NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 00:40 It is currently 26 Apr 2024, 00:40
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

An arithmetic sequence is a sequence in which each term after the firs

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92919
Own Kudos [?]: 619084 [4]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 May 2020, 01:26
4
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

45% (02:41) correct 55% (02:24) wrong based on 85 sessions
Hide Show timer Statistics

Competition Mode Question



An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?


(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
E
User avatar
L
freedom128
Director
Director
Joined: 30 Sep 2017
Posts: 956
Own Kudos [?]: 1256 [3]
Given Kudos: 402
GMAT 1: 720 Q49 V40
GPA: 3.8
Send PM
Reviews Badge
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 May 2020, 04:11
1
Kudos
2
Bookmarks
An increasing arithmetic sequence N = -ve integers only.
An increasing arithmetic sequence P = +ve integers only.
The sequence C contains all the terms of arithmetic sequences N and P.

Q. Is sequence C an arithmetic sequence?

(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.
- If N = {-5,-3,-1} and P={1,3,5} then sequence C is an arithmetic sequence
-If N = {-7,-5,-3} and P={3,5,7} then sequence C is NOT an arithmetic sequence. Sequence C lacks of elements {-1, 1} to be qualified as arithmetic sequence.
NOT SUFFICIENT

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.
- If N = {-5,-3,-1} and P={1,3,5} then sequence C is an arithmetic sequence
-If N = {-7,-5,-3} and P={3,5,7} then sequence C is NOT an arithmetic sequence. Sequence C lacks of elements {-1, 1} to be qualified as arithmetic sequence.
NOT SUFFICIENT

Combined (1) and (2)
- If N = {-5,-3,-1} and P={1,3,5} then sequence C is an arithmetic sequence
-If N = {-7,-5,-3} and P={3,5,7} then sequence C is NOT an arithmetic sequence. Sequence C lacks of elements {-1, 1} to be qualified as arithmetic sequence.
NOT SUFFICIENT

FINAL ANSWER IS (E)

Posted from my mobile device
User avatar
D
exc4libur
SVP
SVP
Joined: 24 Nov 2016
Posts: 1720
Own Kudos [?]: 1344 [2]
Given Kudos: 607
Location: United States
Send PM
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 May 2020, 04:43
2
Kudos
Quote:
An arithmetic sequence is a sequence in which each term after the first is equal to the sum of the preceding term and a constant, which is also known as the common difference of that arithmetic sequence. An increasing arithmetic sequence N consists of a set of distinct negative integers and an increasing arithmetic sequence P consists of a set of distinct positive integers. The sequence C contains all the terms of arithmetic sequences N and P such that the number of terms in sequence C is equal to the number of terms in arithmetic sequences N and P. Is sequence C an arithmetic sequence?

(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.
(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.


C=AP?

(1) insufic

tnN+aP=0
-1+1=0; [-3,-1,1,2,3]≠AP
-1+1=0; [-2,-1,1,2,3]=AP

(2) insufic

[-3,-1,1,2,3]≠AP
[-3,-1,1,3]=AP

(1/2) insufic

[-3,-1,1,2,3]≠AP
[-3,-1,1,3]=AP

Ans (E)
User avatar
L
MayankSingh
Senior Manager
Senior Manager
Joined: 08 Jan 2018
Posts: 297
Own Kudos [?]: 257 [1]
Given Kudos: 249
Location: India
Concentration: Operations, General Management
Schools: McDonough '25 (A) Marshall '25 (D) Tepper '25 (WA$) Kenan-Flagler '25 (A) ISB '25 (WL) IIMC '25 (A) Owen '26 (A$$$$)
GMAT 1: 640 Q48 V27
GMAT 2: 730 Q51 V38
GPA: 3.9
WE:Project Management (Manufacturing)
Send PM
GMAT ToolKit User Reviews Badge
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 May 2020, 08:34
1
Kudos
IMO E

N = {N1, N2, N3 ,................., N9 } [assume 9 elements]
N1-N9 : Negative integers ; Common difference = D (+ve)
P= {P1, P2, ..........................,P9}
P1-P9 : Positive integers ; Common difference = K (+ve)


