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

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Director
Joined: 08 Jul 2004
Posts: 558
A set of numbers has the property that for any number t in  [#permalink]

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Updated on: 04 Aug 2012, 04:00
1
14
00:00

Difficulty:

45% (medium)

Question Stats:

54% (00:25) correct 46% (00:34) wrong based on 466 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html

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Regards, S

Originally posted by saurya_s on 12 Apr 2005, 09:30.
Last edited by Bunuel on 04 Aug 2012, 04:00, edited 2 times in total.
Edited the question and added the OA.
Senior Manager
Joined: 19 Feb 2005
Posts: 438
Location: Milan Italy

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12 Apr 2005, 10:19
2
1
D for me.
We know for sure that t (-1) is in the set
so t+2=+1 is in the set
so 1+2=3 is in the set
so 3+2=5 is in the set

-1 could be the first element of the set, so -3 can't be said to belong to the set
Director
Joined: 08 Jul 2004
Posts: 558

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12 Apr 2005, 11:18
thearch wrote:
D for me.
We know for sure that t (-1) is in the set
so t+2=+1 is in the set
so 1+2=3 is in the set
so 3+2=5 is in the set

-1 could be the first element of the set, so -3 can't be said to belong to the set

I am not sure ; if -1 is in the set then either it is t ot t+2. if it is t, then the other number is t+2 ie 1. If -1 is t+2 then, t is -3. So according to me answer should be C.
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Regards, S
VP
Joined: 18 Nov 2004
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12 Apr 2005, 11:47
"B"....ques says for a number t , t+2 shd be there we know -1 is there so
-1+2 = 1 MUST be there. I don't think we can extrapolate this and make this an infinite series. Surya do u have the OA ?
Senior Manager
Joined: 15 Mar 2005
Posts: 394
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12 Apr 2005, 17:37
banerjeea_98 wrote:
"B"....ques says for a number t , t+2 shd be there we know -1 is there so
-1+2 = 1 MUST be there. I don't think we can extrapolate this and make this an infinite series. Surya do u have the OA ?

Hey Baner, but we already have this as an infinite series in one direction (positive). But I agree with you - this could be an infinite series in one direction, starting with -1. So we cannot assume the presence of numbers lower than -1.
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Manager
Joined: 25 Oct 2004
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12 Apr 2005, 17:54
I think the answer should be D. I think its safe o assume that the series is an infinite series starting with -1. Any thoughts???

Whats the OA
Director
Joined: 18 Feb 2005
Posts: 620

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12 Apr 2005, 20:04
banerjeea_98 wrote:
"B"....ques says for a number t , t+2 shd be there we know -1 is there so
-1+2 = 1 MUST be there. I don't think we can extrapolate this and make this an infinite series. Surya do u have the OA ?

if t+2 exists in the set then it would be t for another number......So it should be valid for all the numbers given.

A number's existence is enough to qualify itself to become t
VP
Joined: 18 Nov 2004
Posts: 1334

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12 Apr 2005, 21:03
I agree this is another of those controversial ques, u can argue it both ways....let's wait for the OA...I bet OA is not "E" Surya can u post OA plz and OE if available.
VP
Joined: 25 Nov 2004
Posts: 1385
Re: PS Set of numbers  [#permalink]

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12 Apr 2005, 22:40
2
I was thinking B first. but, what does "A set of numbers has the property that for any number t in the set, t + 2 is in the set"?

i think any number indicates to an infinite series. if so, it should be E.
t could be any number in the series. if t is in the series, t+2 is also in the series. if t=t+2, then t+2=t+4. then if t+2=t, then t=t-2.

Correct, if any........
Senior Manager
Joined: 19 Feb 2005
Posts: 438
Location: Milan Italy

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13 Apr 2005, 03:08
saurya_s wrote:
I am not sure ; if -1 is in the set then either it is t ot t+2. if it is t, then the other number is t+2 ie 1. If -1 is t+2 then, t is -3. So according to me answer should be C.

you're right, but the stem doesn't ask for numbers that COULD be in the set (because I agree with you that -3 COULD be in the set, but we're not sure of that, so we can't say that it MUST be there)

desperately waiting for the OA
Intern
Joined: 11 Mar 2005
Posts: 21

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13 Apr 2005, 04:32
banerjeea_98 wrote:
"B"....ques says for a number t , t+2 shd be there we know -1 is there so
-1+2 = 1 MUST be there. I don't think we can extrapolate this and make this an infinite series. Surya do u have the OA ?

Question says if t is there, then t+2 must be there. That's an infinite series, if ever there was one. However, we can only be sure of this series in one direction

Go with D.
Director
Joined: 27 Dec 2004
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13 Apr 2005, 06:52
I pick C.

Let t = -1,
Then we know t + 2 = -1 + 2 = 1.

Then let t + 2 = -1
Then t = -1 -2 = -3

All other info that can be applied are assumptions so for sure I think 1 and -3 are certainly in the set thus C.
Director
Joined: 27 Dec 2004
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13 Apr 2005, 06:54
Same reasoning here.
I anticipate the OA though
Director
Joined: 08 Jul 2004
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13 Apr 2005, 14:14
The OA I have got is D. I am not convinced though. Why it has to go in postive direction only. For me it should be C. can any one justify D as answer convincingly.
S
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Regards, S
SVP
Joined: 03 Jan 2005
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Re: PS Set of numbers  [#permalink]

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14 Apr 2005, 14:45
saurya_s wrote:
A set of numbers has the property that for any number t in the set, t + 2 is in the set. If â€“1
is in the set, which of the following must also be in the set?
I. -3
II. 1
III. 5

If -1 is in the set, then -1+2=1 is in the set, then 1+2=3 is in the set, then 3+2=5 is in the set. We don't know about -3, however, since we don't have t-2 in the set if t in the set.

_________________
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keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
Senior Manager
Joined: 07 Sep 2010
Posts: 256
Re: A set of numbers has the property that for any number t in  [#permalink]

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04 Aug 2012, 03:28
Hi,
Can someone please clarify my doubts..

Question is
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?

Doubt 1 -
Lets say t= -1 ; then t+2 is is set = i.e. 1 is in set.

Since question stem is Must be True, how do we make sure that this pattern will continue.
i.e if 1 is in set, then 3 will be in set and so on..

Also

Doubt 2 -
Cant we assume that
t+2 = -1
then t= -3(should also be in set)

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 55266
Re: A set of numbers has the property that for any number t in  [#permalink]

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04 Aug 2012, 04:00
3
2
imhimanshu wrote:
Hi,
Can someone please clarify my doubts..

Question is
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?

Doubt 1 -
Lets say t= -1 ; then t+2 is is set = i.e. 1 is in set.

Since question stem is Must be True, how do we make sure that this pattern will continue.
i.e if 1 is in set, then 3 will be in set and so on..

Also

Doubt 2 -
Cant we assume that
t+2 = -1
then t= -3(should also be in set)

Thanks

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.

1. The question says "a set of numbers has the property that for ANY number t in the set, t + 2 is in the set", so if 1 is in the set then 1+2=3 MUST be in the set.

2. 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.

Similar questions to practice:
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.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-i-if-x-is-in-k-then-x-96907.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
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Re: A set of numbers has the property that for any number t in  [#permalink]

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27 Aug 2018, 19:17
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Re: A set of numbers has the property that for any number t in   [#permalink] 27 Aug 2018, 19:17
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