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Weird Problem
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GMATGuruNY
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Write it out until you see a pattern.A(n) = A(n-1) + ((-1)^(n+1))(n²)
A(1) = 1.
A(15) - A(13)?
14
29
169
196
421
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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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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Another easier way would be:knight247 wrote:OA is B
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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pappueshwar
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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.
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:Write it out until you see a pattern.A(n) = A(n-1) + ((-1)^n)(n²)
A(1) = 1.
A(15) - A(13)?
14
29
169
196
421
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.
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
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- GMAT Score:790
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.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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
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].
Student Review #1
Student Review #2
Student Review #3
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].
Student Review #1
Student Review #2
Student Review #3