(1) The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.
N9+P1=0
N9= - P1

------(N9-D).........N9............0.........N1..........(N1+K)
To be an AP,
D=(N1-N9)=K
So not sufficient

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.
C= { -8,-6,-4 , 4, 6, 8 } - Not in AP
C= {-12,-4,4,12} - In AP
Not sufficient

Together:C= { -8,-6,-4 , 4, 6, 8 } - Not in AP
C= {-12,-4,4,12} - In AP
Not sufficient.
User avatar
B
aka007
Intern
Intern
Joined: 15 Nov 2019
Posts: 13
Own Kudos [?]: 9 [1]
Given Kudos: 75
Send PM
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 May 2020, 10:29
1
Kudos
IMO the answer is E

S1:
largest term on N is -1 & smallest of P is +1 (condition of S1 satisfied)
now, whether C is a AP or not entirely depends on the common difference D.
If the next term on N is -2 whereas the next term on P is +5. NOT AP
If N (-3,-1) and P (1,3) then yes AP

Hence the statement is not sufficient.

S2:

the terms are of equal magnitude
N(-3,-1) and P (1,3) yes AP
N(-2,-1) and P (1,2) no AP

statement is not sufficient

Combining both the statements we do not get any addl value, therefore the answer is E
User avatar
P
Lipun
Manager
Manager
Joined: 05 Jan 2020
Posts: 148
Own Kudos [?]: 132 [1]
Given Kudos: 288
Send PM
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   23 May 2020, 06:01
1
Kudos
Let S(N)=N1+(N-1)C1, N1 is the first term
Let S(P)=P1+(P-1)C2, P1 is the first term

1. Given the largest of S(N) is equal to smallest of S(P)
No info about the constants. Not sufficient.

2. Given for every integer in S(N), there is an integer value in S(P) having same magnitude.
If C1=4 and C2=2, then also the above statement holds good, but the set S(C) will not be in arithmetic sequence.

Considering 1 and 2 together also not sufficient info.

Note: For the overall sequence S(C) to be in arithmetic sequence, largest of S(N) - smallest of S(P) = C1 = C2
avatar
G
Vigasimrair
Intern
Intern
Joined: 06 Feb 2019
Posts: 40
Own Kudos [?]: 34 [1]
Given Kudos: 370
Location: Russian Federation
Schools: INSEAD Sept'21 Intake (WL)
GMAT 1: 690 Q45 V40
Send PM
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   23 May 2020, 07:47
1
Kudos
the answer is E.
Let's imagine that we have the following 2 sequences:

First case
(N) -10; -8; -6
(P) 6;8;10

or the following 2 sequences:

Second case
(N) -7; -5; -3; -1;
(P) 1;3;5;7

Both pieces of information are not sufficient, because in the first case we don't have an arithmetic sequence and in the second case we have arithmetic sequence.
User avatar
P
debjit1990
Senior Manager
Senior Manager
Joined: 26 Dec 2017
Posts: 301
Own Kudos [?]: 269 [0]
Given Kudos: 22
Location: India
GMAT 1: 580 Q42 V27
Send PM
Reviews Badge
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   24 May 2020, 07:30
Ans: B

Statement 1: The sum of the largest term of the sequence N and the smallest term of the sequence P is zero.

N={-9,-7,-5,-3,-1}
P={1,2,3,4,5}
C={-9,-7,-5,-3,-1,1,2,3,4,5}, so C is not an arithmatic sequence
N={-9,-7,-5,-3,-1}
P={1,3,5,7,9}
C={-9,-7,-5,-3,-1,1,3,5,7,9}, so C is an arithmatic sequence

No Statement 1 not sufficient.

(2) For every integer in sequence N, there exists an integer in sequence P with the same magnitude.
N={-9,-7,-5,-3,-1}
P={1,3,5,7,9}
C={-9,-7,-5,-3,-1,1,3,5,7,9}, so C is an arithmatic sequence
Sufficient.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink] New post   22 Dec 2021, 23:00
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: An arithmetic sequence is a sequence in which each term after the firs [#permalink]
22 Dec 2021, 23:00
Moderator:
Bunuel
Math Expert
92918 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions