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

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A set of numbers has the property that for any number t in t [#permalink]  09 Aug 2010, 07:18
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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
[Reveal] Spoiler: OA
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Re: Sequence problem from QR 2nd PS158 [#permalink]  09 Aug 2010, 07:20
If $$-1$$ in the set, why would the set not include all odd numbers?

If $$-1$$ in the set, then $$-1$$ could be $$t + 2$$ and $$t$$ would be $$-3$$. Shouldn't the problem state $$t = -1$$ if this isn't the case?
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Re: Sequence problem from QR 2nd PS158 [#permalink]  09 Aug 2010, 07:40
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Expert's post
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

If $$-1$$ in the set, why would the set not include all odd numbers?

If $$-1$$ in the set, then $$-1$$ could be $$t + 2$$ and $$t$$ would be $$-3$$. Shouldn't the problem state $$t = -1$$ if this isn't the case?

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.

Now, about your question: we don't know which is the source integer in the set, if it's -1 than odd number less than it won't be in the set but if source integer is let's say -11 than -3 will be in the set. So -3 may or may not be in the set.

Hope it's clear.
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Re: Sequence problem from QR 2nd PS158 [#permalink]  09 Aug 2010, 08:54
jpr200012 wrote:
must/could ARGH!

I did not spot the difference the first time. Slowly getting into the groove .
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Re: HELP [#permalink]  06 Jan 2011, 23:07
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)
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A set of numbers has the property that for any number t in [#permalink]  05 Apr 2012, 11:58
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?

Last edited by Bunuel on 05 Apr 2012, 12:15, edited 1 time in total.
Edited the question
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Re: A set of numbers has the property that for any number t in [#permalink]  05 Apr 2012, 12:23
Expert's post
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?

Merging similar topics. Your doubt is addressed in the posts above (for example: a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html#p761683).

Similar questions to practice:
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.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

Hope it helps.
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Re: A set of numbers has the property that for any number t in [#permalink]  05 Apr 2012, 19:27
Expert's post
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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6229 Location: Pune, India Followers: 1677 Kudos [?]: 9618 [2] , given: 197 Re: A set of numbers has the property that for any number t in t [#permalink] 04 Aug 2012, 04:06 2 This post received KUDOS Expert's post 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... _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: A set of numbers has the property that for any number t in t [#permalink]  04 Aug 2012, 05:14
Hi Karishma,
Awesome Explanation. Wonderful Analogy.. Hats Off..

Thanks Again !
H

VeritasPrepKarishma wrote:
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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Re: Sequence problem from QR 2nd PS158 [#permalink]  04 Aug 2012, 17:37
Bunuel wrote:
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

If $$-1$$ in the set, why would the set not include all odd numbers?

If $$-1$$ in the set, then $$-1$$ could be $$t + 2$$ and $$t$$ would be $$-3$$. Shouldn't the problem state $$t = -1$$ if this isn't the case?

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.

Now, about your question: we don't know which is the source integer in the set, if it's -1 than odd number less than it won't be in the set but if source integer is let's say -11 than -3 will be in the set. So -3 may or may not be in the set.

Hope it's clear.

i selected E thinking the same way as above....now i realize what i should be thinking while answering Thanks Bunuel.
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Re: A set of numbers has the property that for any number t in t [#permalink]  14 Jul 2014, 07:13
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Re: A set of numbers has the property that for any number t in t [#permalink]  01 Aug 2014, 02:24
If -1 is in the set, then

-1 + 2 = 1 is in the set
hence
1 + 2 = 3 is in the set
hence
3+2 = 5 is in the set.

So II and III are correct.

if -1 is in the set, -3 COULD be in the set, but we don't know that, the set could also "begin" with -1.

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Re: A set of numbers has the property that for any number t in t [#permalink]  19 Aug 2015, 08:35
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).

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Re: A set of numbers has the property that for any number t in t   [#permalink] 19 Aug 2015, 08:35
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