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

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Manager
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A set of numbers has the property that for any number t in [#permalink]  17 Oct 2005, 06:49
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III
Senior Manager
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Ans is D

If -1 is in set, then t+2 = 1 can be in set (Hence II)

If 1 can be in set then t+2 = 3 can be in set.
If 3 can be in set then t+2 = 5 can be in set. (Hence III)
Manager
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E.

-3 + 2 = -1
- 1
and 5.
Senior Manager
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jainvineet wrote:
E.

-3 + 2 = -1
- 1
and 5.

The question did not mention anything about -3. How did you get that?
VP
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D is correct in my opinion

You can not assume that the first number of the set has a realtion with -1
Maybe the set begins with -2 and the numbers are then higher and higher. So you can not be sure that -3 is inside it.
It doesn't say that all numbers have the property to have a relation with other numbers by doing t-2. So you can only go in the way t+2.
Director
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Re: p/s - # [#permalink]  17 Oct 2005, 08:50
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III

Logically, just because -1 is in the set doesn't mean that -3 is in the set. Yes, -3 COULD be in the set but the question stem asks for what numbers MUST be in the set. You must always start with the numbers that are given to you and not extrapolate backwards on a problem like this (IMHO). I will go with D.
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Another D. Agree with explanations above about not being E.

OA?
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Re: p/s - # [#permalink]  19 Oct 2005, 10:00
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III

If t then t+2 doesn't mean that if t+2 then t, or if t then t-2.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
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Re: p/s - # [#permalink]  19 Oct 2005, 15:30
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III

1 must be in the set because we are given -1 as one of the number. I didn't choose 5 because we don't know how many numbers are in the set.

5 COULD be in the set of numbers but it doesn't have to be.
Director
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Re: p/s - # [#permalink]  19 Oct 2005, 15:36
TeHCM wrote:
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III

1 must be in the set because we are given -1 as one of the number. I didn't choose 5 because we don't know how many numbers are in the set.

5 COULD be in the set of numbers but it doesn't have to be.

I hope this trickygmat guy posts the OA; hopefully in the next millenium at the very least.
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Re: p/s - # [#permalink]  19 Oct 2005, 17:32
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III
this is one of the most discussed question.

should be D. if t, then t+2 means 1 and 5 are in the set since -1 is in the set but not -3 (=-1-2).
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If t = -1, then t+2 = 1. This number 1 will then become another t, which gives t+2 of 3, and the proess is repeated to give us 5.

If t+2 = -1, then t = -3. -1 will then give 1, 3, 5 as sequences of t and t+2.

I'll take E.
VP
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Ywilfried

you know that T+2 is in the set
Moreover it is not said that ONLY T+2 are in the set

so let's say T=-1, T could be in the set and not comes from a T-2 number, however T will bring T+2 into the set

if a number is in the set, it will bring this number+2
Now imagine the set begins with 2 as the smallest value for example. So you will not find 0 inside this set (it will 2,4,6,8,10,...). However you will find 4 and 6

if there is a disscussion it should be between B and D
can we consider t+2 as t ?

i stick with D, if you have T, you have T+2 in the set and it is said that any number in the set then has T+2...
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Antmavel wrote:
Ywilfried

you know that T+2 is in the set
Moreover it is not said that ONLY T+2 are in the set

so let's say T=-1, T could be in the set and not comes from a T-2 number, however T will bring T+2 into the set

if a number is in the set, it will bring this number+2
Now imagine the set begins with 2 as the smallest value for example. So you will not find 0 inside this set (it will 2,4,6,8,10,...). However you will find 4 and 6

if there is a disscussion it should be between B and D
can we consider t+2 as t ?

i stick with D, if you have T, you have T+2 in the set and it is said that any number in the set then has T+2...

Your explanation was for the case if -1 is the first number in the series. However, you picked D. How do you know 3 is not the last in the series? If 3 is the last number in the series, there's no 5.

The question says for every T, there is a T+2. This T and T+2 value is not fixed at a certain number. The number -1 is the T value of 1, and the T+2 value of -3. Similarly, 5 is the T+2 value of 3, but 3 is the T value of 5 and T+2 value of 1. You get the picture? I think this is an infinite series, since each value has a relationship with another number.

I'll stick with E
VP
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I understand your way of reasonning now

OA will decide our fate
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Antmavel wrote:
I understand your way of reasonning now

OA will decide our fate

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Re: p/s - # [#permalink]  19 Oct 2005, 20:51
trickygmat wrote:
A set of numbers has the property that for any number t in the set t+2 is also 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 & II only
D. II & III Only
E. I, II & III

My answer is B. The question stem says that for any t there is a t+2, and not the opposite. So if -1 is there then 1 should be there. -3 would belong to this set only when we say for every t+2 there is a t.

I would say B for this.
Director
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Antmavel wrote:
I understand your way of reasonning now

OA will decide our fate

Your fates may never come my friends. This guy (or girl i should say) trickygmat is very bad about posting the OA.
Manager
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I dont know how reliable the OA is.... but it is D.
Manager
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It must be D.

The reasoning for why -3 is not is the set is well explained.

B is wrong because 5 must be in the set if -1 is part of it. The stem states that if t then t+2 is there as well. This creates an infinite set of numbers. Size is not a factor. If -1 is part of the set you know that 1, 3, 5, 7, 9, .... etc. every positive odd number is part of the set.

Brendan.

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