Very difficult Problem....help?

[BosRoGMAT]

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?

[neerajkumar1_1]

he gets loan from bank and friend for a total of 5100

so let money from friend = f
and monry from bank = b

f + b = 5100

also given

0.16f = 0.18b ....... interest from both is same

put value of f from this equation in the first equation, u will get b= 2400
which is what we want..

Pick A

[BosRoGMAT]

I had a gut feeling of choosing A myself and I did....but I still don't understand how to solve it. Can you or anyone kindly take me step by step?

[neerajkumar1_1]

I had a gut feeling of choosing A myself and I did....but I still don't understand how to solve it. Can you or anyone kindly take me step by step?

well for starters understand the language of the problem and break it down into smaller parts..

We know that John is looking for financing his car of 5100...

so he picks up a loan from 2 sources...
what this means is that instead of taking a direct loan of 5100 from one source...

he splits the amount and takes from 2 diff sources...
here it is bank and friend...
so that total amount which he would have taken for loan will be the sum of the amounts from the 2 diff sources...
i.e b + f = 5100
where b = amt received from bank
and f = amount received from friend...

Also overall the quesstion asks to find that b component from the total loan...

Now its obvious that the question will give us some more data to solve the above equation...

What it says is that the interest amount is the same from the bank and friend...

interest amt from bank will be 18/100 * b
and while interest amt from friend will be 16/100 * f

this is because Interest = rate% * base amt... .

since they are same 18/100 b = 16/100 f
or f = 18/16b
now that we have a second equation... put this value inthe first and u will get ur answer...

Hope this Helps!!!!

[BosRoGMAT]

Got it, thanks!

The last part after you get 18/16B=F you are basically plugging in numbers from the answer choices to solve it. Thank god I guessed A.

[GMATGuruNY]

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.

[rehandossani]

Answer is A

x = Bank Loan
Friends Loan= 5100 - x

y = interest

18/100 * x = y
16/100 * (5100 - x) = y

solve both simultaneously, you will get x = 2400

[majorsheetal]

Thanks GMATGuruNY,

Your approach is always very quick and easy to understand..