Sep 22 08:00 PM PDT  09:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE Sep 23 08:00 AM PDT  09:00 AM PDT Join a free 1hour webinar and learn how to create the ultimate study plan, and be accepted to the upcoming Round 2 deadlines. Save your spot today! Monday, September 23rd at 8 AM PST Sep 28 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn two proprietary ways to PreThink assumptions and ace GMAT CR in 10 days.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58095

A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
09 Aug 2010, 08:18
Question Stats:
55% (00:51) correct 45% (01:07) wrong based on 929 sessions
HideShow timer Statistics
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 Problem Solving Question: 158 Category: Arithmetic Properties of numbers Page: 83 Difficulty: 600 The Official Guide For GMAT® Quantitative Review, 2ND Edition
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 58095

A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
13 Mar 2014, 02:25
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.
_________________




Manager
Joined: 31 Oct 2011
Posts: 215

A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
09 Aug 2010, 09:54
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 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
Why not 3? "for any number t in the set, t + 2 is in the set"  > t + 2 = r t = r 2 if 1 = r, t can be 3 ( 3 = 1 2)
What's wrong with my logic?



Retired Moderator
Joined: 02 Sep 2010
Posts: 735
Location: London

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
07 Jan 2011, 00:07
dc123 wrote: 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, then which must also be in the set
3 1 5
I II I and II II and III all 3 Since 1 is in the set, 1 must be there Since 1 is there, 3 must be there Since 3 it there, 5 must be there 1 may or may not be there So answer is II and III (D)
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
05 Apr 2012, 20:27
eybrj2 wrote: 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 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
Why not 3? "for any number t in the set, t + 2 is in the set"  > t + 2 = r t = r 2 if 1 = r, t can be 3 ( 3 = 1 2)
What's wrong with my logic? Question says that if t is in the set, 't+2' must be in the set. It doesn't say that 't+2' can be in the set only if t is in the set too. Say, if I put 10 in the set, I have to put 12 and then 14 and then 16 etc. I don't necessarily have to put 8 in the set. 8 may or may not be there. Similarly, if 1 is in the set, 1, 3 and 5 (and 7 etc) must be in the set. 3 may or may not be.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
04 Aug 2012, 05:06
jpr200012 wrote: 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 Responding to a pm: Forget this question. Consider this: If I go to the movies, my friend Disha must go with me. If Disha goes to the movies, Ari must go to the movies too. So now what can you say if I tell you that I went to the movies? You can say that Disha went too. And further, you can say that Ari went too. What if I tell you Disha went to the movies? Does it mean I went too? If I go, Disha must go. But if Disha goes, is it necessary for me to go? No, she has no such hang ups. She can easily go with or without me. But if Disha goes, Ari must go too. So we can say that Ari went to the movies. The question is very similar. If 't' is in the set, 't+2' must be in the set too. But is it essential for 't2' to be in the set? No! Just like Disha doesn't need me, 't+2' doesn't need 't'. 't+2' needs only 't+4'. If 't+2' is in the set, 't+4' must be picked too. If 't+4' is there, 't+6' must be there too and so on...
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Math Expert
Joined: 02 Sep 2009
Posts: 58095

A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
15 Mar 2014, 10:51



Intern
Joined: 20 Nov 2013
Posts: 25

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
04 Jun 2014, 23:39
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.



Manager
Joined: 04 Jan 2014
Posts: 72

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
12 Apr 2015, 08:15
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: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
12 Apr 2015, 09:33
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.



Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 187
Location: India
Concentration: Finance, International Business

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
18 Jul 2017, 22:54
I have trouble understanding this question. so the question says that if t is there then t+2 must be there. So 1 can be t or t+2. So if t+2=1 then t=3 therefore 3 is in the set. I know iam wrong somewhere in my concept. Can someone please clarify this to me . Thanks.



Math Expert
Joined: 02 Sep 2009
Posts: 58095

A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
18 Jul 2017, 23:22
longhaul123 wrote: I have trouble understanding this question. so the question says that if t is there then t+2 must be there. So 1 can be t or t+2. So if t+2=1 then t=3 therefore 3 is in the set. I know iam wrong somewhere in my concept. Can someone please clarify this to me . Thanks. The question says, if some number is in the set, then 2 more than that number is also in the set. It does not say that if some number is in the set, then 2 less than that number is in the set. We know that 1 is in the set, so 1 + 2 = 1 must also be in the set. We cannot say whether 3 is in the set because we are not told that 1 2 is in the set but that 1 + 2 must be in the set.
_________________



Intern
Joined: 14 Aug 2017
Posts: 1

Re: A set of numbers has the property that for any number t in the set, 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: 58095

Re: A set of numbers has the property that for any number t in the set, 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
_________________



NonHuman User
Joined: 09 Sep 2013
Posts: 12517

Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
Show Tags
01 May 2019, 03:38
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: A set of numbers has the property that for any number t in the set, t
[#permalink]
01 May 2019, 03:38






