Joan took out a mortgage from her local bank. Each monthly

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varun289: Master | Next Rank: 500 Posts; Posts: 298; Joined: Sun Jun 03, 2012 6:42 amFollowed by: 7 members; Location: New delhi; Thanked: 10 times; GMAT Score:590

by varun289 » Mon Apr 29, 2013 9:32 pm

Joan took out a mortgage from her 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 $328,000, how many months will it take Joan to pay back her mortgage?

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is any short cut ?

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Source: Beat The GMAT — Problem Solving | Mon Apr 29, 2013 9:32 pm

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Anju@Gurome: GMAT Instructor; Posts: 511; Joined: Wed Aug 11, 2010 9:47 amFollowed by: 86 members; Location: Delhi, India; Thanked: 344 times

by Anju@Gurome » Mon Apr 29, 2013 10:19 pm

varun289 wrote:Joan took out a mortgage from her 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 $328,000, how many months will it take Joan to pay back her mortgage?

This is a geometrical progression problem which requires the formula for the sum of the terms of a geometrical progression. The sum of n consecutive terms of a geometric progression is given by:

S(n) = a(râ�¿ - 1)/(r - 1), where a is the first term, r is the common ratio of the geometric progression and n = number of terms.

In this case, a = 100, r = 3 and S(n) = 328,000
We need to determine n.

So, 100*(3â�¿ - 1)/(3 - 1) = 328000
--> (3â�¿ - 1)/2 = 3280
--> (3â�¿ - 1) = 6560
--> 3â�¿ = 6561

Now, units digit of any power of 3 is 1 only when the power is a multiple of 4.
So, n must be a multiple of 4.
Only option B works.

The correct answer is B.

Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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