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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 remainder of 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
At a certain supplier, a machine of type A costs $20,000 and
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- fskilnik@GMATH
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Money values will be presented in thousands of dollars.AAPL wrote:GMAT Prep
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 remainder of 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
$$\left\{ \matrix{
\,A\,\,\, \to \,\,\,\,{\rm{each}}\,\,::\,\,\$ 20\,\,\,,\,\,\,{\rm{\$ 4}}\,\,{\rm{down}}\,\,{\rm{and}}\,\,{\rm{\$ 16}}\,\,{\rm{at}}\,\,{\rm{40\% }} \hfill \cr
\,B\,\,\, \to \,\,\,\,{\rm{each}}\,\,::\,\,\$ 50\,\,\,,\,\,\,{\rm{\$ 10}}\,\,{\rm{down}}\,\,{\rm{and}}\,\,{\rm{\$ 40}}\,\,{\rm{at}}\,\,{\rm{40\% }} \hfill \cr} \right.$$
$$?\,\,\, = B - 2A\,\, = \left[ {10 + 40 + {4 \over {10}}\left( {40} \right)} \right] - 2\left[ {4 + 16 + {4 \over {10}}\left( {16} \right)} \right] = 66 - 2\left( {20 + 6.4} \right) = 13.2\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)$$
This solution follows the notations and rationale taught in the GMATH method.
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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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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.AAPL wrote:GMAT Prep
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 remainder of 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
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 so 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
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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: E
GMAT assassins aren't born, they're made,
Rich
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: E
GMAT assassins aren't born, they're made,
Rich