GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Mar 2019, 12:09

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

Set S contains N integers. Is S a set of distinct consecutive integers

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

Hide Tags

 
Director
Director
User avatar
V
Joined: 06 Jan 2015
Posts: 605
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 17 Dec 2017, 02:44
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

27% (01:27) correct 73% (01:38) wrong based on 30 sessions

HideShow timer Statistics

Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal

_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1216
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 17 Dec 2017, 04:18
NandishSS wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal


Statement 1: if \(S\) is a set of distinct consecutive integers, then \(S ={a,a+1,a+2..........,a+(N-1)}\), where \(a\) is the first element of the set

Range of consecutive elements in set \(S =[a+(N-1)]-a=N-1\)

As per this statement \(N-1=N => -1=0\), which is not possible. Hence elements in set \(S\) are NOT consecutive. Sufficient

Statement 2: We know nothing about the elements in Set \(S\) and as explained in Statement 1, range of consecutive elements will be \(N-1\).

As per this statement range can be \(N\) or \(N-1\) or any other number. Insufficient

Option A

--------------------------------------------------------

Alternatively take few examples of consecutive set and test the statement. For eg. let S={1,2,3}, here N=3

Statement 1: Range of S = 3-1=2 but as per this statement range =3. hence S is not consecutive. Sufficient

Statement 2: implies Range<3+1, so range can be 3 or 2 or 1 etc. Insufficient
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 53709
Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 17 Dec 2017, 05:24
NandishSS wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal


Similar question to practice: https://gmatclub.com/forum/a-list-conta ... 65873.html
_________________

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

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7415
Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 17 Dec 2017, 05:45
NandishSS wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

(1) The range of S is N

(2) The range of S is less than N+1

Source: expertsglobal



Not a very good formatting of question by the source..
consecutive integers have to be distinct, so mere "Is S a set of consecutive integers?" should have been sufficient.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1438
Location: India
Premium Member
Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 26 Jun 2018, 22:07
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global


So S contains N integers, which could be distinct or there could be repetitions. We have to determine whether S contains distinct consecutive integers or not.
Range of a list of numbers is the: (Max Value in that list) - (Min Value in that list)

(1) So N integers, and range is N only.
Lets take an example. Say there are 5 integers in this list and range is also 5. Can these 5 be consecutive?
NO. Because if we write 5 consecutive integers (x, x+1, x+2, x+3, x+4) then range of these would be '4' (1 less than 5).
So basically if we have N consecutive integers (x, x+1, x+2, x+3... , x+N-1) then their range would be 'N-1' (1 less than N).
Thus we can conclude that this list does NOT contain all distinct consecutive integers. This is thus sufficient to answer the question with a NO.

(2) There are N integers and range is less than N+1.
As explained in analysis of first statement, these integers could be all distinct consecutive, in which case range would be N-1 (which is less than N+1).
Or we could have all integers as same, in which case range would be '0' (still less than N+1).
So we cannot conclude whether this list contains distinct consecutive integers or not. Not sufficient.

Hence A answer
Manager
Manager
User avatar
S
Joined: 13 Feb 2018
Posts: 159
GMAT 1: 640 Q48 V28
Premium Member CAT Tests
Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 27 Jun 2018, 02:13
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global



I dont get the 1st statement, is there a typo?
Manager
Manager
User avatar
B
Joined: 24 Nov 2017
Posts: 59
Location: India
GMAT 1: 720 Q51 V36
Re: Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 27 Jun 2018, 04:49
LevanKhukhunashvili wrote:
pushpitkc wrote:
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N
2. The range of S is less than N+1

Source: Experts Global



I dont get the 1st statement, is there a typo?


There is no typo.

if S is a set of N distinct consecutive integers, the range will be N - 1.
For example, let S = {1, 2, 3, 4, 5}
Number of elements in S = 5. So, N in this case is 5.
Range = 5 - 1 = 4.

If the first of the integers is a, the second one will be a + 1, the third will be a + 2 and the Nth will be a + (N - 1).
So, the range will be a + (N - 1) - a = (N - 1).

If the range as given in statement 1 is N and not (N - 1) {what it will be if these are N consecutive integers}, then the N integers in set S CANNOT be consecutive integers.
So, statement 1 is sufficient.
_________________

An IIM C Alumnus - Class of '94
GMAT Tutor at Wizako GMAT Classes & Online Courses

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Dec 2017
Posts: 385
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
Set S contains N integers. Is S a set of distinct consecutive integers  [#permalink]

Show Tags

New post 27 Jun 2018, 05:50
Set S contains N integers. Is S a set of distinct consecutive integers?

1. The range of S in N

Range a(n)-a(1)=n,

1)Consecutive: "Consecutive integers" means arithmetic progression, in which a(n)=a(1)+(n-1)*d
In our case d=1, because numbers are aconsecutive (+1), hence a(n)=a(1)+n-1a(1)+n-1-a(1)=n, -1=0 - which is NEVER true, so our set S can not be a set of distinct consecutive integers. Sufficient

2. The range of S is less than N+1

Range a(n)-a(1)<n+1

1)Consecutive: a(1)+n-1-a(1)<n+1, -1<1 -set S can be a set of distinct consecutive integers
2)Non-consecutive:let d=2, then a(1)+(n-1)*2-a(1)<n+1, 2n-2<n+1, n<3 - set S can be a set of distinct non-consecutive integers. Let's check {2,4}, where 4-2<2+1. Not sufficient

Answer (A)
GMAT Club Bot
Set S contains N integers. Is S a set of distinct consecutive integers   [#permalink] 27 Jun 2018, 05:50
Display posts from previous: Sort by

Set S contains N integers. Is S a set of distinct consecutive integers

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.