Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 11 Mar 2014, 12:52

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Joan took out a mortgage from hel local bank. Each monthly

Author Message
TAGS:
Manager
Joined: 30 Mar 2012
Posts: 120
Location: United States (TX)
Concentration: Strategy, Entrepreneurship
GMAT Date: 09-14-2013
GPA: 2.64
WE: General Management (Consumer Electronics)
Followers: 3

Kudos [?]: 30 [0], given: 11

Joan took out a mortgage from hel local bank. Each monthly [#permalink]  20 Apr 2012, 23:54
00:00

Difficulty:

25% (low)

Question Stats:

77% (02:59) correct 22% (01:16) wrong based on 86 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?

A. 6
B. 8
C. 10
D. 11
E. 13

[Reveal] Spoiler:
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!
[Reveal] Spoiler: OA

_________________

Stats by August 2014
28, Asian-American, Raised in the Bronx, NY. Moved to Houston by myself to graduate HS.
2.64 (downward trend) Economics degree from UT-Austin in Dec. 2009. No excuse, I spent 100% building a student organization that I'm still very active with today.
GMAT Goal: 710+, exam scheduled for September 14, 2013 at 8AM CST

WE: Sales Team Manager at Apple - business development and strategies for the Apple Online Store, Australia. I've also built my own consulting practice working with a successful Startup in Austin, TX, managing their online brand and helping them with analytics.
Post-MBA Goals: Strategy Consulting or Brand Management in Tech/Fashion

EC: 3 years of National Council on Fraternity (VP, President), Current Chairman of Texas Exes, Asian Alumni Network (2012-2014)
Target: (1) Stern (2) Fuqua (3) McCombs (FT/PT)
Giving this 110%. I appreciate all advice and encouragement. Thank you, everyone.

Last edited by Bunuel on 21 Apr 2012, 00:08, edited 1 time in total.
 Veritas Prep GMAT Discount Codes Knewton GMAT Discount Codes Kaplan GMAT Prep Discount Codes
Math Expert
Joined: 02 Sep 2009
Posts: 16899
Followers: 2778

Kudos [?]: 17665 [2] , given: 2235

Re: Need help with exponents problem (bothering me) [#permalink]  21 Apr 2012, 00:13
2
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?

[Reveal] Spoiler:
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.

P.S. Please always post answer choices for PS problems and do not reword or shorten the questions.
_________________
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 237
Schools: Johnson '15
Followers: 2

Kudos [?]: 19 [1] , given: 16

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  21 Apr 2012, 05:59
1
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?

A. 6
B. 8
C. 10
D. 11
E. 13

[Reveal] Spoiler:
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!

followed long manual method of calculating the amount
1st month = 100
2: 300
3: 900
4: 2700
5: 8100
6: 24300
7: 72900
8: 217800
9: more than 6L

hence if we add 8 to 1 months amount it should be more than 328000

_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

Satyameva Jayate - Truth alone triumphs

Intern
Joined: 04 Jan 2012
Posts: 7
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  21 Apr 2012, 08:06
An alternate way of solving this is as follows - Brunei plz confirm it.

Its geometric progression defined as Cn = 100 x (3 ^ (n-1) ) (100 times 3 raised to power of n-1)

100+300+900+....+100 x 3 ^ (n-1) = 3280 x 100

3^0 + 3 + 3^2 +....+3^(n-2) + 3^(n-1) = 3280 ..... Equation A
3 + 3^2 +....+3^(n-2) + 3^(n-1) = 3280 - 1 = 3279
3(1 + 3 +.....+3^(n-2)) = 3279
1 + 3 +.....+3^(n-2) = 1093

Putting above value in equation A

1093+3^(n-1) = 3280
3(n-1) = 2187 = 3 x 729 = 3 x 81 x 9 = 3^7

n-1 = 7 so n =8
Manager
Joined: 30 Mar 2012
Posts: 120
Location: United States (TX)
Concentration: Strategy, Entrepreneurship
GMAT Date: 09-14-2013
GPA: 2.64
WE: General Management (Consumer Electronics)
Followers: 3

Kudos [?]: 30 [0], given: 11

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?

[Reveal] Spoiler:
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.

