At a certain supplier, a machine of type A costs $20,000 and

1 machine of type B will cost: 20% down payment of 50,000 = 10,000 plus remaining sum (50,000-10,000=40,000) with 40% of finance charges 40,000*1.4=56,000 --> 10,000+56,000=66,000;

2 machine of type A will cost: 20% down payment of 2*20,000 = 8,000 plus remaining sum (40,000-8,000=32,000) with 40% of finance charges 32,000*1.4=44,800 --> 8,000+44,800=52,800;

Difference = 66,000 - 52,800 = 13,200.

Answer: E.
_________________

Let us set up a table as follows:



As you can clearly see, the difference = 66000-52800 = 13200.

Hence the answer is E.

2 A type machines cost: 40000.
20% down payment: 40000/5 = 8000
Remainder: 40000-8000=32000
Financial charges on remainder=32000*40/100=12800
Total money spent for 2 type A's = 12800+8000+32000=52800

1 B type machine cost: 50000
20% down payment: 50000/5=10000
Remainder: 50000-10000=40000
Financial charges on remainder=40000*40/100=16000
Total money spent for 1 type B = 16000+10000+40000=66000

Difference: 66000-52800=13200

Ans: "E"

The cost of 2 machines of type A is 40,000 while the cost of one machine of type B is 50,000.
The down payment and rate of interest are the same for both the cases. So all expenses will be same for both the cases except for the extra 10,000 to be paid in case of machine B and extra interest calculated as 40% of 8000 = 3200 (because out of 10,000, 20% down payment is 2000 and rest 8000 is the loaned amount)
So we need to pay a total of 13,200 extra in case of machine B.

E as well.
Although, is it ok to consider total cost at the end of payment period when there is no specific mention abt it?

Yes, it will be the cost at the end of the period. The question stem says
"how much less would 2 machines of type A cost than 1 machine of type B?"

Consider this: I want to buy a car - either a Camry or an Accord
Camry down payment 20%, 6% interest on rest
Accord down payment 15%, 6% interest on rest
price of Camry $$$, Price of Accord $$$ etc etc....
How much less would an Accord cost as compared to Camry?

It has to be the overall cost.

Cost of 2 Type A machines \(= 8000 + \frac{80}{100} * 40000 * \frac{140}{100}\)

Cost of Type B machine \(= 10000 + \frac{80}{100} * 50000 * \frac{140}{100}\)

Difference \(= 2000 + \frac{140}{100} * \frac{80}{100} * 10000 = 13200\)

Answer = E

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
_________________

Hi All,

This question is really just about basic arithmetic and staying organized. Based on the information in the prompt, there are two 'total costs' that we have to calculate...

Total cost of purchasing 2 Type A machines =

Base Price = (2)($20,000) = $40,000
The 20% down payment = (.2)(2)($20,000) = $8,000
40% Finance Charge on the remainder = (.4)($32,000) = $12,800

Total = $40,000 + $12,800 = $52,800

Total cost of purchasing 1 Type B machine =

Base Price = $50,000
The 20% down payment = (.2)($50,000) = $10,000
40% Finance Charge on the remainder = (.4)($40,000) = $16,000

Total = $50,000 + $16,000 = $66,000

The difference in those two totals is... $66,000 - $52,800 = $13,200

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Cost of N unit of Machine= Nx (20% downpayment + 80% remaining sum + 40% of the 80% remaining sum)
= Nx (cost of 100% machine + cost of 32% machine)
= N x (cost of 132% machine)

Cost of B Machine= 1x 132% x 50,000

Cost of A machines= 2 x 132% x 20,000=132% x 40,000

Cost of B machine-Cost of A machines= 132% x (50,000-40,000)=13,200

Answer: E

Lets Understand if we can find whats the FC :

DP = 20 % of CP
Remaining amount is = 80% CP
Finance Charges are = 40% (Remaining amount)= 40 % (80% CP)
Which means
Finance Charges are= 32% CP
Irrespective of Costs of Machine the Finance Charges are always 32% CP

The additional amount over the cost we are paying for each machine is 32% CP as Finance Charges
Total cost of machine would then be = Intial Cost Price + 32%CP
Total Buying Price of each machine = 132% CP




B- 2 (Type A) = 132% (Difference in Initial cost) = 132%( 50K -2(20K)) = 132% (10K) = 13200


Alternatively
Note :
Difference in cost + Difference in Finance charges

= 10K + 32% ( Difference in cost )= 13200

Total Cost Price of Two type A machines = 40K
Total Finance Charges of Type A = 32% (40K)

Total Cost of two Type A Machines: Total Cost Price of Two type A machines + Total Finance Charges of Type A = 40K +32%(40K)

Cost of Type B Machine= 50K
Finance Charges of Type B = 32% (50K)
Total Cost of Type B= 50K+32%(50K)
_________________

Down payment reduces the cost of the machine and Finance charges increase the cost of the machine.


Total Cost of Machine A = 20000 * 2 = 40,000

Total Cost of Machine B = 50,000


Difference in Cost = 50000 - 40000 = 10,000

20% Down payment = 0.2 * 10000 = 2,000


The finance charges are on Calculated on 10000 - 2000 = $8000


Difference in Finance charges = 40% of 8000 = 0.4 * 8000 = 3,200


Total Difference = 10000 + 3200 = $13,200


Option E

Arun Kumar
_________________

Given: 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.

Asked: If the finance charges= 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B?

Total cost of machine A = 20,000*20% + 20,000*80%*140% = 4000 + 16000 + 6400 = 26,400
Total cost of machine B = 50,000*20% + 50,000*80%*140% = 10,000 + 40,000 + 16,000 = 66,000
Total cost of machine B - 2* Total cost of machine A = 66,000 - 2*26,400 = 66,000 - 52,800 = 13,200

IMO E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________