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

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A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 09 Aug 2010, 08:18
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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

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A set of numbers has the property that for any number t in the set, t  [#permalink]

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

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New post 09 Aug 2010, 09:54
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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?
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 07 Jan 2011, 00:07
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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)
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 05 Apr 2012, 20:27
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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.
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 04 Aug 2012, 05:06
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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 't-2' 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...
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A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 15 Mar 2014, 10:51
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Similar questions to practice:
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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

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New post 12 Apr 2015, 08:15
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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..
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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

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New post 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.
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A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 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.
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 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.
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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New post 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/for-a-certain ... 61920.html
http://gmatclub.com/forum/for-a-certain ... 36580.html
http://gmatclub.com/forum/a-set-of-numb ... 98829.html
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http://gmatclub.com/forum/k-is-a-set-of ... 03005.html
http://gmatclub.com/forum/k-is-a-set-of ... 66908.html
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Re: A set of numbers has the property that for any number t in the set, t  [#permalink]

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