Last visit was: 12 Aug 2024, 22:12 It is currently 12 Aug 2024, 22:12
Toolkit
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

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.

# A set of numbers has the property that for any number t in the set

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649111 [221]
Given Kudos: 86922
Tutor
Joined: 16 Oct 2010
Posts: 15218
Own Kudos [?]: 67300 [64]
Given Kudos: 437
Location: Pune, India
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649111 [63]
Given Kudos: 86922
Tutor
Joined: 16 Oct 2010
Posts: 15218
Own Kudos [?]: 67300 [36]
Given Kudos: 437
Location: Pune, India
Re: A set of numbers has the property that for any number t in the set [#permalink]
27
Kudos
9
Bookmarks
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.
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649111 [24]
Given Kudos: 86922
Re: A set of numbers has the property that for any number t in the set [#permalink]
7
Kudos
17
Bookmarks
General Discussion
Manager
Joined: 31 Oct 2011
Posts: 200
Own Kudos [?]: 8017 [7]
Given Kudos: 18
Re: A set of numbers has the property that for any number t in the set [#permalink]
5
Kudos
1
Bookmarks
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: 613
Own Kudos [?]: 2976 [4]
Given Kudos: 25
Location: London
Q51  V41
Re: A set of numbers has the property that for any number t in the set [#permalink]
2
Kudos
2
Bookmarks
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)
Intern
Joined: 20 Nov 2013
Posts: 21
Own Kudos [?]: 30 [3]
Given Kudos: 188
Schools: LBS '17
Re: A set of numbers has the property that for any number t in the set [#permalink]
2
Kudos
1
Bookmarks
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: 55
Own Kudos [?]: 56 [2]
Given Kudos: 20
Re: A set of numbers has the property that for any number t in the set [#permalink]
2
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
Joined: 20 Jan 2013
Status:I am not a product of my circumstances. I am a product of my decisions
Posts: 95
Own Kudos [?]: 278 [2]
Given Kudos: 71
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 [#permalink]
1
Kudos
1
Bookmarks
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
Joined: 03 Jul 2017
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Posts: 145
Own Kudos [?]: 33 [0]
Given Kudos: 27
Location: India
Re: A set of numbers has the property that for any number t in the set [#permalink]
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: 94906
Own Kudos [?]: 649111 [0]
Given Kudos: 86922
Re: A set of numbers has the property that for any number t in the set [#permalink]
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
Own Kudos [?]: 0 [0]
Given Kudos: 55
Re: A set of numbers has the property that for any number t in the set [#permalink]

I am confused why E is not the answer.
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649111 [1]
Given Kudos: 86922
Re: A set of numbers has the property that for any number t in the set [#permalink]
1
Bookmarks
sahoop wrote:

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:
https://gmatclub.com/forum/for-a-certain ... 61920.html
https://gmatclub.com/forum/for-a-certain ... 36580.html
https://gmatclub.com/forum/a-set-of-numb ... 98829.html
https://gmatclub.com/forum/if-p-is-a-set ... 96630.html
https://gmatclub.com/forum/k-is-a-set-of ... 96907.html
https://gmatclub.com/forum/k-is-a-set-of ... 03005.html
https://gmatclub.com/forum/k-is-a-set-of ... 66908.html
Intern
Joined: 25 Nov 2020
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 6
Re: A set of numbers has the property that for any number t in the set [#permalink]
Bunuel 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

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.

BUT who says that the set contains of 4 numbers? 5 COULD be in there but it is also possible that the set only contains of 3 numbers? or am I thinking too complex
Math Expert
Joined: 02 Sep 2009
Posts: 94906
Own Kudos [?]: 649111 [1]
Given Kudos: 86922
Re: A set of numbers has the property that for any number t in the set [#permalink]
1
Kudos
kluni94 wrote:
Bunuel 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

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.

BUT who says that the set contains of 4 numbers? 5 COULD be in there but it is also possible that the set only contains of 3 numbers? or am I thinking too complex

Any number COULD be in the set but we are asked "which of the following MUST also be in the set?" and only II and III MUST be in the set.
Intern
Joined: 03 May 2021
Posts: 37
Own Kudos [?]: 14 [0]
Given Kudos: 13
Location: Kuwait
Re: A set of numbers has the property that for any number t in the set [#permalink]
Based on the condition, for any number "t" in the set, "t + 2" is also in the set.

Doesn't this mean you can have a set like this:

{10, 12, 18, 20, 31, 33}

If we are given that -1 is in the set, we can only determine that 1 is also in the set.

Where am I going wrong here?
Director
Joined: 05 Jul 2020
Posts: 581
Own Kudos [?]: 303 [0]
Given Kudos: 151
GMAT 1: 720 Q49 V38
WE:Accounting (Accounting)
Re: A set of numbers has the property that for any number t in the set [#permalink]
GK002 wrote:
Based on the condition, for any number "t" in the set, "t + 2" is also in the set.

Doesn't this mean you can have a set like this:

{10, 12, 18, 20, 31, 33}

If we are given that -1 is in the set, we can only determine that 1 is also in the set.

Where am I going wrong here?

GK002, Basically, this set never ends and the set that you have suggested doesn't fulfil the condition. You're correct to say that if -1 is in the set, 1 will be in the set. But if 1 is in the set, we need 3. If 3 is in the set, we need 5 and this loop continues. The set will contain all the odd numbers.
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4914
Own Kudos [?]: 7857 [0]
Given Kudos: 221
Location: India
Re: A set of numbers has the property that for any number t in the set [#permalink]
Top Contributor
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

if -1 is there , then -1 + 2 = 1 should be there.
So if 1 is there, 1 +2 = 3 should be there.
Following the same pattern , we can say 1, 3 , 5 , 7.. should be there in set if -1 is there.

Ans is option (D) II and III only

Thanks,
Clifin J Francis
GMAT SME
Intern
Joined: 03 Nov 2021
Posts: 2
Own Kudos [?]: 1 [0]
Given Kudos: 15
Location: Azerbaijan
GMAT 1: 490 Q34 V22
Re: A set of numbers has the property that for any number t in the set [#permalink]
GK002 wrote:
Based on the condition, for any number "t" in the set, "t + 2" is also in the set.

Doesn't this mean you can have a set like this:

{10, 12, 18, 20, 31, 33}

If we are given that -1 is in the set, we can only determine that 1 is also in the set.

Where am I going wrong here?

Well, I am not a Gmat expert but I have some ideas sometimes.
The important thing is "MUST". I have answered many questions and I have faced many questions that depend on "MUST".
So, there could be 1 in our list, because we already have -1, so according to the statement there must be t+2, so -1+2=1. That is a "MUST". Then, since we have 1 in our list, then there MUST be 3 (t+2 -> 1+2=3). Again, since we have 3 on our list, then we MUST have 5 (3+2).

However, when it comes to -3, we can not say that "-3 MUST be in our list". What if I say that the beginning number of the set is -1. So in that case there is no -3. In other words, -3 CAN BE in our list, not MUST BE.
Re: A set of numbers has the property that for any number t in the set [#permalink]
1   2
Moderator:
Math Expert
94906 posts