GMAT Prep - Equations

[rickyishere]

A certain business produced x rakes each month from November through February and shipped x/2 rakes at the begining of each month from March to October. The business paid no storage costs for the rakes from November to February but paid $.10 per rake each month March through October for rakes that had not been shipped. In terms of x , what was the storage cost in dollars the business paid for rakes for the 12 months from November - October?

a) .4x
b) 1.2x
c) 1.4x
d) 1.6x
e) 3.2x

Thanks
-Ricky

[kprabhala.mba]

A certain business produced x rakes each month from November through February and shipped x/2 rakes at the begining of each month from March to October. The business paid no storage costs for the rakes from November to February but paid $.10 per rake each month March through October for rakes that had not been shipped. In terms of x , what was the storage cost in dollars the business paid for rakes for the 12 months from November - October?

a) .4x
b) 1.2x
c) 1.4x
d) 1.6x
e) 3.2x

Thanks
-Ricky

The total number rakes produced from Nov to Feb is 4x. The rakes that are *not* shipped for each month from Mar to Oct can be calculated as follows:
(4x - x/2) + (4x - x) + (4x - 3x/2) + (4x - 4x/2) + (4x - 5x/2) + (4x - 6x/2) + (4x - 7x/2) + (4x - 8x/2) = 14x.

Therefore the storage cost = 14x * 0.1 = 1.4x

Answer: C

[GMATGuruNY]

A certain business produced x rakes each month from November through February and shipped x/2 rakes at the begining of each month from March to October. The business paid no storage costs for the rakes from November to February but paid $.10 per rake each month March through October for rakes that had not been shipped. In terms of x , what was the storage cost in dollars the business paid for rakes for the 12 months from November - October?

a) .4x
b) 1.2x
c) 1.4x
d) 1.6x
e) 3.2x

Thanks
-Ricky

Plug in x=10.
Total rakes produced in 4 months = 4*10 = 40.
For each month thereafter, the number shipped = x/2 = 10/2 = 5 rakes per month.
Thus, starting in March, the number that needs to be stored is reduced by 5 each month.
Thus, the number stored over the remaining 8 months = 35+30+25+20+15+10+5+0 = 140.
Cost = 10*140 = 1400 cents = 14 dollars. This is our target.

Now we plug x=10 into all 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.