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Why is 1,4x the correct answer ?
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- GMATinsight
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Please find the explanation in the jpg file below: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
Answer: Option C
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- GMATinsight
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Alternative Approach: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
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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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.
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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Thank you all???Ah , it`s easy. For some reason I started with 4x and not 3,5x. Thank you all !
I thought there is just one responder for this question till now...
All the best!!!
"GMATinsight"Bhoopendra Singh & Sushma Jha
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- Brent@GMATPrepNow
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In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x)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
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
- sapuna
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You`re the type with the long username and multiple posts , I thought "you" were actually a few people xDGMATinsight wrote:Thank you all???Ah , it`s easy. For some reason I started with 4x and not 3,5x. Thank you all !
I thought there is just one responder for this question till now...
All the best!!!
- GMATGuruNY
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Let x=10.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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