Problem Solving

swerve 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 are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?

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

The OA is E.

Source: GMAT Prep

Total cost of two machines of type A = 2(20,000 + 80%*20,000*40%) = 2(20,000 + 6400) = 2*26,400 = $52,800

Total cost of one machine of type B = 50,000 + 80%*50,000*40% = 50,000 + 16000 = $66,000

Two machines of type A would cost $66,000 - 52,000 = $13,200 less than one machine of type B under this arrangement.

The correct answer: E

Hope this helps!

-Jay
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swerve 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 are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?

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

Alternate solution:

We can see that the cost of 1 type B machine is 50,000 - 2 x 20,000 = $10,000 more than 2 type A machines. Of course, besides the extra $10,000, we also have to pay a finance charge on this amount. Since the 40% finance charge is only levied on the cost after the 20% down payment, we see that the 40% finance charge is only levied on 0.8 x 10,000 = $8,000. So the finance charge is 0.4 x 8,000 = $3,200. Therefore, with the finance charge, 1 type B machine costs 10,000 + 3,200 = $13,200 more than 2 type A machines.

Answer: E