Interesting question

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Fri Jul 18, 2014 9:52 am

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

Please find the explanation in the jpg file below:

Answer: Option C

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Fri Jul 18, 2014 9:59 am

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

Alternative Approach:

Total Manufactured Rakes = 4x
Since the remaining rakes are in store for 7 months and the number of rakes are in Arithmatic Progression

Total months = 7 months with average rakes in store =(3.5x + 0.5x)/2 = x

(i.e. Storage average becomes x rakes for 14 months or 14x for a month)

so storage cost = 14x * 0.1 = 1.4x

Answer: Option C

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Fri Jul 18, 2014 10:01 am

Third Method:

Pick some number for x,

Say, x=2

From November to February, manufactured Rakes = 4x=8 rakes were produced and

In March business paid for storage of 8-1=7 rakes, in next month for storage of 6 and so on.

So total storage cost would be: 0.1(7+6+5+4+3+2+1)=2.8 --> as x=2, then 2.8 = 1.4x.

Answer: Option C.

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sapuna: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Thu Jul 17, 2014 11:04 am; Thanked: 3 times; Followed by:2 members

by sapuna » Fri Jul 18, 2014 10:21 am

Ah , it`s easy. For some reason I started with 4x and not 3,5x. Thank you all !

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Fri Jul 18, 2014 10:39 am

Ah , it`s easy. For some reason I started with 4x and not 3,5x. Thank you all !

Thank you all???

I thought there is just one responder for this question till now...

All the best!!!

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

by Brent@GMATPrepNow » Fri Jul 18, 2014 11:02 am

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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sapuna: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Thu Jul 17, 2014 11:04 am; Thanked: 3 times; Followed by:2 members

by sapuna » Fri Jul 18, 2014 11:20 am

GMATinsight wrote:
Ah , it`s easy. For some reason I started with 4x and not 3,5x. Thank you all !
Thank you all???

I thought there is just one responder for this question till now...

All the best!!!

You`re the type with the long username and multiple posts , I thought "you" were actually a few people xD

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

by GMATGuruNY » Fri Jul 18, 2014 1:58 pm

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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