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

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Senior Manager
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The set S of numbers has the following properties: I) If x [#permalink]  09 Nov 2003, 04:10
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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.

ps: stolyar, please wait to answer this question before other guys/gals attempt it...
Manager
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I would say A too.

If we were to consider recursion in the problem then Statement (2) could also give you an answer but that's a different story... n/m
Senior Manager
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try again... why not D..?
wonder_gmat i think u got the point but why do u still prefer A...?
thanks
SVP
Joined: 03 Feb 2003
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seems like a formal logic question

If A, then B =>
If NOT B, then NOT A.

(1) X=1/3 and it is in S, then 1/X=3 is in S; seems OK, but the conclusion is wrong: If 1/X is in S, then X is in S.

(2) X=1 and it is in S

If there is another 1 in S, then:
Since 1 and 1 are in S, then 1+1=2 is in S.
Since 1, 1, and 2 is in S, then 1+2=3 is in S.
But what if S consists of the only member 1?

D is pretty questionable
Senior Manager
Joined: 11 Nov 2003
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I would go for A.

Stolyar,

Are you saying that statement 1 is also not suffecient? I think it is suffecient and I think there is no need to apply the logic rule here. All the statement is saying is that if a number is present in S the inverse of that number is also in S.

I agree with stolyar for the second statement. Not enough.
Manager
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Vicky wrote:
try again... why not D..?
wonder_gmat i think u got the point but why do u still prefer A...?
thanks

Vicky,
I would not pick Statement (2) as well because 1 is the one value that does not satisfy both conditions. If it had been anyother number, I would said Statement (2) is also sufficient.

If one is convinced that condition II can be met by still using 1 then the answer would be D, but since 1/1 is the same as 1 itself, it's hard to make this call.

Analysing Statement (2)
Venue 1:
I) If 1 is in S, then 1/1 is in S.
II) If both 1 and 1/1 are in S, then so is 1 + 1/1
Answer: 1 + 1/1 = 2 so now both 1 and 2 are in S so 1 + 2 = 3 is in S.

Venue 2:
I) If 1 is in S, then 1/1 = 1 is in S.
II) Can't be met because just '1' is in the set.

Venue 1 will lead us to answer D whereas Venue 2 will so to A. This is my approach at least. But other thoughts are certainly welcome. What was yours, Vicky?
Intern
Joined: 27 Jul 2003
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if 1 is there in the set, automatically it would generate the set of all natural numbers by itself.

Hence D.

Bharathi.
GMAT Instructor
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Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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bhars18 wrote:
if 1 is there in the set, automatically it would generate the set of all natural numbers by itself.

Hence D.

Bharathi.

I agree. "X" and "Y" are just variables. IMO, there is no reason why two variables cannot have the same value.
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Manager
Joined: 04 Jun 2003
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I'd vote for D.
(1) is definitely sufficient coz 3 and 1/3 are mutually existed.

But
For me, to (2), I think people normally write an only member of specific set once(one time is enough).
thus S = {1}
That means we cannot reach the value for 3. THEREFORE: SUFFICIENT
CEO
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ann wrote:

vicks , you have an explanation for this one
Senior Manager
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If this question appears at GMAT.
i wud chose D, which also happens to be the Official answer.
Akamai's point is worth noting.
thanks
CEO
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Vicky wrote:
If this question appears at GMAT.
i wud chose D, which also happens to be the Official answer.
Akamai's point is worth noting.
thanks

i did not understand akamai's explanation.

A is sufficient..isnt it .. its a YES

B ... is it a YES or NO?

thanks
Director
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Vicky wrote:
If this question appears at GMAT.
i wud chose D, which also happens to be the Official answer.
Akamai's point is worth noting.
thanks

Okay, WHY would you choose D if you saw this on the actual GMAT?
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