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The ACME company manufactured x brooms per month from Januar [#permalink]
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The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive? A. $x B. $3x C. $4x D. $5x E. $14x
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Originally posted by dcastan2 on 18 Dec 2012, 01:33.
Last edited by Bunuel on 10 Dec 2017, 09:51, edited 2 times in total.
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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18 Dec 2012, 02:33
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dcastan2 wrote: The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?
A. $x B. $3x C. $4x D. $5x E $14x Pick some smart number for \(x\), let \(x=2\) (I chose \(x=2\) as in this case monthly shipments would be \(\frac{x}{2}=1\)). From January to April, inclusive \(4x=8\) brooms were produced and in May the company paid for storage of 81=7 brooms, in next month for storage of 6 and so on. So the total storage cost would be: \(1*(7+6+5+4+3+2+1+0)=28\) > as \(x=2\), then \(28=14x\). Answer: E. Identical question from GMAT Prep to practice: acertainbusinessproducedxrakeseachmonthformnovember101738.html
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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20 Dec 2012, 11:04
In this case if x=4 then how the equation will turn out to be can you please explain
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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January  April : 4 months , so 4x brooms produced. From May its an A.P. with a = 3.5x (since we are counting from May 2nd, so 0.5x has already been sold on May 1st) d =  0.5 x So 8th Term (December ) is  a + 7d = 0 Sum of AP is (first term + last term) * n/2 = 3.5x * 8 / 2 = 14x Hence E
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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21 Dec 2012, 03:50



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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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21 Dec 2012, 04:12
your reply helped me a lot in understanding this question. Are there any 700 + level questions on geomenrty??
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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21 Dec 2012, 04:20



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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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23 Nov 2013, 06:29
Bunuel wrote: dcastan2 wrote: The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?
A. $x B. $3x C. $4x D. $5x E $14x Pick some smart number for \(x\), let \(x=2\) (I chose \(x=2\) as in this case monthly shipments would be \(\frac{x}{2}=1\)). From January to April, inclusive \(4x=8\) brooms were produced and in May the company paid for storage of 81=7 brooms, in next month for storage of 6 and so on. So the total storage cost would be: \(1*(7+6+5+4+3+2+1+0)=28\) > as \(x=2\), then \(28=14x\). Answer: E. Identical question from GMAT Prep to practice: acertainbusinessproducedxrakeseachmonthformnovember101738.htmlHi Bunuel, Can you please post an algebraic solution to this problem? I solved it plugging numbers, but I can't seem to do so algebraically. Thanks



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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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23 Nov 2013, 11:14
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ronr34 wrote: Can you please post an algebraic solution to this problem? I solved it plugging numbers, but I can't seem to do so algebraically. Thanks Hello ron We are given that on 1st of each month x brooms are made from Jan to Apr. that gives us \(4x\) brooms in inventory by end of April. On first of each month from May to December \(\frac{x}{2}\) brooms are sold. Therefore we will have \(4x\frac{x}{2} = \frac{7x}{2}\) brooms on May 2nd > storage cost is $1 per broom per month so in may the company pays \(\frac{7x}{2}\) Similarly we have \(\frac{7x}{2}\frac{x}{2} = \frac{6x}{2}\) brooms on June 2 > storage cost is \(\frac{6x}{2}\). July 2nd \(\frac{5x}{2}\) Continuing this we have \(\frac{x}{2}\) brooms left by Nov 2nd which are sold on Dec 1st, so no more brooms are left on Dec 2nd and no storage costs in december. By adding storage costs as derived above we get \(\frac{7x}{2}+\frac{6x}{2}+\frac{5x}{2}+\frac{4x}{2}+\frac{3x}{2}+\frac{2x}{2}+\frac{x}{2} = \frac{28x}{2} = 14x\) Hope this helps!
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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23 Nov 2013, 13:15
gmatprav wrote: ronr34 wrote: Can you please post an algebraic solution to this problem? I solved it plugging numbers, but I can't seem to do so algebraically. Thanks Hello ron We are given that on 1st of each month x brooms are made from Jan to Apr. that gives us \(4x\) brooms in inventory by end of April. On first of each month from May to December \(\frac{x}{2}\) brooms are sold. Therefore we will have \(4x\frac{x}{2} = \frac{7x}{2}\) brooms on May 2nd > storage cost is $1 per broom per month so in may the company pays \(\frac{7x}{2}\) Similarly we have \(\frac{7x}{2}\frac{x}{2} = \frac{6x}{2}\) brooms on June 2 > storage cost is \(\frac{6x}{2}\). July 2nd \(\frac{5x}{2}\) Continuing this we have \(\frac{x}{2}\) brooms left by Nov 2nd which are sold on Dec 1st, so no more brooms are left on Dec 2nd and no storage costs in december. By adding storage costs as derived above we get \(\frac{7x}{2}+\frac{6x}{2}+\frac{5x}{2}+\frac{4x}{2}+\frac{3x}{2}+\frac{2x}{2}+\frac{x}{2} = \frac{28x}{2} = 14x\) Hope this helps! I was able to do this calculation but I am looking for a general formula for cases like this.... Is there anything of the sort?



