During 2005, a company produced an average of 2,000 products

We need to determine how many products a company will need to produce in order to increase its monthly average of 2,000 products by 200% for the period from 2005 through 2008. Thus, the average has to increase to 3 x 2,000 = 6,000 products.

Since the company produced an average of 2,000 products per month in 2005, the company produced 2,000 x 12 = 24,000 products in 12 months of 2005 (or in all of 2005).

We can let x = the total number of products made from 2006 through 2008, and we know the number of months from 2005 through 2008 is 4 x 12 months = 48 months. Now let’s use the average equation to determine x:

6,000 = (24,000 + x)/48

288,000 = 24,000 + x

x = 264,000

Answer: D

I have a slightly different approach to this exercise:


The final monthly mean has to be 6,000 (200% of 2,000) for the 4-year period, so plugging in the mean formula:

\(Mean =\frac{2,000*12 + x*36}{48}=6000\)

And they are asking for the number of units sold during the last 3-year period in order to get to that mean value, the asked value therefore is \(x*36\).

\(6,000*48 = 24,000+36*x\)

\(36*x=6*10^3*48-24*10^3\)

\(36*x=24*(12*10^3-10^3)\)

\(36*x=24*(11*10^3)\)

\(36*x=264*10^3\) --> Answer D

The current average is 2,000/month and it's asking how many we'd have to produce from 2006 through 2008 to come to a final average from 2005-2008 of 200% more than that 2,000/month.

3(36{2,000}) = 24,000 + 24x... the left side of the equal sign gives me 300% (or 200% MORE) of the three-year total of the 2,000/month average. The right side of the equal sign gives me the 2005 production of 2,000/month plus the 2006-2008 ungiven average per month.

For some reason, though, my equation comes to x=8,000 and 8,000 each month for the 24 months of 2006-2008 is 192,000. Just another 8,000 short of the quota. I can't figure out where I'm messing up, but it's got to be something small.

Any idea anyone?

Four years! I can't believe I missed that. Should have gotten it. I was only figuring three years in 2005-2008. Ugh! Thanks, man.

Hi All,

Although the prompt does not explicitly state it, we're meant to infer that the company continues to produce products EVERY month (in the years 2005 through 2008, inclusive). A 200% increase in the monthly average (from 2005) would be 6,000 products per month for the ENTIRE 4-YEAR period.

Thus, the TOTAL number of products produced during those 4 years would have to be (48 months)(6,000 products/month) = 288,000 products.

In 2005, the total number of products produced was (12 months)(2,000 products/month) = 24,000 products.

To hit the 288,000 product grand total, the company would have to produce 288,000 - 24,000 = 264,000 products in the years 2006 - 2008.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

I was trying to solve this by differentials but couldn't. Would anybody tell me where I'm going wrong here?

OK so we have that 1 year, average is 2k
We need the total average to rise to 6k in the last 3 months

Therefore we have: -4(1) + 3x = 0

x = 4/3. Now this tells us that 4/3 should be the differential. Therefore 6 + 4/3 = 22/3 is supposed to be the key point. That is 22/3*1000, but it doesn't make any sense in the context of the answer choices

Many thanks
Hope its clear

Cheers
J

Sum in 2005: \(2*12000=24000\)
Required average of 200% for 1 year: \(6000*12=72000\) --> means we need 24.000+48.000 to get 72.000 in 2005
=> 3*72.000 + 48.000 = 264.000

Hi,

I have solved this question by weighted average that is,

6000 = x + 2000*12/36+12 -->x=264,000

is it right??

hi, it seems to me that the rule of average and weigh cannot be applied to this question. I have tried and failed. Also, I think conventional calculation is the best fit to solve this question.

Since all the numbers in answer choices are in form of abc000, we can safely divide all numbers in our calculations by 1,000.

Then:
2,000 (monthly average for 2005) = 2
6,000 (monthly average for 2005 - 2008) = 6

Monthly average for 2005-2008:
(1*2+ 3*x)/4 = 6, where 1 is one year (2005) and 3 is 3 years (2006, 2007, 2008); 4 = 4 years for average; 2 - monthly average for 2005; x - monthly average for any of the rest 3 years.

x = 7+1/3

To find produced products over 12*3 months during 2006-2008, we simply multiply x by 12*3:
(7+1/3) * 3 * 12 = 264

Now, in our abc000 abc=264 -> D

Why are we using 4 years? 2005 through 2008 i assumed meant 2005-2006, 2006-2007 & 2007-2008?

Is X through Y then always including the last year, Y as well?

Hi,
here are my two cents for this questions.

The deviation technique.

Let us assume that average goods produced per month from in 2006, 2007, 2008 be 2000 per month .

6000=2000+\(\frac{n}{4}\)

n =16000

this 16000 gets divided by 3 years and add this to assumed per month . we get 7333.3 per month in each of year 2006, 2007 and 2008 .

So no of goods produced will be ( \(\frac{16000}{3}\) + 20000 ) * 36 = 264000

Alternatively

So for all three years combined we have Assumed average 2000 per month. =2000+2000+2000= 6000

Let n be difference between Actual - Assumed

6000=2000+\(\frac{n}{4}\)

n=16000

So actual cumulative average per month ( average number of goods produces per month in 2006 + average number of goods produces per month in 2007+ average number of goods produces per month in 2008)=> 16000+6000 = 22000

So in a year we would produce 22000*12= 264000.

So if we produces 264000 goods from 2006 to 2008 then the average goods produced from 2005 to 2008 would be 6000 per month.

Let x = # of products manufactured in 2006 - 2008. Need x?

To simplify calculations, don't include 1000.

# of products in 2005 = 2* 12 = 24
Total months = 48
New Average = (24 + x)/48 = 6
x = 288 - 24 = 264

ANSWER: D

given that avg in 2005 is 2000 per month ;
so an increase of 200% ; 2000+2000*(200/100) ; 6000 per month
period 2005 through 2008 ; 48 months
so total ∆ increase required ; ( 6000*48) - (2000*12) ; 264000
OPTION D

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Ignore the 000s. Say monthly avg in 2005 was 2. A 200% increase means the new average should be 6.

So the number of products added should provide the extra 4 for the 12 months of 2005 and should provide 6 each for every one of the 36 months from 2006 to 2008.

Hence, number of products added = 12*4 + 36*6 = 264

Answer (D)

­
Why can't we simply do this to find no. products from 2006-2008 --> 6000 x 3 (years) x 12 (months) = 216000­. Can please somebody help me to understand the question.