BosRoGMAT wrote:John is looking for $5100 for a new car. He gets a loan from both the bank and one from his friend. The funding from the bank is at 18% interest and from his friend at 16% interest. The interest amount is the same. How much did the bank give him total? Sums below I believe include interest + principal from bank. Remember interest amount is the same.
Reason for 6 choices is I believe I forgot one when I took the practice test but it was between 2400 and 2900.
A) 2400
B) 2500
C) 2600
D) 2700
E) 2800
F) 2900
How do you solve this?
A very quick way to solve:
Let B = amount from bank, F = amount from friend.
.18B = .16F.
B/F = 16/18 = 8/9.
Since 8+9=17, B = 8/17 of the total amount.
B = (8/17)*5100 = 2400.
The correct answer is A.
Another quick approach would be to plug in the answers, which represent the amount of the bank loan. The correct answer must be less than 5100/2 = 2550, because the interest rate from the bank is higher but the amounts of interest from the bank and from the friend are the same. Eliminate C, D, E and F.
Answer choice B:
B = 2500, F = 5100-2500 = 2600
.18B = .18*2500 = 450
.16F = .16*2600 = 416
Doesn't work. The interest amounts are not equal.
The correct answer must be A.
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