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The set S of numbers has the following properties: I) If x

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The set S of numbers has the following properties: I) If x [#permalink] New post 28 Feb 2007, 17:57
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A
B
C
D
E

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(N/A)

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0% (00:00) correct 100% (01:29) wrong based on 6 sessions
The set S of numbers has the following properties:

I) If x is in S, then 1/x is in S.
II) If both x and y are in S, then so is x + y.

Is 3 in S?

(1) 1/3 is in S.
(2) 1 is in S.
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 [#permalink] New post 28 Feb 2007, 19:45
I get A as well.

If 1/3 is in S, the 1 / 1/3, or 3, is also in S

Having 1 be in S says nothing about 3
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 [#permalink] New post 01 Mar 2007, 19:49
I too thought it was A but with a confusing explanation is mentioned as D
Can anyone explain this please?

Consider (1) alone. Since 1/3 is in S, we know from Property I that 1/(1/3) = 3 is in S. Hence, (1) is sufficient.
Consider (2) alone. Since 1 is in S, we know from Property II that 1 + 1 = 2 (Note, nothing in Property II prevents x and y from standing for the same number. In this case both stand for 1.) is in S. Applying Property II again shows that 1 + 2 = 3 is in S. Hence, (2) is also sufficient. The answer is D.
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 [#permalink] New post 01 Mar 2007, 22:13
statement 2 says

that if 1 is in the set then 1/1 is in the set..i.e x=1, then say y=1 also,..which means 2 is in the set..

taking both statements, if 1/x,x and y are in the set then 3 is also in the set...

statement 2 is sufficient
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 [#permalink] New post 01 Mar 2007, 22:40
One cant win with these DS crap...u always miss some angle..I guess PRACTICE is the key. Good catch guys...I tend to agree its (D)...unless somepne pulls something totally different :shock:
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 [#permalink] New post 02 Mar 2007, 06:18
yep you are right..D

wow, good DS problem!
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Re: DS - number properties [#permalink] New post 16 Jun 2009, 04:24
I dont think this problem is confusing at all.

1) If 1/3 is in the set then 1 must also be in the set and then 3 must also be in the set
2) If 1 is in the set then 3 must also be in the set

For those of you answering A, try do first look at the second statement and solve it without knowing that the first statement says.
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Re: DS - number properties [#permalink] New post 16 Jun 2009, 07:39
yeah i got D as well. I thought of A right away as many others did but then thought to myself "this question must be "difficult" "so i looked at 2 closely and got D. Since most are doing computer test we can probably gauge how difficult problems become and hopefully not jump to conclusions so quickly.
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Re: DS - number properties [#permalink] New post 18 Jun 2009, 08:36
shaselai wrote:
yeah i got D as well. I thought of A right away as many others did but then thought to myself "this question must be "difficult" "so i looked at 2 closely and got D. Since most are doing computer test we can probably gauge how difficult problems become and hopefully not jump to conclusions so quickly.


Sorry But where does the Q say that X and Y are different/same. It does say that if X and Y are in the set, X + Y is also in the set

Just because X and Y are different letters does not mean they have different values, X can be equal to Y.

Or they could be very well the same

It is very well possible that the same 1 can refer to X and Y be 4

I mean 1 is in S, then 1/1 is also in S. With a single 1, we can satisfy the statement (1). We dont need another 1 to satisfy the statement 1.

The set does not need to have more than 1 number. Consider the set {1},

Statement 1 is good, 1 is in Set S, 1/1 is also in the Set. We dont need to satisfy statement 2 as Set S does not have two numbers.

Am I just hallucinating or Do I have a point in saying that x and 1/x could very well be the same one?
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Re: DS - number properties [#permalink] New post 23 Aug 2009, 08:49
X and Y could be the same value but that doesn't take away the solution.

Statement 1 confirms that 3 is in the set as 1/x of 1/3 = 3
Statement 2 says 1 is in set S . Applying the fact that if both x and y are in S , then so is x+y.
Taking x = y = 1 , leads to x+y=2 is in S , further down , x=1,y=2 leads to x+y=3 .

Hence D.


icandy wrote:
shaselai wrote:
yeah i got D as well. I thought of A right away as many others did but then thought to myself "this question must be "difficult" "so i looked at 2 closely and got D. Since most are doing computer test we can probably gauge how difficult problems become and hopefully not jump to conclusions so quickly.


Sorry But where does the Q say that X and Y are different/same. It does say that if X and Y are in the set, X + Y is also in the set

Just because X and Y are different letters does not mean they have different values, X can be equal to Y.

Or they could be very well the same

It is very well possible that the same 1 can refer to X and Y be 4

I mean 1 is in S, then 1/1 is also in S. With a single 1, we can satisfy the statement (1). We dont need another 1 to satisfy the statement 1.

The set does not need to have more than 1 number. Consider the set {1},

Statement 1 is good, 1 is in Set S, 1/1 is also in the Set. We dont need to satisfy statement 2 as Set S does not have two numbers.

