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(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?

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.

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.
Answer: Inconclusive.

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?

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

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