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by GMATGuruNY » Sun Feb 12, 2012 5:03 am
A(n) = A(n-1) + ((-1)^(n+1))(n²)
A(1) = 1.
A(15) - A(13)?

14
29
169
196
421
Write it out until you see a pattern.

A(1) = 1.
A(2) = 1 + ((-1)^3)(2²) = -3.
A(3) = -3 + ((-1)^4)(3²) = 6.
A(4) = 6 + ((-1)^5)(4²) = -10.
A(5) = -10 + ((-1)^6)(5²) = 15.
A(6) = 15 + ((-1)^7)(6²) = -21.

|A(3) - A(1)| = |6-1| = 5.
|A(4) - A(2)| = |-10-(-3)| = 7.
|A(5) - A(3)| = |15-6| = 9.
|A(6) - A(4)| = |-21-(-10)| = 11.

The distances form a sequence of consecutive odd integers, starting with 5.
The ascending values in RED imply that |A(15) - A(13)| will be the 13th value in the sequence.
Look at the answer choices.
The only viable odd answer choice is B; C and E are far too great.

The correct answer is B.
Last edited by GMATGuruNY on Wed Feb 29, 2012 8:01 am, edited 1 time in total.
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by [email protected] » Sun Feb 12, 2012 7:50 pm
knight247 wrote:OA is B
Another easier way would be:
A(15)=A(14)+15^2
=A(13)-14^2+15^2


So A(15)-A(13)=15^2-14^2
=(15+14)(15-14)
=29
Hence OA is B
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by pappueshwar » Wed Feb 29, 2012 7:47 am
hi mitch,

i am confused as to how did u get 3 in place of n. it should be 2 right?

A(n) = A(n-1) + ((-1)^n)(n²)
A(2) = 1 + ((-1)^3)(2²) = -3.

GMATGuruNY wrote:
A(n) = A(n-1) + ((-1)^n)(n²)
A(1) = 1.
A(15) - A(13)?

14
29
169
196
421
Write it out until you see a pattern.

A(1) = 1.
A(2) = 1 + ((-1)^3)(2²) = -3.
A(3) = -3 + ((-1)^4)(3²) = 6.
A(4) = 6 + ((-1)^5)(4²) = -10.
A(5) = -10 + ((-1)^6)(5²) = 15.
A(6) = 15 + ((-1)^7)(6²) = -21.

|A(3) - A(1)| = |6-1| = 5.
|A(4) - A(2)| = |-10-(-3)| = 7.
|A(5) - A(3)| = |15-6| = 9.
|A(6) - A(4)| = |-21-(-10)| = 11.

The distances form a sequence of consecutive odd integers, starting with 5.
The ascending values in RED imply that |A(15) - A(13)| will be the 13th value in the sequence.
Look at the answer choices.
The only viable odd answer choice is B; C and E are far too great.

The correct answer is B.
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by GMATGuruNY » Wed Feb 29, 2012 8:07 am
pappueshwar wrote:hi mitch,

i am confused as to how did u get 3 in place of n. it should be 2 right?

A(n) = A(n-1) + ((-1)^(n+1))(n²)
A(2) = 1 + ((-1)^3)(2²) = -3.
In my original post, there was a typo in the question: the exponent (shown in red here) is n+1. Thanks for calling my attention to the typo, which I have corrected.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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