A certain business produced x rakes each month form November

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imane81: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Wed Jan 13, 2010 7:17 pmFollowed by: 1 member; Thanked: 1 times

by imane81 » Tue Feb 09, 2010 3:38 pm

Your input here will be much appreciated. Thank you

A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?

A. 0.40x
B. 1.20x
C. 1.40x
D. 1.60x
E. 3.20x

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Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 3:38 pm

abhi332: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Dec 30, 2009 1:57 pmFollowed by: 1 member; Location: India; Thanked: 4 times

by abhi332 » Tue Feb 09, 2010 4:38 pm

In 4 months(Nov-Feb) company had produced = 4x

from march to oct , number of racks available = x * n/2(2a+(n-1)d) = x* |7/2(-2*3.5+(7-1)0.5)| -- negative sign as quantity decreases

from march to oct , number of racks available = x * 14

for march to oct expenditure will be = x * 14 * 0.1 = 1.4 x

therefore, ans is C

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Tue Feb 09, 2010 4:53 pm

imane81 wrote:Your input here will be much appreciated. Thank you

A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?

A. 0.40x
B. 1.20x
C. 1.40x
D. 1.60x
E. 3.20x

At the start of February we have 3.5 x rakes in storage and it pays .35x as storage fee
In march, similarly it pays 0.30x
... so on

Total storage fee paid = 0.35x + 0.30x +....+0.05x = 7/2(0.35+0.05)x = 1.4x

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Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Tue May 31, 2011 8:16 am

Can an Expert please explain this problem? Thanks

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Thouraya: Master | Next Rank: 500 Posts; Posts: 112; Joined: Wed Jan 20, 2010 5:46 am; Thanked: 1 times

by Thouraya » Tue May 31, 2011 8:17 am

Can an Expert please explain this problem? Thanks

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 31, 2011 8:35 am

imane81 wrote:Your input here will be much appreciated. Thank you

A certain business produced x rakes each month form November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months form November through October?

A. 0.40x
B. 1.20x
C. 1.40x
D. 1.60x
E. 3.20x

Let x=10.
Total rakes produced over 4 months November through February = 4*10 = 40.
From March through October, the number shipped = x/2 = 10/2 = 5 rakes per month.
Thus, starting in March, the number of rakes to be stored is reduced by 5 each month.
Thus, the number stored over the remaining 8 months March through October = 35+30+25+20+15+10+5+0 = 140.
Total storage cost at 10 cents per rake = 10*140 = 1400 cents = 14 dollars. This is our target.

Now we plug x=10 into the answers to see which yields our target of 14.

Only answer choice C works:
1.4x = 1.4*10 = 14.

The correct answer is C.

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winniethepooh: Master | Next Rank: 500 Posts; Posts: 370; Joined: Sat Jun 11, 2011 8:50 pmFollowed by: 2 members; Location: Arlington, MA.; Thanked: 27 times

by winniethepooh » Sun Jun 19, 2011 3:34 am

Is there an assumption here that the business pays no storage cost for the period of November to February?

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bblast: Legendary Member; Posts: 1077; Joined: Mon Dec 13, 2010 1:44 amFollowed by: 33 members; Thanked: 118 times; GMAT Score:710

by bblast » Tue Jul 05, 2011 1:28 am

Hi Mitch,

I failed to reach a solution in the cat as i took .40$ as the cost for march and not .35$. I know test pressure caused this error, however even looking at the question otherwise I am not too convinced about it. What if the march stuff was shipped on 31st march and we still had to pay the storage cost for all .40$ rakes ?

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Anaira Mitch: Master | Next Rank: 500 Posts; Posts: 235; Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members; Thanked: 3 times

by Anaira Mitch » Sat Jan 14, 2017 1:58 pm

Please find solution in algebraic form.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 14, 2017 2:04 pm

A certain business produced x rakes each month from November through February and shipped x/2 rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November to February, but it paid storage costs of 0.10$ per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?

A) 0.40x
B) 1.20x
C) 1.40x
D) 1.60x
E) 3.20x

In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x)

On March 1, x/2 rakes are SHIPPED, leaving 3.5x rakes for which the company must pay storage fees.
On April 1, x/2 rakes are SHIPPED, leaving 3x rakes for which the company must pay storage fees.
On May 1, x/2 rakes are SHIPPED, leaving 2.5x rakes for which the company must pay storage fees.
etc... (this pattern continues until no rakes remain).

The total NUMBER of rakes (for which storage fees are paid) = 3.5x + 3x + 2.5x . . . + 1x + 0.5x
= 14x

The charge is $0.1/rake, so the total FEE = (0.1)(14x) = [spoiler]1.4x = C[/spoiler]

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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