________ Did you find this post helpful?... Please let me know through the Kudos button. Thanks To The Almighty - My GMAT Debrief GMAT Reading Comprehension: 7 Most Common Passage Types ##### General Discussion Manager Joined: 08 Nov 2014 Posts: 84 Location: India GPA: 3 WE: Engineering (Manufacturing) Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 13 Mar 2015, 10:51 1 [align=]It can be solved by weighted average formula, which is =( x1*n1+x2*n2+x3*n3+......................)/(n1+n2+n3+...............) where, x1,x2,x3 are values assigned and, n1,n2,n3 are the frequency or no. of repetition of x1,x2,x3 respwctively. As problem states: x1*n1=x2*n2=x3*n3=x4*n4 LCM of (x i )1,1.5,1.2,and 2 is 6 Therefore n1=6, n2=4, n3=5and n4= 3 Calculating average using above formula Avg.= 4*6/(6+4+5+3) = 1.33[/align] _________________ "Arise, Awake and Stop not till the goal is reached" Board of Directors Joined: 17 Jul 2014 Posts: 2645 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 15 Feb 2016, 18:55 my approach was to pick a number that would be easy to divide by all the prices given. suppose company spent 12 each year.
1st year - used 12 units
2nd year - 8 units
3rd year - 10 units
4th year - 6 units
total, we have 36 units.
since 12$/year was spent, in all 4 years was spent 48$.
now, avg price is total $/total # units = 48/36 = 4/3 or 1.33 A. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8531 Location: Pune, India Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 15 Feb 2016, 21:01 Safal wrote: The cost per unit of electricity during a 4 year period is as follows: Year 1,$1 per unit;
Year 2, $1.5 per unit; Year 3,$1.2 per unit;
Year 4, $2 per unit. If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period? A.$1.333
B. $1.250 C.$1.425
D. $1.175 E.$1.500

Here is another method for the more mathematically inclined. When we talk about equal amount of money spent, the average price is the harmonic mean of all the prices.

$$1/1 + \frac{1}{1.5} + \frac{1}{1.2} + \frac{1}{2} = \frac{4}{H}$$

$$\frac{6}{6} + \frac{4}{6} + \frac{5}{6} + \frac{3}{6} = \frac{4}{H}$$

$$H = \frac{4}{3} = 1.333$$

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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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15 Feb 2016, 23:56
1
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit; Year 2,$1.5 per unit;
Year 3, $1.2 per unit; Year 4,$2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333 B.$1.250
C. $1.425 D.$1.175
E. $1.500 Hi all, you cannot apply AVERAGE straightway as the units are not the same for each year, example the expense at$1 is higher than at $2.. Also we cannot apply weighted average as we have four quantities and that too in not proper form.. there can be two ways... arithmetic way choose a number, which is LCM of all four, say 6 here.. how much can you purchase Year 1,$1 per unit; ---- 6/1=6 units
Year 2, $1.5 per unit; -- 6/1.5=4 units Year 3,$1.2 per unit; -- 6/1.2=5 units
Year 4, $2 per unit. ---- 6/2=3 units... total units = 6+4+5+3=18 units.. cost incurred = 6*4=24.. avg cost= 24/18=1.333 Weighted average lets test weighted average for two pairs separately.. also since overall expenditure is same each year, the units will be proportional to cost.. 1)$1 and $2.. the ratio of units is 2:1, so the weighted average will be 1+(2-1)* 1/(1+2)= 1.333 2)$1.5 and %1.2..
ratio of units = 1.5:1.2...
so weighted average= 1.2 + 1.5/(1.2+1.5)= 1.2+(1.5-1.2)*1.5/2.7= 1.2 + 3*1.5/27= 1.2+ 1/6= 1.2+ 0.1333= 1.333..

now we have two quantities with the same average rate= 1.333,
so their combined averge rate will also be 1.333

NOTE:- the answer will be lesser than the average of the cost, as while doing so we take the qty at each price to be same, whereas the quantities are higher for lower values..
so average< (1+1.5+1.2+2)/4= 1.425.. you can straight way eliminate C and E..
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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16 Feb 2016, 07:08
VeritasPrepKarishma wrote:
Safal wrote:
The cost per unit of electricity during a 4 year period is as follows:

Year 1, $1 per unit; Year 2,$1.5 per unit;
Year 3, $1.2 per unit; Year 4,$2 per unit.

If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period?

A. $1.333 B.$1.250
C. $1.425 D.$1.175
E. $1.500 Here is another method for the more mathematically inclined. When we talk about equal amount of money spent, the average price is the harmonic mean of all the prices. $$1/1 + \frac{1}{1.5} + \frac{1}{1.2} + \frac{1}{2} = \frac{4}{H}$$ $$\frac{6}{6} + \frac{4}{6} + \frac{5}{6} + \frac{3}{6} = \frac{4}{H}$$ $$H = \frac{4}{3} = 1.333$$ Answer (A) Hi Karishma, Is there any mathematical principal for this ? Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4209 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 16 Feb 2016, 07:54 1 1 Safal wrote: The cost per unit of electricity during a 4 year period is as follows: Year 1,$1 per unit;
Year 2, $1.5 per unit; Year 3,$1.2 per unit;
Year 4, $2 per unit. If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period? A.$1.333
B. $1.250 C.$1.425
D. $1.175 E.$1.500

Since equal dollars is spent on electricity each year we take the LCM of 1, 1.2, 1.5 & 2 ; ie - 6

So, We get the factory spent $6 dollar each year ( Year 1 - Year 4 ), so during the 4 years they spent$ 24

Now, calculate the unit of electricity consumed.

Unit of electricity consumed = Total Cost /Cost per unit of electricity

Now, calculate the consumption Year wise-

Year 1 = 6/1 =>6 units

Year 2 = 6/1.5 => 4 units

Year 3 = 6/1.2 => 5 units

Year 4 = 6/2 => 3 units

Total consumption during the four years is ( 6+4+5+3) 18 units.

We are asked to find -
Quote:
the average cost of a unit of electricity during the 4 year period

Average cost of a unit of electricity = Total cost of electricity during the 4 years / Total Consumption during the 4 years.

Average cost of a unit of electricity = 24 /18 =>1.33

Hence answer is (A)

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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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25 Mar 2016, 17:51
bumped again into this question..started to consider some coefficients for units used..but then...considered 6$as total spent. I believe this is the LCM of 1, 1.5, 1.2, and 2. 1st year - 6 units 2nd year - 4 units 3rd year - 5 units 4th year - 3 units total = 18 units. total$ spent = 24$. 24/18 = 4/3 = 1.33 Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4170 Location: United States (CA) Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 15 Mar 2018, 09:09 Safal wrote: The cost per unit of electricity during a 4 year period is as follows: Year 1,$1 per unit;
Year 2, $1.5 per unit; Year 3,$1.2 per unit;
Year 4, $2 per unit. If a factory spent equal dollars on electricity each year, what was the average cost of a unit of electricity during the 4 year period? A.$1.333
B. $1.250 C.$1.425
D. $1.175 E.$1.500

We can assume the factory spent \$18 a year on electricity. Thus, it used

Year 1: 18 units of electricity

Year 2: 12 units of electricity

Year 3: 15 units of electricity

Year 2: 9 units of electricity

Therefore, the average cost per unit is:

(4 x 18)/(18 + 12 + 15 + 9)

72/54

4/3

1.333

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Re: The cost per unit of electricity during a 4 year period is a &nbs [#permalink] 15 Mar 2018, 09:09
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