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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] New post 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] New post 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] New post 09 Aug 2010, 07:40
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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

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.

Answer: D.

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] New post 09 Aug 2010, 08:54
jpr200012 wrote:
must/could ARGH!


:-D :-D :-D I did not spot the difference the first time. Slowly getting into the groove :) .
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Re: HELP [#permalink] New post 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] New post 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.
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Re: A set of numbers has the property that for any number t in [#permalink] New post 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] New post 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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Re: A set of numbers has the property that for any number t in t [#permalink] New post 04 Aug 2012, 04:06
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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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Re: A set of numbers has the property that for any number t in t [#permalink] New post 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] New post 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.

Answer: D.

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] New post 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] New post 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.

What about one?

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.

Thus answer D.
Re: A set of numbers has the property that for any number t in t   [#permalink] 01 Aug 2014, 02:24
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