swerve wrote: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 to February, but it paid storage costs for $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. \(3.20x\)

The OA is C

Source: GMAT Prep

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) = 1.4x = C

Cheers,
Brent