At a certain supplier, a machine of

NandishSS wrote:At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the rremainderof the cost, how much less would 2 machines of type A cost than 1 machine of type B?

A. $10,000
B. $11,200
C. $12,000
D. $12,800
E. $13,200

OA:E

Source:GMATPrep

A: (full cost 20,000):
20% down payment = 4000.
Remainder = 16000.
Finance charges = 40% of 16,000 = 6400.
Total cost = 4000 + 16000 + 6400 = 26,400.
(Cost of 2 = 2*26,400 = 52,800.)

B: (full cost 50,000):
20% down payment =10,000.
Remainder = 40000.
Finance charges = 40% of 40,000 = 16,000
Total cost = 10,000 + 40,000 + 16,000 = 66,000

Difference = 66,000 - 52,800 = 13,200 The answer is E

A shortcut: the difference in price has two components. First, there's the difference in initial cost. Then there's the additional finance charge.

We're comparing 2 A's (initial cost = 40,000) and 1 B (initial cost = 50,000) So that's 10,000 difference

The finance charge is computed after a 20% downpayment has been made, so this charge is on 80% of the remaining cost. And the charge is 40% of this value. So we can compute the additional finance as follows 10,000 * .80 * .40 = 3200 difference

Difference in cost = 10,000 + 3200 = 13200.

NandishSS wrote:At a certain supplier, a machine of type A costs $20,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.If the finance charges= 40 percent of the rremainderof the cost, how much less would 2 machines of type A cost than 1 machine of type B?

A. $10,000
B. $11,200
C. $12,000
D. $12,800
E. $13,200

We are given that a machine of type A costs $20,000, and that a machine of type B costs $50,000. We are also given that each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time.

We need to determine the difference in cost between 2 machines of type A and 1 machine of type B.

Let’s determine the cost, with finance charges, of 1 machine of type A.

Down payment = 20,000 x 0.2 = 4,000
Remainder = 20,000 - 4,000 = 16,000

Since the remainder of the cost is 16,000, the finance charge is 0.4 x 16,000 = 6,400.

Thus, machine A would cost 20,000 + 6,400 = 26,400, and two machines of type A would cost 26,400 x 2 = 52,800.

Now we can calculate the cost, with finance charges, of 1 machine of type B.

Down payment = 50,000 x 0.2 = 10,000
Remainder = 50,000 - 10,000 = 40,000

Since the remainder of the cost is 40,000, the finance charge is 0.4 x 40,000 = 16,000.

Thus, 1 machine of type B would cost 50,000 + 16,000 = 66,000.

The difference in cost between 2 machines of type A and 1 machine of type B is:

66,000 - 52,800 = 13,200

Answer: E