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triple payment plan

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by Jay92 » Sat Apr 04, 2015 11:12 am
I found this question on the Gmatpill
"Marina is borrowing $10,930 from Peter under a special repayment plan. Starting from 12
months after the loan, Marina will repay $10 in the first month and each subsequent
month's repayment will be triple that of of the prior month's repayment. How many
months from the date she borrows will it take for Marina to repay her loan?"

(A)7
(B)13
(C)16
(D)17
(E)19

After lots of calculations I've answered A. But this is not correct.
How can I solve this in under two min. ?
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by DavidG@VeritasPrep » Tue Apr 07, 2015 8:36 am
Marina is borrowing $10,930 from Peter under a special repayment plan. Starting from 12
months after the loan, Marina will repay $10 in the first month and each subsequent
month's repayment will be triple that of of the prior month's repayment. How many
months from the date she borrows will it take for Marina to repay her loan?"

(A)7
(B)13
(C)16
(D)17
(E)19
Use the answer choices and a bit of logic. Marina isn't going to start paying off the loan until 12 months have passed, so A is out.

B: Her payment at 13 months will be $10. Clearly not enough. This is out.

C: Her payment schedule:
month 13 --> $10
month 14 ---> $30
month 15 ---> $90
month 16 ---> $270

The above numbers will clearly not sum to anything close to 10,390, so C is out.


D: Her payment schedule:
month 13 --> $10
month 14 ---> $30
month 15 ---> $90
month 16 ---> $270
month 17---> $810
Again, the sum will not be close to 10,390, so D is out.

We're left with E, which is the answer.
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by [email protected] » Tue Apr 07, 2015 11:43 am
Hi Jay92,

TESTing THE ANSWERS (David's approach) is a great way to tackle this problem. From a logical standpoint, there is another way to think about this though.

Since each payment is TRIPLE the payment that came before it, we're dealing with 'powers of 3'

eg.

1st payment = 10
2nd payment = (3^1)(10) = 30
3rd payment = (3^2)(10) = 90
Etc.

The LAST payment will be HUGE relative to all of the others, so we can focus on finding THAT payment (by counting the 'powers of 3' and multiplying by 10)

3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729 --> 7290 has got to be it (it's more than half of the $10,930 and the payment after this one would be too big).

This means that we have the first month ($10) and then 6 months of "triples" --> 7 months total AFTER the first 12 months have gone by. Total = 19 months.

Final Answer: E

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Rich
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