Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Joan took out a mortgage from hel local bank. Each monthly [#permalink]
20 Apr 2012, 23:54

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

66% (03:06) correct
34% (01:59) wrong based on 143 sessions

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage?

Re: Need help with exponents problem (bothering me) [#permalink]
21 Apr 2012, 00:13

2

This post received KUDOS

Expert's post

jxatrillion wrote:

Joan took out a mortgage from her bank. Each monthly payment she makes must triple the amount of the previous month's payment. If her first payment is $100, and the total that she must pay back is $328,000, how many months will it take Joan to pay her mortgage?

The answer, according to Veritas is "8." I put 6, which seems to be incorrect. Really bothers me but if you guys can help... kudos!

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage? A. 6 B. 8 C. 10 D. 11 E. 13

Since her first payment is $100 and all subsequent payments must be three times as many as the payment for the previous month, then her monthly payments will be: $100; $300; $900; $2,700; ...

As you can see we have a geometric progression with the first term of 100 and the common ratio of 3. The sum of the first n terms of geometric progression is given by: sum=\frac{b*(r^{n}-1)}{r-1}, (where b is the first term, n # of terms and r is a common ratio \neq{1}).

So, \frac{100*(3^{n}-1)}{3-1}=$328,000 --> 3^n-1=6,560 --> 3^n=6,561. Now, the unit's digit of 3 in a positive integer power repeats in pattern of 4: {3, 9, 7, 1}. Since the last digit of 3^n is 1 then n can be 4 (3^4=81), 8, 12, ... only 8 is present among options.

Answer: B.

P.S. Please always post answer choices for PS problems and do not reword or shorten the questions. _________________

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]
21 Apr 2012, 05:59

1

This post received KUDOS

jxatrillion wrote:

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage?

Re: Need help with exponents problem (bothering me) [#permalink]
21 Apr 2012, 11:06

Bunuel wrote:

jxatrillion wrote:

Joan took out a mortgage from her bank. Each monthly payment she makes must triple the amount of the previous month's payment. If her first payment is $100, and the total that she must pay back is $328,000, how many months will it take Joan to pay her mortgage?

The answer, according to Veritas is "8." I put 6, which seems to be incorrect. Really bothers me but if you guys can help... kudos!

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage? A. 6 B. 8 C. 10 D. 11 E. 13

Since her first payment is $100 and all subsequent payments must be three times as many as the payment for the previous month, then her monthly payments will be: $100; $300; $900; $2,700; ...

As you can see we have a geometric progression with the first term of 100 and the common ration of 3. The sum of the first n terms of geometric progression is given by: sum=\frac{b*(r^{n}-1)}{r-1}, (where b is the first term, n # of terms and r is a common ratio \neq{1}).

So, \frac{100*(3^{n}-1)}{3-1}=$328,000 --> 3^n-1=6,560 --> 3^n=6,561. Now, the unit's digit of 3 in positive integer power repeats in pattern of 4: {3, 9, 7, 1}. Since the last digit of 3^n is 1 then n can be 4 (3^4=81), 8, 12, ... only 8 is present among options.

Answer: B.

P.S. Please always post answer choices for PS problems and do not reword or shorten the questions.

I apologize. I wasn't able to copy and paste from the online application so I must've missed something from typing it. Thank you for your and everyone's answers though. I really appreciate it.

I'm not sure how I got 6 now. Was just really bugging me how I didn't see 8 last night. Thanks again, team. _________________

Don't let a low GPA destroy your dreams of a business education.

Re: Need help with exponents problem (bothering me) [#permalink]
25 Sep 2012, 02:29

Bunuel wrote:

jxatrillion wrote:

Joan took out a mortgage from her bank. Each monthly payment she makes must triple the amount of the previous month's payment. If her first payment is $100, and the total that she must pay back is $328,000, how many months will it take Joan to pay her mortgage?

The answer, according to Veritas is "8." I put 6, which seems to be incorrect. Really bothers me but if you guys can help... kudos!

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage? A. 6 B. 8 C. 10 D. 11 E. 13

Since her first payment is $100 and all subsequent payments must be three times as many as the payment for the previous month, then her monthly payments will be: $100; $300; $900; $2,700; ...