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.
_________________

Stats by August 2014
28, Asian-American, Raised in the Bronx, NY. Moved to Houston by myself to graduate HS.
2.64 (downward trend) Economics degree from UT-Austin in Dec. 2009. No excuse, I spent 100% building a student organization that I'm still very active with today.
GMAT Goal: 710+, exam scheduled for September 14, 2013 at 8AM CST

WE: Sales Team Manager at Apple - business development and strategies for the Apple Online Store, Australia. I've also built my own consulting practice working with a successful Startup in Austin, TX, managing their online brand and helping them with analytics.
Post-MBA Goals: Strategy Consulting or Brand Management in Tech/Fashion

EC: 3 years of National Council on Fraternity (VP, President), Current Chairman of Texas Exes, Asian Alumni Network (2012-2014)
Target: (1) Stern (2) Fuqua (3) McCombs (FT/PT)
Giving this 110%. I appreciate all advice and encouragement. Thank you, everyone.

Intern
Joined: 19 Apr 2012
Posts: 28
Followers: 0

Kudos [?]: 2 [0], given: 8

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  21 Apr 2012, 12:55
Is that really a sub level 600 question ?!
Math Expert
Joined: 02 Sep 2009
Posts: 16899
Followers: 2778

Kudos [?]: 17665 [0], given: 2235

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  21 Apr 2012, 13:02
Expert's post
Alexmsi wrote:
Is that really a sub level 600 question ?!

No, it's not. I'd say it's around 650 level question.
_________________
Manager
Joined: 02 Nov 2009
Posts: 144
Followers: 2

Kudos [?]: 13 [0], given: 97

Joan took a mortgage from her bank [#permalink]  17 Sep 2012, 12:04
Joan took a mortgage from her bank each payment she makes must be triple the amount of the previous year if er first month payment is 100$and the total amount she must pay back is 328000 hovv many months she vvill take to pay back her mortgage 8 can please advice hovv to best solve this problem Math Expert Joined: 02 Sep 2009 Posts: 16899 Followers: 2778 Kudos [?]: 17665 [0], given: 2235 Re: Joan took a mortgage from her bank [#permalink] 17 Sep 2012, 12:08 Expert's post venmic wrote: Joan took a mortgage from her bank each payment she makes must be triple the amount of the previous year if er first month payment is 100$ and the total amount she must pay back is 328000 hovv many months she vvill take to pay back her mortgage

8

Merging similar topics. Please refer to the solution above.
_________________
Intern
Joined: 12 Dec 2011
Posts: 14
Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE: Management Consulting (Consulting)
Followers: 0

Kudos [?]: 7 [0], given: 5

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?

[Reveal] Spoiler:
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 16899
Followers: 2778

Kudos [?]: 17665 [0], given: 2235

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?

[Reveal] Spoiler:
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.

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?

Check here: sequences-progressions-101891.html It might help.
_________________
Senior Manager
Joined: 03 Sep 2012
Posts: 339
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
GPA: 3.88
WE: Medicine and Health (Health Care)
Followers: 8

Kudos [?]: 52 [0], given: 31

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

Director
Status: Gonna rock this time!!!
Joined: 22 Jul 2012
Posts: 551
Location: India
GMAT 1: 640 Q43 V34
GMAT 2: 630 Q47 V29
WE: Information Technology (Computer Software)
Followers: 2

Kudos [?]: 22 [0], given: 561

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  06 Jan 2013, 08:40
bunuel,
do we really need to know ap gp & hp for gmat?
_________________

hope is a good thing, maybe the best of things. And no good thing ever dies.

Who says you need a 700 ?Check this out : http://gmatclub.com/forum/who-says-you-need-a-149706.html#p1201595

My GMAT Journey : end-of-my-gmat-journey-149328.html#p1197992

Intern
Joined: 02 Nov 2012
Posts: 36
Followers: 0

Kudos [?]: 2 [0], given: 11

Re: Joan took out a mortgage from hel local bank. Each monthly [#permalink]  07 Jan 2013, 01:35
I came to this 100 * 3^t = 328000 --> 3^t = 32800, is this correct and how do I calculate t from this? Can somebody please help. Thanks in advance
Re: Joan took out a mortgage from hel local bank. Each monthly   [#permalink] 07 Jan 2013, 01:35
Similar topics Replies Last post
Similar
Topics:
Question for anyone with mortgage banking experience? 0 28 Jan 2011, 10:19
1 Profile evaluation- Civil eng + mortgage banking 1 23 Sep 2012, 09:32
Profile evaluation- Civil eng + mortgage banking 3 25 Sep 2012, 07:02
Profile evaluation- Civil eng + mortgage banking 1 25 Sep 2012, 07:03
3 One hallmark of the mortgage-banking crisis, robo-signing, 5 19 Nov 2013, 22:23
Display posts from previous: Sort by