Last visit was: 24 Apr 2026, 03:05 It is currently 24 Apr 2026, 03:05
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
honchos
User avatar
Joined: 17 Apr 2013
Last visit: 30 Aug 2021
Posts: 358
Own Kudos:
2,489
 [13]
Given Kudos: 298
Status:Verbal Forum Moderator
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
GMAT 3: 790 Q51 V49
Posts: 358
Kudos: 2,489
 [13]
The first and second numbers in a sequence of numbers are pl Updated on: 31 Dec 2017, 14:53
Originally posted by honchos on 16 Sep 2013, 22:56.
Last edited by Bunuel on 31 Dec 2017, 14:53, edited 4 times in total.
Edited the question.
4
Kudos
Add Kudos
9
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

45% (02:06) correct 55% (01:56) wrong based on 258 sessions

History

Date
Time
Result
Not Attempted Yet
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

(1) Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
(2) The first number in the sequence is 3.
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,386
 [9]
Given Kudos: 141
Posts: 478
Kudos: 3,386
 [9]
The first and second numbers in a sequence of numbers are pl 16 Sep 2013, 23:10
9
Kudos
Add Kudos
Bookmarks
Bookmark this Post
honchos
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

1.Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
2. The first number in the sequence is 3.
Show more

From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \(\frac{(8x-7)-(2x-1)}{(4x-3)-x}\) = \(\frac{6(x-1)}{3(x-1)}\)

The slope will be 2, if \(x\neq{1}\) and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that \(x\neq{1}\) and hence, the slope is 2. Sufficient.

C.
General Discussion
avatar
nspatel
avatar
Joined: 23 Jul 2013
Last visit: 23 Jan 2015
Posts: 3
Own Kudos:
7
Given Kudos: 1
Location: United States
Concentration: Finance, General Management
Schools: HBS '16 (S) Tuck '16 (S) Johnson '16 (S) Duke '16 (S) Tepper '16 (I) Sloan '16 (S) Anderson '16 (S) Darden '16 (S) Kellogg '16 (S)
GMAT 1: 750 Q51 V40
GPA: 3.11
WE:Engineering (Computer Software)
Schools: HBS '16 (S) Tuck '16 (S) Johnson '16 (S) Duke '16 (S) Tepper '16 (I) Sloan '16 (S) Anderson '16 (S) Darden '16 (S) Kellogg '16 (S)
GMAT 1: 750 Q51 V40
Posts: 3
Kudos: 7
The first and second numbers in a sequence of numbers are pl 16 Sep 2013, 23:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mau5
honchos
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

1.Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
2. The first number in the sequence is 3.

From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \(\frac{(8x-7)-(2x-1)}{(4x-3)-x}\) = \(\frac{6(x-1)}{3(x-1)}\)

The slope will be 2, if \(x\neq{1}\) and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that \(x\neq{1}\) and hence, the slope is 2. Sufficient.

C.
Show more



The mistake in your solution is that you assumed that there are just 4 points. But the question does not say this. It says " and all subsequent pairs in the sequence" which means there are more than 4 terms in the sequence. In case of 2 points you will a straight line. But if the number of points is more than 2, you wont get a straight line. So both statements are not sufficient.

So E.
User avatar
mau5
User avatar
Verbal Forum Moderator
Joined: 10 Oct 2012
Last visit: 31 Dec 2024
Posts: 478
Own Kudos:
3,386
Given Kudos: 141
Posts: 478
Kudos: 3,386
The first and second numbers in a sequence of numbers are pl 17 Sep 2013, 00:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nspatel
mau5
honchos
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

1.Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
2. The first number in the sequence is 3.

From F.S 1, we have the series as x,2x-1,4x-3,8x-7 .. etc

Now, as per the question stem, the two co-ordinates will be : (x,2x-1) and (4x-3,8x-7) --> The slope of the line : \(\frac{(8x-7)-(2x-1)}{(4x-3)-x}\) = \(\frac{6(x-1)}{3(x-1)}\)

The slope will be 2, if \(x\neq{1}\) and undefined if x = 1. However, we don't know that. Insufficient.

From F.S 2, all we know is the first term, clearly Insufficient.

Taking both statements together, we know that \(x\neq{1}\) and hence, the slope is 2. Sufficient.

C.



The mistake in your solution is that you assumed that there are just 4 points. But the question does not say this. It says " and all subsequent pairs in the sequence" which means there are more than 4 terms in the sequence. In case of 2 points you will a straight line. But if the number of points is more than 2, you wont get a straight line. So both statements are not sufficient.

So E.
Show more

I have assumed no such thing.Make a list of all the terms you keep getting based on F.S 1, you will get the same expression for slope, and hence it is a part of the straight line.

For eg: x,2x-1,4x-3,8x-7,16x-15,32x-31,64x-63,128x-127,etc..
avatar
ItsABrainGame
avatar
Joined: 20 Dec 2014
Last visit: 01 Jun 2015
Posts: 5
Own Kudos:
2
Given Kudos: 24
Posts: 5
Kudos: 2
The first and second numbers in a sequence of numbers are pl 23 Dec 2014, 02:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
From 1, we can have the line going +ve upwards or -ve downward based on first number. NS.
From 2, clearly not sufficient.

1&2: limits it to be upwards. Sufficient.

honchos
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

(1) Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
(2) The first number in the sequence is 3.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,803
Own Kudos:
810,925
 [2]
Given Kudos: 105,868
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,803
Kudos: 810,925
 [2]
The first and second numbers in a sequence of numbers are pl 31 Dec 2017, 14:53
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
honchos
The first and second numbers in a sequence of numbers are plotted as the x and y coordinates, respectively, of a point on the coordinate plane, as are the third and fourth numbers, and all subsequent pairs in the sequence, and a line is formed by connecting these points, what would be the slope of the line?

(1) Except for the first number, the sequence of numbers is formed by doubling the previous number and then subtracting 1.
(2) The first number in the sequence is 3.
Show more

VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: A

When using the sequence described in statement 1, almost any number you start with will produce a line with a slope of 2. The exception is if you start with 1. However, in this case, all the points are the same point, and you will not have formed a line. The stem specifies that a line is formed, so the sequence cannot begin with 1. This statement can also be handled without picking numbers. If the first number is x, the first 4 numbers are x, 2x - 1, 4x - 3, 8x - 7. That gives us the points (x, 2x -1) and (4x - 3, 8x - 7). To calculate slope, put the difference between the y values over the difference between the x values.

This gives us \(\frac{(8x - 7)-(2x - 1)}{(4x - 3) - x}) = \frac{(6x−6)}{(3x−3)} = 2*\frac{(3x−3)}{(3x−3)} = 2\). Accordingly, the statement is sufficient.

NOTE: The slope fraction above is undefined when x = 1, since we can't ever have 0 in the denominator. This shows us that we will not get a line when x = 1.

Although statement 2 provides us with the first number in the sequence, it does not enable us to determine any subsequent numbers. As a result, we cannot determine the slope, and this statement is insufficient. Therefore, the correct answer is A.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,966
Own Kudos:
1,117
Posts: 38,966
Kudos: 1,117
The first and second numbers in a sequence of numbers are pl 09 May 2023, 05:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109803 posts
kingbucky
498 posts
Gmat860sanskar
212 posts