Quantitative

[amanjena]

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

[GMATGuruNY]

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.

[Brent@GMATPrepNow]

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