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

Redeem

Sequence

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
GMAT Score:760

by nisagl750 » Thu Aug 30, 2012 3:15 am
shrey2287 wrote:122. An=An-2+11, n>2. Is 633 in the sequence?
1) A1=39
2) A2=43


OA : A
Since An=An-2+11, it represents an AP with d=11/2 = 5.5(A3=A1+11, A5=A3+11 and so on, So A2 = A1+5.5 & A3=A2+5.5),
nth term of an A.P sequence is given by N=a+(n-1)d, here N = 633 (we want to find whether is in the series or not)
Statement1: a=39, N=633, d=5.5
633=39(n-1)5.5
5.5(n-1)=594
(n-1)=108
n=109
So 633 is 109th term of the series if A1=39 Sufficient

Statement2: 43=39, N=633, d=5.5
633=43(n-1)5.5
5.5(n-1)=590
(n-1)=107.272727.......
n=108.2727.....
since n is a number, it can't be in decimal. Insufficient

Hence, A
Top
User avatar
Community Manager
Posts: 1060
Joined: Fri May 13, 2011 6:46 am
Location: Utrecht, The Netherlands
Thanked: 318 times
Followed by:52 members

by neelgandham » Thu Aug 30, 2012 3:27 am
An=An-2+11, n>2. Is 633 in the sequence?
1) A1=39
Let n = 3 then A3 = A1 + 11. A3 = 39 + 11
A5 = A3 + 11 = 39 + 11 + 11 = 39 + 2*(11)
A7 = A5 + 11 = 39 + 2*(11) + 11 = 39 + 3*(11)
Now, we know that An = 39 + [(n-1)/2]*11, where n is the number of the term and a positive integer.
Let us check if 633 is one of the terms
633 = 39 + [(n-1)/2]*11
594 = [(n-1)/2]*11
54 = [(n-1)/2]
n = 109. So there exists an n which is an integer and 633 is a term in the series. So, statement I is sufficient to answer the question.
post statement - We don't know the values of the even terms.
2) A2=43
An=An-2+11
A4 = A2 + 11 = 43 + 11
A6 = A4 + 11 = 43 + 11 + 11 = 43 + 2*11
A8 = A6 + 11 = 43 + 2*11 + 11 = 43 + 3*11
So, An = 43 + [(n-2)/2]*11
Let us check if 633 is one of the terms
633 = 43 + [(n-2)/2]*11
590 = [(n-2)/2]*11
(1180/11) + 2 = n = Not an integer.
So, 633 is not one of the EVEN terms. Since we are not sure if 633 is one of the ODD terms, statement II is insufficient to answer the question.

IMO A
Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Thu Aug 30, 2012 3:40 am
shrey2287 wrote:
122. An=An-2+11, n>2. Is 633 in the sequence?
1) A1=39
2) A2=43


OA : A
An = An-2 + 11, n > 2
A3 = A1 + 11, A5 = A3 + 11.... (so the odd numbers are in AP with initial term as A1 and common difference as 11)
A4 = A2 + 11, A6 = A4 + 11 ... (so the even numbers are also in AP with initial term as A2 and common difference as 11)
But the whole series taken is not in AP with common difference 5.5.
The series can be thought as two AP series with terms one term from one AP and the next term from another AP Series. but both has common difference 11.
The series can be written as a,b,a+11,b+11,a+22,b+22 (a1,b1,a2,b2,a3,b3)...

consider 1st option,
it is given a as 39
633 = 39 + (n-1)11
n = 54
so it will be a54, which is A107 of the original series.
if it is a1,a2,a3,.. series then it will be in A1,A2,A3... series too.

consider 2nd option,
633 = 43 + (n-1)11
n = 53.63 which is not an integer
so it is not part of b1,b2,b3.. series and we can`t answer whether it is a1,a2,a3.. series

Hence, It is A
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
GMAT Score:760

by nisagl750 » Thu Aug 30, 2012 3:49 am
Anurag@Gurome wrote: But the whole series taken is not in AP with common difference 5.5.
Got it, thanks
Top
Post new topic Post Reply
• Page 1 of 1