GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 02 Aug 2021, 14:17
Register
GMAT Club Tests
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
The sequence of four numbers a1, a2 , a3 and a4 is such that
10 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

avatar
pritishmohan
Intern
Intern
Joined: 14 Jan 2013
Posts: 1
GMAT ToolKit User
The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  18 May 2013, 00:25
2
Kudos
24
Bookmarks
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

76% (01:15) correct 24% (01:40) wrong based on 496 sessions

Hide Show timer Statistics

The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

(1) \(a_2=15\)

(2) \(a_4 = 29\)
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Expert Reply
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 78155
Premium Member CAT Tests Forum Quiz Mode Top Member of the Month
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  30 Oct 2014, 01:52
2
Kudos
3
Bookmarks
Expert Reply
alexa wrote:
Bunuel please solve this question, I don't understand the solution for statement #2.

Thank you!


The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

Each number after the first is \(a_1-1\) greater than preceding number means that:
\(a_2=a_1+(a_1-1)=2a_1-1\)
\(a_3=a_2+(a_1-1)=3a_1-2\)
\(a_4=a_3+(a_1-1)=4a_1-3\)

(1) \(a_2=15\). We can find \(a_1\). Sufficient.

(2) \(a_4 = 29\). We can find \(a_1\). Sufficient.

Answer: D.

Hope it's clear.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
General Discussion
User avatar
Zarrolou
Director
Director
Joined: 02 Sep 2012
Status:Far, far away!
Posts: 940
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
GMAT ToolKit User
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  18 May 2013, 00:37
3
Kudos
The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?


\(a_n=a_{n-1}+(a_1-1)\)

1. \(a_2=15\)
\(a_2=a_{1}+(a_1-1)\)
\(15=2a_{1}-1\)
\(a_1=8\)
Sufficient

2. \(a_4 = 29\)
From the main formula above we can write \(a_4\) as \(a_4=a_{1}+3(a_1-1)\)
\(29=a_{1}+3(a_1-1)\)
\(29=4a_{1}-3\)
\(a_1=8\)
Sufficient

D
User avatar
SrinathVangala
Intern
Intern
Joined: 05 Mar 2013
Posts: 36
Location: India
Concentration: Entrepreneurship, Marketing
GMAT Date: 06-05-2013
GPA: 3.2
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  18 May 2013, 04:10
pritishmohan wrote:
The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

1. \(a_2=15\)

2. \(a_4 = 29\)



given:- a2 - a1 = a1 - 1 => a2 = 2a1 - 1

similarly we can get a3 = 3a1 - 2 and a4 = 4a1 - 3.

AD/BCE

statement 1:- a2 = 15 => 2a1 - 1 = 15.So we can get the value of a1. A alone is sufficient BCE out.

statement2:- a4 = 29 => 4a1-3 = 29 .So we can get the value of a1. B alone is sufficient.

Answer is D
avatar
doe007
Senior Manager
Senior Manager
Joined: 16 Dec 2011
Posts: 255
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  19 May 2013, 03:35
pritishmohan wrote:
The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

1. \(a_2=15\)

2. \(a_4 = 29\)

From the given information, we know that \(a_n = a_{n-1} + (a_1 - 1) = na_1 - (n - 1)\)

1. \(a_2 = 15\)
--> \(a_2 = a_1 + (a_1 - 1) = 2a_1 - 1\) ----> \(2a_1 - 1 = 15\) ----> \(2a_1 = 16\) ----> \(a_1 = 8\)
Sufficient.

2. \(a_4 = 29\)
Now, \(a_4 = 4a_1 - 3\)
--> \(4a_1 - 3 = 29\) ----> \(4a_1 = 32\) ----> \(a_1 = 8\)
Sufficient.

Correct answer is D.
User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 78155
Premium Member CAT Tests Forum Quiz Mode Top Member of the Month
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  19 May 2013, 03:40
4
Bookmarks
Expert Reply
pritishmohan wrote:
The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

1. \(a_2=15\)

2. \(a_4 = 29\)


Similar questions to practice:
the-sequence-a1-a2-a3-an-of-n-integers-is-such-that-76926.html
the-numbers-above-form-a-sequence-t1-t2-and-t3-which-is-106213.html
if-a1-a2-a3-an-is-a-sequence-such-that-an-2n-129753.html
an-infinite-sequence-of-positive-integers-is-called-a-127696.html

Hope it helps.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
avatar
alexa
Intern
Intern
Joined: 06 Oct 2011
Posts: 2
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  29 Oct 2014, 20:19
Bunuel please solve this question, I don't understand the solution for statement #2.

Thank you!
User avatar
TeamGMATIFY
Senior Manager
Senior Manager
Joined: 20 Aug 2015
Posts: 366
Location: India
GMAT 1: 760 Q50 V44
The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  12 Nov 2015, 03:25
Expert Reply
pritishmohan wrote:
The sequence of four numbers \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) is such that each number after the first is \(a_1-1\) greater than preceding number . What is the value of \(a_1\)?

(1) \(a_2=15\)

(2) \(a_4 = 29\)


Given: \(a_1\), \(a_2\) , \(a_3\) and \(a_4\) and
\(a_2\) = \(a_1\) + \(a_1-1\) - (i)
\(a_3\) = \(a_1\) + 2\(a_1-1\) - (ii)
\(a_4\) = \(a_1\) + 3\(a_1-1\) - (iii)

Required: \(a_1\) = ?

Statement 1: \(a_2=15\)
Using (i) we can find the value of \(a_1\)
SUFFICIENT

Statement 2: \(a_4 = 29\)
Using (iii), we can find the value of \(a_1\)
SUFFICIENT

Hence Option D

Note: You do not need to solve for the values of \(a_1\). This can save precious time on the test.
User avatar
B
merajul
Manager
Manager
Joined: 05 Oct 2014
Posts: 141
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE:Project Management (Energy and Utilities)
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  22 Oct 2017, 02:10
Nth term in AP is denoted as tn=a+(n-1)d .

(1) says, 15=a1+(4-1)(a1-1) => 15=a1+3(a1-1) , from this a1 can be found. SUFFICIENT.

(2) says, 29=a1+(4-1)(a1-1) => 29=a1+3(a1-1) , from this a1 can be found. SUFFICIENT.

Thus answer D.
_________________
I DON'T FEAR FAILING, I FEAR NOT TRYING

PLEASE UPVOTE IF YOU LIKE MY EXPLANATIONS
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 20062
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink] New post  19 May 2021, 05:37
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: The sequence of four numbers a1, a2 , a3 and a4 is such that [#permalink]
19 May 2021, 05:37
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
10175 posts
Bunuel
Math Expert
78155 posts
GMATBusters
GMAT Tutor
2009 posts
nick1816
DS Forum Moderator
2295 posts

cron

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