It is currently 26 Jun 2017, 22:59

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# M03#29

Author Message
Intern
Joined: 22 Jan 2009
Posts: 1

### Show Tags

14 Mar 2009, 19:14
2
This post was
BOOKMARKED
A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -3

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 39704

### Show Tags

03 Jan 2011, 04:07
4
KUDOS
Expert's post
gmatdelhi wrote:
tingle15 wrote:
I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?

When we see "consecutive integers" it ALWAYS means integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, .... For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.

But in the original question, stem says consecutive terms of the sequence A (which is given to be arithmetic progression) and not consecutive integers, so the common difference is not necessary to be 1 in this case.

As for the question:

A computer generated a sequence $$A$$ of numbers using the following formula: $$A_n = A_1 + (n-1)d$$. $$d$$ is the common difference between any two consecutive terms of the sequence $$A$$. If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?
A. 3
B. 2
C. 1
D. -1
E. -3

Given:
$$a_2+a_5=(a_1+d)+(a_1+4d)=2a_1+5d=8$$;
$$a_3+a_7=(a_1+2d)+(a_1+6d)=2a_1+8d=14$$;

Subtract 1 from 2: $$3d=6$$ --> $$d=2$$ --> as $$2a_1+5d=8$$ then $$2a_1+5*2=8$$ -> $$a_1=-1$$.

Hope it helps.
_________________
Director
Joined: 04 Jan 2008
Posts: 898

### Show Tags

14 Mar 2009, 21:48
1
KUDOS
its AP
A, A+d,A+2d,A+3d,.........,A+(n-1)d
sorry I cant able to write the equation here but its a simple problem
solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:
Quote:

A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(C) 2008 GMAT Club - m03#29

* 3
* 2
* 1
* -1
* -3

$$\left{ \begin{eqnarray*} A_2+A_5 &=& A_1 + d + A_1 + 4d = 2A_1 + 5d = 8\\ A_3+A_7 &=& A_1 + 2d + A_1 + 6d = 2A_1 + 8d = 14\\ \end{eqnarray*}$$
$$\left{ \begin{eqnarray*} d &=& 2\\ A_1 &=& -1\\ \end{eqnarray*}$$

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

_________________

http://gmatclub.com/forum/math-polygons-87336.html
http://gmatclub.com/forum/competition-for-the-best-gmat-error-log-template-86232.html

Senior Manager
Joined: 13 Dec 2009
Posts: 262

### Show Tags

22 May 2010, 08:24
1
KUDOS
The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.
_________________

My debrief: done-and-dusted-730-q49-v40

Manager
Joined: 07 Jul 2007
Posts: 137

### Show Tags

16 Mar 2009, 08:51
nitya34 wrote:
its AP
A, A+d,A+2d,A+3d,.........,A+(n-1)d
sorry I cant able to write the equation here but its a simple problem
solve 2 equations for 2 unknowns(A and d)

ThinkingHat wrote:
Quote:

A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(C) 2008 GMAT Club - m03#29

* 3
* 2
* 1
* -1
* -3

$$\left{ \begin{eqnarray*} A_2+A_5 &=& A_1 + d + A_1 + 4d = 2A_1 + 5d = 8\\ A_3+A_7 &=& A_1 + 2d + A_1 + 6d = 2A_1 + 8d = 14\\ \end{eqnarray*}$$
$$\left{ \begin{eqnarray*} d &=& 2\\ A_1 &=& -1\\ \end{eqnarray*}$$

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

Response:
---------------------------------------------------------------------------------------------------------------------------------------------------------------

It is an arithmetic progression sequence where you have formula:

$$a_n = a_1 + (n-1)d$$

And now if you put n = 5, n = 2, n =7 you will get these forumuas.
Senior Manager
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 408
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB

### Show Tags

30 Sep 2010, 09:28
2a+5d=8 and 2a+8d=14 => d=3 and a = -1. Answer D wins.
_________________

Support GMAT Club by putting a GMAT Club badge on your blog

Manager
Joined: 08 Sep 2010
Posts: 226
Location: India
WE 1: 6 Year, Telecom(GSM)

### Show Tags

30 Sep 2010, 10:04
An=A1-(n-1)d
is the formula for nth term in an arithmetic progression.
hence 7th term A7=A1-(7-1)d
Similarly,2nd term A2=A1-(2-1)d
3rd term A3=A1-(3-1)d
and 5th term A5=A1-(5-1)d