Am I just hallucinating or Do I have a point in saying that x and 1/x could very well be the same one?
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Re: DS - number properties [#permalink] New post 23 Aug 2009, 18:50
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S is a set!!!

and "set" can't have duplication values!

therefore there is only one "1" in S.

The answer should be A
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Last edited by flyingbunny on 24 Aug 2009, 05:46, edited 1 time in total.
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Re: DS - number properties [#permalink] New post 24 Aug 2009, 05:27
I am still going with A
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Re: DS - number properties [#permalink] New post 24 Aug 2009, 06:46
There is a set of numbers S with n elements in it. A letter is assigned to each number.
let x=1.
By the property of the set, there should be another element y=1/x=1. It is possible for two elements in the multiset (see note) to be same. Using the first property of the set and one element of that set x=1, we can conclude that S=(1,1,....).
Now using the second property, there should be z=x+y=2 and there should be 1/z (but we do not need this one to answer the question). If z=2, there should be c=z+x=2+1=3 and there should be d=z+y=1+2=3...S=(1,1,2,3,3,...) ..

Note: If S is a set, then all elements should be different. But if S is a multiset , elements are not required to be different. My solution is based on the assumption that s is a multiset...and one element can be repeated more than once...I think the auther of the question had a multiset in mind (just based on the correct answer).

Last edited by LenaA on 24 Aug 2009, 07:06, edited 1 time in total.
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Re: DS - number properties [#permalink] New post 24 Aug 2009, 06:56
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LenaA wrote:
I think it should be D because statement 2 is sufficient.
There is a set of numbers S with n elements in it. A letter is assigned to each number.
let x=1.
By the property of the set, there should be another element y=1/x=1. It is possible for two elements in the set to be same. Using the first property of the set and one element of that set x=1, we can conclude that S=(1,1,....).
Now using the second property, there should be z=x+y=2 and there should be 1/z (but we do not need this one to answer the question). If z=2, there should be c=z+x=2+1=3 and there should be d=z+y=1+2=3...S=(1,1,2,3,3,...) ..


It is not possible.
Please check the definition of "set".
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Re: DS - number properties [#permalink] New post 24 Aug 2009, 07:11
flyingbunny wrote:
LenaA wrote:
I think it should be D because statement 2 is sufficient.
There is a set of numbers S with n elements in it. A letter is assigned to each number.
let x=1.
By the property of the set, there should be another element y=1/x=1. It is possible for two elements in the set to be same. Using the first property of the set and one element of that set x=1, we can conclude that S=(1,1,....).
Now using the second property, there should be z=x+y=2 and there should be 1/z (but we do not need this one to answer the question). If z=2, there should be c=z+x=2+1=3 and there should be d=z+y=1+2=3...S=(1,1,2,3,3,...) ..


It is not possible.
Please check the definition of "set".


It is a very good point, but set S can be a multiset...it is obvious that the auther had a multiset in mind based on the correct solution D....My initial answer though was A...i am not sure the question is phrased well. We should be given if it is possible to have 2 same elements.
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Re: DS - number properties [#permalink] New post 25 Aug 2009, 06:26
I am with A.

OA please
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Re: DS - number properties [#permalink] New post 25 Aug 2009, 09:11
defoue wrote:
I am with A.

OA please


amd08 posted the question and she/he says that it's D. She/he also gives the original explanation...see at the beginning of this thread amd08's posts

Last edited by LenaA on 25 Aug 2009, 09:56, edited 1 time in total.
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Re: [#permalink] New post 25 Aug 2009, 09:38
amd08 wrote:
I too thought it was A but with a confusing explanation is mentioned as D
Can anyone explain this please?

Consider (1) alone. Since 1/3 is in S, we know from Property I that 1/(1/3) = 3 is in S. Hence, (1) is sufficient.
Consider (2) alone. Since 1 is in S, we know from Property II that 1 + 1 = 2 (Note, nothing in Property II prevents x and y from standing for the same number. In this case both stand for 1.) is in S. Applying Property II again shows that 1 + 2 = 3 is in S. Hence, (2) is also sufficient. The answer is D.



This way S will have infinite values...... or hence any no can be in S... I dont think this is worth enough.. What is the source of this ques
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Re: Re: [#permalink] New post 23 Nov 2009, 04:37
rohansherry wrote:
amd08 wrote:
I too thought it was A but with a confusing explanation is mentioned as D
Can anyone explain this please?

Consider (1) alone. Since 1/3 is in S, we know from Property I that 1/(1/3) = 3 is in S. Hence, (1) is sufficient.
Consider (2) alone. Since 1 is in S, we know from Property II that 1 + 1 = 2 (Note, nothing in Property II prevents x and y from standing for the same number. In this case both stand for 1.) is in S. Applying Property II again shows that 1 + 2 = 3 is in S. Hence, (2) is also sufficient. The answer is D.



This way S will have infinite values...... or hence any no can be in S... I dont think this is worth enough.. What is the source of this ques


This is true... if this was intended then any no. given in set S will result in the answer being D
Re: Re:   [#permalink] 23 Nov 2009, 04:37
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