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

 It is currently 16 Nov 2018, 16:57

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

November 17, 2018

November 17, 2018

07:00 AM PST

09:00 AM PST

Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### GMATbuster's Weekly GMAT Quant Quiz # 9

November 17, 2018

November 17, 2018

09:00 AM PST

11:00 AM PST

Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50619
A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

13 Mar 2014, 01:25
2
1
17
00:00

Difficulty:

45% (medium)

Question Stats:

55% (00:52) correct 45% (01:08) wrong based on 896 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each 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:
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!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

15 Mar 2014, 09:51
3
14
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.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-both-161920.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
k-is-a-set-of-numbers-such-that-166908.html
_________________
##### General Discussion
Intern
Joined: 20 Nov 2013
Posts: 25
Schools: LBS '17
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

04 Jun 2014, 22:39
2
1
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, 03:09
why can't we say :

-1 = t+2
t=-3 ?
Manager
Joined: 04 Jan 2014
Posts: 87
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

12 Apr 2015, 07:15
1
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: 118
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, 08:33
1
1
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: 539
GMAT 1: 630 Q49 V27
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

12 Apr 2015, 09:14
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: 87
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

13 Apr 2015, 03:54
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, 20:20
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: 50619
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

24 Nov 2016, 22:56
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.

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
_________________
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, 22:10

I am confused why E is not the answer.
Math Expert
Joined: 02 Sep 2009
Posts: 50619
Re: A set of numbers has the property that for any number t in t  [#permalink]

### Show Tags

07 Dec 2017, 22:51
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:
http://gmatclub.com/forum/for-a-certain ... 61920.html
http://gmatclub.com/forum/for-a-certain ... 36580.html
http://gmatclub.com/forum/a-set-of-numb ... 98829.html
http://gmatclub.com/forum/if-p-is-a-set ... 96630.html
http://gmatclub.com/forum/k-is-a-set-of ... 96907.html
http://gmatclub.com/forum/k-is-a-set-of ... 03005.html
http://gmatclub.com/forum/k-is-a-set-of ... 66908.html
_________________
Re: A set of numbers has the property that for any number t in t &nbs [#permalink] 07 Dec 2017, 22:51
Display posts from previous: Sort by

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

 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®.