Now According to question,A2+A5=8 i.e 2A1+5d=8
and A3+A7=14 i.e, 2A1+8d=14

Solving these two we will get A1=-1

_________________

Consider KUDOS if You find it good

Intern
Joined: 19 Jul 2010
Posts: 5

### Show Tags

30 Sep 2010, 16:12
Arithmetic sequence.
Intern
Joined: 18 Aug 2010
Posts: 29
Concentration: Entrepreneurship, Finance
GPA: 3.6
WE: Engineering (Telecommunications)

### Show Tags

30 Sep 2010, 17:04
D.

I tried back-substitution and didn't get anywhere. had to solve it the old-fashioned - 2 equations, 2 variables way.
Manager
Joined: 15 Apr 2010
Posts: 167

### Show Tags

12 Oct 2010, 13:27
sidhu4u wrote:
The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.

I agree... Can someone please provide a resolution for this...
Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia

### Show Tags

03 Jan 2011, 01:16
tingle15 wrote:
sidhu4u wrote:
The wording of the question is rather confusing. When I did this question the wording was:

A computer generated a consecutive set of numbers A using the following formula:

Can someone remove the word consecutive from the question? It totally misled me into thinking that the set of numbers are consecutive integers like 1,2,3..

The question should be phrased like below:

A computer generated a consecutive set of numbers $$A$$using the following formula:

$$An = A1 + (n-1)d$$ where $$d$$is the common difference between any number and the next number in the set $$A$$.

I agree... Can someone please provide a resolution for this...

I had the same issue. Because it said consecutive, I assumed d = 1. Are we wrong in some way?
_________________

1st Feb '11 -- Actual GMAT : 730 (Q48 V42) AWA 6.0

My Practice GMAT Scores
29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38)
23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36)
19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37)
15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42)
11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44)
6th Jan '11 -- Kaplan#2 : 620 (Q40 V35)
28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35)
30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35)
12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37)
6th Dec '09 -- PR CAT #1 : 650 (Q44 V37)
25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)

If you feel like you're under control, you're just not going fast enough.
A goal without a plan is just a wish.
You can go higher, you can go deeper, there are no boundaries above or beneath you.

Manager
Joined: 20 Nov 2010
Posts: 218

### Show Tags

04 Oct 2011, 11:02
Easy one. Its an AP with d as common difference and A1 as first term.
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Manager
Joined: 11 Feb 2011
Posts: 74

### Show Tags

04 Oct 2011, 17:21
Manager
Joined: 16 Sep 2010
Posts: 220
Location: United States
Concentration: Finance, Real Estate
GMAT 1: 740 Q48 V42

### Show Tags

14 Nov 2011, 23:19
ThinkingHat wrote:
A computer generated a sequence $$A$$ of numbers using the following formula:
$$A_n = A_1 + (n-1)d$$

$$d$$ is the common difference between any two consecutive terms of the sequence $$A$$

If the sum of the second and the fifth terms of the sequence is 8 and the sum of the third and the seventh terms is 14, what is the first term of the sequence?

(A) 3
(B) 2
(C) 1
(D) -1
(E) -3

[Reveal] Spoiler: OA
D

Source: GMAT Club Tests - hardest GMAT questions

Can someone explain this? I am not quite sure how the above notations transform...

Thanks!

Its pretty easy when you set it up as equations to solve.

Equation one is =
A + (2-1)d + A + (5-1)d = 8 => 2A + 5d = 8

Equation two is =
A + (3-1)d + A + (7-1)d = 14 => 2A + 8d = 14

Since the only difference between the two equations is 3d = 6 we know that d = 2. Plug that into one of the equations and you get A = -1.
Senior Manager
Joined: 23 Oct 2010
Posts: 383
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38

### Show Tags

17 Dec 2011, 04:34
a2+a5=8

a3+a7=14 or a2+d+a6+d=14 a2+24+a5+d=14 8+3d=14 d=2

a1+d+a1+4d=8 2a1+5d=8 2a1=5*2=8 a1=-1
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Director
Status: Final Countdown
Joined: 17 Mar 2010
Posts: 537
Location: India
GPA: 3.82
WE: Account Management (Retail Banking)

### Show Tags

04 Oct 2012, 12:04
i don't know how long the GMAC will continue to ask such question in the real test because this one is easy yet time consuming.

A2+A5
=> { A1+(2-1)d}+{A1+(5-1)d=8
=> 2A1+5d=8----------------------------------(i)

A3+A7
=> {A1+(3-1)d}+{A1+(7-1)d=14
=> 2A1+8d=14-------------------------------(ii)

solve (i) & (ii)

d=2

putting the value of d in (i) [or (ii)]

A1=-1

D wins
_________________

" Make more efforts "
Press Kudos if you liked my post

Re: M03#29   [#permalink] 04 Oct 2012, 12:04
Display posts from previous: Sort by

# M03#29

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.