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Intern  Joined: 24 Jan 2014
Posts: 10
Schools: SMU Singapore
The cost per unit of electricity during a 4 year period is a  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 62% (02:30) correct 38% (02:16) wrong based on 245 sessions

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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, 22:18. Last edited by Bunuel on 08 Apr 2014, 01:31, edited 4 times in total. Edited the question ##### Most Helpful Community Reply VP  Joined: 02 Jul 2012 Posts: 1161 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Try this out! [#permalink] ### Show Tags 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

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Manager  Joined: 08 Nov 2014
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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

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

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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) _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Math Expert V Joined: 02 Aug 2009 Posts: 7415 Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 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.. _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html 4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html GMAT Expert Intern  Joined: 11 Oct 2012 Posts: 33 GMAT 1: 610 Q42 V32 Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags 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.

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

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

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

Hi Karishma,
Is there any mathematical principal for this ?
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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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 $24 Now, calculate the unit of electricity consumed. Unit of electricity consumed = Total Cost /Cost per unit of electricity Now, calculate the consumption Year wise- Year 1 = 6/1 =>6 units Year 2 = 6/1.5 => 4 units Year 3 = 6/1.2 => 5 units Year 4 = 6/2 => 3 units Total consumption during the four years is ( 6+4+5+3) 18 units. We are asked to find - Quote: the average cost of a unit of electricity during the 4 year period Average cost of a unit of electricity = Total cost of electricity during the 4 years / Total Consumption during the 4 years. Average cost of a unit of electricity = 24 /18 =>1.33 Hence answer is (A) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Board of Directors P Joined: 17 Jul 2014 Posts: 2562 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: The cost per unit of electricity during a 4 year period is a [#permalink] ### Show Tags bumped again into this question..started to consider some coefficients for units used..but then...considered 6$ 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
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Re: The cost per unit of electricity during a 4 year period is a  [#permalink]

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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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# The cost per unit of electricity during a 4 year period is a

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