BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

sequence & mean

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 109
Joined: Mon Sep 08, 2008 12:47 am

by smallsorrow » Tue Oct 28, 2008 10:07 am
a^n +b^n / a^n-1 + b^n-1 = a + b /2

a^n+b^n/a^n / a^-1+b^nb^-1 = a+b/2

cross multiply
2 (a^n+b^n)=(a+b)(a^na^-1+b^nb^-1)
factor out
2 (a^n+b^n)=(a+b)(a+b)(a^n+b^n)
a^n+b^n=a^2+b^2
n=2

could this be?
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 248
Joined: Mon Aug 11, 2008 9:51 am
Thanked: 13 times

by earth@work » Tue Oct 28, 2008 10:18 am
but the correct answer is 1
Top
Legendary Member
Posts: 574
Joined: Sun Jun 01, 2008 8:48 am
Location: Bangalore
Thanked: 28 times

by vishubn » Tue Oct 28, 2008 10:38 am
yaa
IMO =1

uff took a while to factorize it

last but one step of the factorizing process is

[b*a^(n+1)]+[a*b^(n+1)]=[a^2*b^n]+[b^2*a^n]

so condition is satisfied only when n=1

HTH

vishu
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 248
Joined: Mon Aug 11, 2008 9:51 am
Thanked: 13 times

by earth@work » Tue Oct 28, 2008 10:45 am
m not able to factorize it correctly still
Top
Legendary Member
Posts: 574
Joined: Sun Jun 01, 2008 8:48 am
Location: Bangalore
Thanked: 28 times

by vishubn » Tue Oct 28, 2008 10:54 am
UFF ! wil try and scan the working layout ... its way too much to type :( I will get back on this sooon and yes nice question ! it was fun doing it

Vishu
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Tue Oct 28, 2008 11:06 am
Where is this question from? The factoring is incredibly complicated and the question itself needs more info to be answerable.

Here's the factoring:

(a^n + b^n)/(a^n-1 + b^n-1) = (a+b)/2
2(a^n + b^n) = (a+b)(a^n-1 + b^n-1)
2(a^n) + 2(b^n) = a(a^n-1) + b(b^n-1) + a(b^n-1) + b(a^n-1)
2(a^n) + 2(b^n) = a^n + b^n + a(b^n-1) + b(a^n-1)
2(a^n) - a^n + 2(b^n) - b^n = a(b^n-1) + b(a^n-1)
a^n + b^n = a(b^n-1) + b(a^n-1)
a^n - b(a^n-1) = a(b^n-1) - b^n
a^n-1(a-b) = b^n-1(a-b)
a^n-1 = b^n-1

Which is only true for ALL a and b if n - 1 = 0 or n = 1.

However, the question doesn't mention all a and b or tell us that a doesn't equal b. So, if we chose a=3 and b=3, then the two sides would be equal for all values of n. If we chose a=3 and b=-3, then the two sides would be equal for all odd values of n.

If the question told us that |a| != |b|, then 1 would be the correct answer. In future, please post all the answer choices.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 248
Joined: Mon Aug 11, 2008 9:51 am
Thanked: 13 times

by earth@work » Tue Oct 28, 2008 11:33 am
Thanks Stuart and vishu for help.

Stuart i was getting stuck with factorization, thanks again
this question was from a chapter i was doing on sequence and it did not have multiple answer choices.
Top
Post new topic Post Reply
• Page 1 of 1