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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 09 Nov 2003, 04:10
00:00
A
B
C
D
E

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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...
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 [#permalink] New post 09 Nov 2003, 16:52
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 :-D
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 [#permalink] New post 09 Nov 2003, 19:44
try again... why not D..?
wonder_gmat i think u got the point but why do u still prefer A...?
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 [#permalink] New post 11 Nov 2003, 00:09
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
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 [#permalink] New post 11 Nov 2003, 10:01
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.
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 [#permalink] New post 11 Nov 2003, 12:04
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.
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?
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 [#permalink] New post 17 Nov 2003, 22:58
if 1 is there in the set, automatically it would generate the set of all natural numbers by itself.

Hence D.

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 [#permalink] New post 18 Nov 2003, 01:23
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.
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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

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 [#permalink] New post 19 Nov 2003, 19:32
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
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 [#permalink] New post 23 Nov 2003, 14:52
ann wrote:
What is the official answer?


vicks , you have an explanation for this one
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 [#permalink] New post 23 Nov 2003, 19:30
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
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 [#permalink] New post 23 Nov 2003, 19:56
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
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 [#permalink] New post 25 Nov 2003, 20:57
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?
  [#permalink] 25 Nov 2003, 20:57
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