It is currently 16 Jan 2018, 11:34

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The first and second numbers in a sequence of numbers are pl

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 596

Kudos [?]: 680 [2], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 16 Sep 2013, 21:56
2
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

55% (01:20) correct 45% (01:16) wrong based on 117 sessions

HideShow timer Statistics

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.
[Reveal] Spoiler: OA

_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html


Last edited by Bunuel on 31 Dec 2017, 13:53, edited 4 times in total.
Edited the question.

Kudos [?]: 680 [2], given: 298

8 KUDOS received
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 624

Kudos [?]: 1436 [8], given: 136

Premium Member
Re: The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 16 Sep 2013, 22:10
8
This post received
KUDOS
honchos wrote:
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.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1436 [8], given: 136

Intern
Intern
avatar
Joined: 22 Jul 2013
Posts: 3

Kudos [?]: 7 [0], given: 1

Location: United States
Concentration: Finance, General Management
GMAT 1: 750 Q51 V40
GPA: 3.11
WE: Engineering (Computer Software)
Re: The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 16 Sep 2013, 22:56
mau5 wrote:
honchos wrote:
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.

Kudos [?]: 7 [0], given: 1

Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 624

Kudos [?]: 1436 [0], given: 136

Premium Member
Re: The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 16 Sep 2013, 23:22
nspatel wrote:
mau5 wrote:
honchos wrote:
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.


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..
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1436 [0], given: 136

Intern
Intern
avatar
Joined: 20 Dec 2014
Posts: 19

Kudos [?]: [0], given: 24

Re: The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 23 Dec 2014, 01:55
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 wrote:
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.

Kudos [?]: [0], given: 24

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

Re: The first and second numbers in a sequence of numbers are pl [#permalink]

Show Tags

New post 31 Dec 2017, 13:53
honchos wrote:
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.


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 139200 [0], given: 12779

Re: The first and second numbers in a sequence of numbers are pl   [#permalink] 31 Dec 2017, 13:53
Display posts from previous: Sort by

The first and second numbers in a sequence of numbers are pl

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.