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The ACME company manufactured x brooms per month from Januar

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The ACME company manufactured x brooms per month from Januar [#permalink] New post 18 Dec 2012, 01:33
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Dec 2012, 02:28, edited 1 time in total.
Renamed the topic.
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Re: The ACME company manufactured x brooms per month from Januar [#permalink] New post 18 Dec 2012, 02:33
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 8-1=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: a-certain-business-produced-x-rakes-each-month-form-november-101738.html
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Re: The ACME company manufactured x brooms per month from Januar [#permalink] New post 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] New post 20 Dec 2012, 11:36
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] New post 21 Dec 2012, 03:50
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skamal7 wrote:
In this case if x=4 then how the equation will turn out to be can you please explain


Sure. Say x=4, in this case monthly shipments would be \frac{x}{2}=2. Then from January to April, inclusive 4x=16 brooms were produced and in May the company paid for storage of 16-2=14 brooms, in next month for storage of 12 and so on.

So the total storage cost would be: 1*(14+12+10+8+6+4+2+0)=56 --> as x=4, then 56=14x.

Answer: E.
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Re: The ACME company manufactured x brooms per month from Januar [#permalink] New post 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] New post 21 Dec 2012, 04:20
skamal7 wrote:
your reply helped me a lot in understanding this question.
Are there any 700 + level questions on geomenrty??


Check here: ds-question-directory-by-topic-difficulty-128728.html (DS) and here: gmat-ps-question-directory-by-topic-difficulty-127957.html (PS).

Hope it helps.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!, 11 New DS set. NEW!!!


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Re: The ACME company manufactured x brooms per month from Januar   [#permalink] 21 Dec 2012, 04:20
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