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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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24 Nov 2013, 06:58
ronr34 wrote: gmatprav wrote: ronr34 wrote: Can you please post an algebraic solution to this problem? I solved it plugging numbers, but I can't seem to do so algebraically.
Hello ron We are given that on 1st of each month x brooms are made from Jan to Apr. that gives us \(4x\) brooms in inventory by end of April. On first of each month from May to December \(\frac{x}{2}\) brooms are sold. Therefore we will have \(4x\frac{x}{2} = \frac{7x}{2}\) brooms on May 2nd > storage cost is $1 per broom per month so in may the company pays \(\frac{7x}{2}\) Similarly we have \(\frac{7x}{2}\frac{x}{2} = \frac{6x}{2}\) brooms on June 2 > storage cost is \(\frac{6x}{2}\). July 2nd \(\frac{5x}{2}\) Continuing this we have \(\frac{x}{2}\) brooms left by Nov 2nd which are sold on Dec 1st, so no more brooms are left on Dec 2nd and no storage costs in december. By adding storage costs as derived above we get \(\frac{7x}{2}+\frac{6x}{2}+\frac{5x}{2}+\frac{4x}{2}+\frac{3x}{2}+\frac{2x}{2}+\frac{x}{2} = \frac{28x}{2} = 14x\) Hope this helps! I was able to do this calculation but I am looking for a general formula for cases like this.... Is there anything of the sort? This problem is not a generic problem that warrants a formula. If you solved it like this then you are on right track. You mentioned how to do it without plugging in numbers Note that I did not plug in numbers. We can create a formula for similar problems, but in the end it will be harder to remember the formula than to solve it directly.
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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04 Apr 2014, 00:49
gmatprav wrote: ronr34 wrote: Can you please post an algebraic solution to this problem? I solved it plugging numbers, but I can't seem to do so algebraically. Thanks Hello ron We are given that on 1st of each month x brooms are made from Jan to Apr. that gives us \(4x\) brooms in inventory by end of April. On first of each month from May to December \(\frac{x}{2}\) brooms are sold. Therefore we will have \(4x\frac{x}{2} = \frac{7x}{2}\) brooms on May 2nd > storage cost is $1 per broom per month so in may the company pays \(\frac{7x}{2}\) Similarly we have \(\frac{7x}{2}\frac{x}{2} = \frac{6x}{2}\) brooms on June 2 > storage cost is \(\frac{6x}{2}\). July 2nd \(\frac{5x}{2}\) Continuing this we have \(\frac{x}{2}\) brooms left by Nov 2nd which are sold on Dec 1st, so no more brooms are left on Dec 2nd and no storage costs in december. By adding storage costs as derived above we get \(\frac{7x}{2}+\frac{6x}{2}+\frac{5x}{2}+\frac{4x}{2}+\frac{3x}{2}+\frac{2x}{2}+\frac{x}{2} = \frac{28x}{2} = 14x\) Hope this helps! Did in the same way ; with just a addition Wrote \(4x = \frac{8x}{2}\) for the simplicity of calculation & proceeded As denominator is same, just add the numerator & then divide by 2 Addition of 1 to 7; used formula \(\frac{n(n+1)}{2} = 7 * \frac{8}{2} = 28\) Dividing by 2 28/2 = 14
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Re: The ACME company manufactured x brooms per month from Januar [#permalink]
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dcastan2 wrote: The ACME company manufactured x brooms per month from January to April, inclusive. On the first of each month, during the following May to December, inclusive, it sold x/2 brooms. At the beginning of production on January 1st, the ACME company had no brooms in its inventory. If storage costs were $1 per month per broom, approximately how much, in terms of x, did the ACME company pay for storage from May 2nd to December 31st, inclusive?
A. $x B. $3x C. $4x D. $5x E $14x first, let's see how many x were manufactured. January X February X March X April X total manufactured: 4x May 1st sold 0.5x = remained till end of the month 3.5x  paid 3.5x for storage June 1st sold 0.5x = remained till end of the month 3x  paid 3x for storage July 1st sold 0.5x = remained till end of the month 2.5x  paid 2.5x for storage August 1st sold 0.5x = remained till end of the month 2x  paid 2x for storage September 1st sold 0.5x = remained till end of the month 1.5x  paid 1.5x for storage October 1st sold 0.5x = remained till end of the month 1x  paid 1x for storage November 1st sold 0.5x = remained till end of the month 0.5x  paid 0.5x for storage December 1st sold 0.5x = remained till end of the month 0x  paid 0. so total paid: 3.5x + 3x + 2.5x + 2x + 1.5x + 1x + 0.5x 3.5x + 2.5x = 6x 3x + 2x + 1x = 6x 1.5x + 0.5x = 2x 6x+6x+2x=14x answer is E.



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