Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44573

A set of numbers has the property that for any number t in t [#permalink]
Show Tags
13 Mar 2014, 02:25
Question Stats:
54% (00:37) correct 46% (00:49) wrong based on 769 sessions
HideShow timer Statistics
The Official Guide For GMAT® Quantitative Review, 2ND EditionA set of numbers has the property that for any number t in the set, t + 2 is in the set. If 1 is in the set, which of the following must also be in the set? I. 3 II. 1 III. 5 (A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III Problem Solving Question: 158 Category: Arithmetic Properties of numbers Page: 83 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition  Quantitative Questions ProjectEach week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 44573

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
15 Mar 2014, 10:51
1
This post received KUDOS
Expert's post
13
This post was BOOKMARKED
SOLUTIONA set of numbers has the property that for any number t in the set, t + 2 is in the set. If 1 is in the set, which of the following must also be in the set?
I. 3 II. 1 III. 5(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III The question is which of the following must be in the set, not could be in the set. If 1 is in the set so must be 1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that 1 is in the set we can say that ALL odd numbers more than 1 are also in the set. Answer: D. Similar questions to practice: foracertainsetofnumbersifxisinthesetthenboth161920.htmlforacertainsetofnumbersifxisinthesetthenx136580.htmlasetofnumbershasthepropertythatforanynumbertint98829.htmlifpisasetofintegersand3isinpiseverypositive96630.htmlkisasetofnumberssuchthatiifxisinkthenx96907.htmlkisasetofintegerssuchthatiftheintegerrisink103005.htmlkisasetofnumberssuchthat166908.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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 20 Nov 2013
Posts: 27

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
04 Jun 2014, 23:39
2
This post received KUDOS
Tricky one ! The idea here is the *MUST* condition makes it strict to move forward from the seed number 1 since for any t , t+2 exists. The set could start from 1 and not have 3 in it.



Intern
Joined: 10 May 2011
Posts: 1

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
12 Apr 2015, 04:09
why can't we say :
1 = t+2 t=3 ?



Manager
Joined: 04 Jan 2014
Posts: 95

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
12 Apr 2015, 08:15
1
This post received KUDOS
But how could we assume that the set has n numbers in it when it is not given.. The set could also have 1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that 3 is also in that set, as they dint pinpoint that 1 is the starting number in that set. The starting number can also be 3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question..



Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 128
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

A set of numbers has the property that for any number t in t [#permalink]
Show Tags
12 Apr 2015, 09:33
1
This post received KUDOS
1
This post was BOOKMARKED
sheolokesh wrote: But how could we assume that the set has n numbers in it when it is not given.. The set could also have 1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that 3 is also in that set, as they dint pinpoint that 1 is the starting number in that set. The starting number can also be 3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question.. Maybe I can explain this. Don't know how much of this will be helpful.
The point here is 1 is our reference number i.e. t= 1 Now, since the question is "MUST BE TRUE", we have to find numbers that "RESULT FROM" the operation t+2.
When you say that 3 is present (it could be), we are in fact saying that the operation t+2 "RESULTS IN" the number 1. So here we are making t+2 the reference value and 1 the result of the operation.
In a vague way, when we say Ron is Sam's brother, its not necessary that Sam is also Ron's brother. Sam could be Ron's sister too.
Hope so it clears some of your doubt.



Director
Joined: 07 Aug 2011
Posts: 568
Concentration: International Business, Technology

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
12 Apr 2015, 10:14
Oceana wrote: why can't we say :
1 = t+2 t=3 ? sure, are we given that 1 is not the first element of the set ? if the first element of the set is 1 then 3 cannot exist . but, yes, as you have shown 3 can exist when 1 is not the first element . hope it is clear .
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



Manager
Joined: 04 Jan 2014
Posts: 95

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
13 Apr 2015, 04:54
Ashishmathew01081987 wrote: sheolokesh wrote: But how could we assume that the set has n numbers in it when it is not given.. The set could also have 1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that 3 is also in that set, as they dint pinpoint that 1 is the starting number in that set. The starting number can also be 3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question.. Maybe I can explain this. Don't know how much of this will be helpful.
The point here is 1 is our reference number i.e. t= 1 Now, since the question is "MUST BE TRUE", we have to find numbers that "RESULT FROM" the operation t+2.
When you say that 3 is present (it could be), we are in fact saying that the operation t+2 "RESULTS IN" the number 1. So here we are making t+2 the reference value and 1 the result of the operation.
In a vague way, when we say Ron is Sam's brother, its not necessary that Sam is also Ron's brother. Sam could be Ron's sister too.
Hope so it clears some of your doubt.
Yes that's fine.. But there is another clarification need to be done in my question... How could we say 5 must be in the set unless we know the number of elements in the set then.. I have entwined presence of 5 and 3 here.. If 5 is a must be present, then we are assuming the set has 3+ elements.. But what if the set has only 2 elements of 1 and 3 alone..? isnt that an presumption then?



Intern
Joined: 11 Jun 2016
Posts: 5

A set of numbers has the property that for any number t in t [#permalink]
Show Tags
24 Nov 2016, 21:20
Hi Bunuel,
Can you please explain the mathematical distinction between MUST be and COULD be question stems? I don't understand that.



Math Expert
Joined: 02 Sep 2009
Posts: 44573

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
24 Nov 2016, 23:56
NatC wrote: Bunuel wrote: SOLUTION
A set of numbers has the property that for any number t in the set, t + 2 is in the set. If 1 is in the set, which of the following must also be in the set?
I. 3 II. 1 III. 5
(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III
The question is which of the following must be in the set, not could be in the set.
If 1 is in the set so must be 1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that 1 is in the set we can say that ALL odd numbers more than 1 are also in the set.
Answer: D.
Hi Bunuel, Can you please explain the mathematical distinction between MUST be and COULD be question stems? I don't understand that. Must be true means that something should be true for ANY (ALL) value (cases). Could be true means that something could be true for SOME (at least one) value (case). Check here: search.php?search_id=tag&tag_id=193
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Aug 2017
Posts: 1

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
07 Dec 2017, 23:10
Would the answer be E, Had the question have "could be" instead of "must be"?
I am confused why E is not the answer.



Math Expert
Joined: 02 Sep 2009
Posts: 44573

Re: A set of numbers has the property that for any number t in t [#permalink]
Show Tags
07 Dec 2017, 23:51
sahoop wrote: Would the answer be E, Had the question have "could be" instead of "must be"?
I am confused why E is not the answer. If 1 is the source integer in the set, so if 1 is the smallest integer in the set, then 3 will not be in the set. For example, the set could be {1, 1, 3, 5, 7, ...}. So, again, knowing that 1 is in the set we can say that ALL odd numbers more than 1 are also in the set but we cannot be sure about the numbers less than 1. Check similar questions to understand the concept better: http://gmatclub.com/forum/foracertain ... 61920.htmlhttp://gmatclub.com/forum/foracertain ... 36580.htmlhttp://gmatclub.com/forum/asetofnumb ... 98829.htmlhttp://gmatclub.com/forum/ifpisaset ... 96630.htmlhttp://gmatclub.com/forum/kisasetof ... 96907.htmlhttp://gmatclub.com/forum/kisasetof ... 03005.htmlhttp://gmatclub.com/forum/kisasetof ... 66908.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? Extrahard Quant Tests with Brilliant Analytics




Re: A set of numbers has the property that for any number t in t
[#permalink]
07 Dec 2017, 23:51