As you can see we have a geometric progression with the first term of 100 and the common ratio of 3. The sum of the first n terms of geometric progression is given by: sum=\frac{b*(r^{n}-1)}{r-1}, (where b is the first term, n # of terms and r is a common ratio \neq{1}).

So, \frac{100*(3^{n}-1)}{3-1}=$328,000 --> 3^n-1=6,560 --> 3^n=6,561. Now, the unit's digit of 3 in a positive integer power repeats in pattern of 4: {3, 9, 7, 1}. Since the last digit of 3^n is 1 then n can be 4 (3^4=81), 8, 12, ... only 8 is present among options.

Answer: B.

P.S. Please always post answer choices for PS problems and do not reword or shorten the questions.

Hi Bunuel, I solved this question in 10 minutes by logic, but how do you get geometric progression formula, could you please give me any explainations? Thanks in advance

Re: Need help with exponents problem (bothering me) [#permalink]
25 Sep 2012, 05:52

Expert's post

mario1987 wrote:

Bunuel wrote:

jxatrillion wrote:

Joan took out a mortgage from her bank. Each monthly payment she makes must triple the amount of the previous month's payment. If her first payment is $100, and the total that she must pay back is $328,000, how many months will it take Joan to pay her mortgage?

The answer, according to Veritas is "8." I put 6, which seems to be incorrect. Really bothers me but if you guys can help... kudos!

Joan took out a mortgage from hel local bank. Each monthly mortgage payment she makes must be triple the amount of the previous month's payment. If her first payment is $100, and the total amount she must pay back is $328000, how many months will it take Joan to pay back her mortgage? A. 6 B. 8 C. 10 D. 11 E. 13

Since her first payment is $100 and all subsequent payments must be three times as many as the payment for the previous month, then her monthly payments will be: $100; $300; $900; $2,700; ...

As you can see we have a geometric progression with the first term of 100 and the common ratio of 3. The sum of the first n terms of geometric progression is given by: sum=\frac{b*(r^{n}-1)}{r-1}, (where b is the first term, n # of terms and r is a common ratio \neq{1}).

So, \frac{100*(3^{n}-1)}{3-1}=$328,000 --> 3^n-1=6,560 --> 3^n=6,561. Now, the unit's digit of 3 in a positive integer power repeats in pattern of 4: {3, 9, 7, 1}. Since the last digit of 3^n is 1 then n can be 4 (3^4=81), 8, 12, ... only 8 is present among options.

Answer: B.

P.S. Please always post answer choices for PS problems and do not reword or shorten the questions.

Hi Bunuel, I solved this question in 10 minutes by logic, but how do you get geometric progression formula, could you please give me any explainations? Thanks in advance

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]
27 Sep 2012, 22:41

Joan starts off with 100 $ .. which is to be tripled every month

Her monthly payments look like this :

100 , 300 , 900 , 2700 ......... Upto 328000

This can be re written as :

100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 ...... 100 x 3280

So we have 1 , 3 , 9 , 27 ..... 32800 in GP

We know that a =1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula Tn = a3^n-1 ...)

Therefore to find the Sum of n terms of a GP we use this formula :

Sn = a (1-r^n) / 1 -r

Using this and plugging in the information we get ...

3280 = 1 - 3^n / 1-3 ; 1-3^n / -2

Cross multiplying we get

3280 x -2 = 1- 3^n

- 6560 = 1 - 3^n

- 6561 = - 3 ^n

6561 = 3 ^n (negatives cancel out)

6561 can also be re written as 3 ^ 8

Therefore ; 3 ^8 = 3 ^n

Thus n = 8 (B) _________________

"When you want to succeed as bad as you want to breathe, then you’ll be successful.” - Eric Thomas

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]
19 Jul 2014, 01:56

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. _________________

It’s been a long time, since I posted. A busy schedule at office and the GMAT preparation, fully tied up with all my free hours. Anyways, now I’m back...

Ah yes. Funemployment. The time between when you quit your job and when you start your MBA. The promised land that many MBA applicants seek. The break that every...