The set S of numbers has the following properties

Question

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.

Bunuel · Accepted Answer

The wording is a little bit strange but anyway:

(1) 1/3 is in S --> according to (i)  \frac{1}{\frac{1}{3}}=3  must also be in S. Sufficient.

(1) 1 is in S --> according to (i)  \frac{1}{1}=1  (another 1) must also be in S, then according to (ii)  1+1=2  must also be in S -->  1+2=3  must also be in S. Sufficient.

Answer: D.

You can check quality questions and theory on the topic in the links below:

20. Descriptive Statistics 
     Theory   
 Statistics Made Easy - All in One Topic! 
 GMAT Statistics 101 
 Math: Standard Deviation 
 How to Quickly Solve Standard Deviation Questions on the GMAT 
     Questions   
 Standard Deviation Problems 
 DS Questions 
 PS Questions

Hope it helps.

sjayasa · Answer

1 - Sufficient. If 1/3 is in S, then 3 is in S
2 - Insufficient.

IMO A

sjayasa · Answer

Splendid...+1! Dint look at it that way. Thanks for the explanation.
OA Please! (Not that I doubt it is D)

hardnstrong · Answer

OA is D

But my point is (in stmt 2), if 1 is in set then according to (i) we have 1/1 in set, that mean another 1 . so x=1 and y =1 
Now acc. to (ii) we have 1+1 =2 (x + y = z) in set 
Now, can we again take the value of x or y as 2 
How can x+y = x or y when neither x nor y is 0

Can we assume having more than one value of x or y?
or does it mean x and y are any two values in set? But question dosent say any two values, it just say x and y (two specific values)
Please explain?

Bunuel · Answer

As I said the wording is quite strange, GMAT won't use such language. But as OA given as D, then the stem is meant to be understood as I did in my solution. One note though: x and y are variables not exact values.

hardnstrong · Answer

Thanks for your explanation It was helpful as always :-D

IanStewart · Answer

Technically in a set you can't have repeated values, which is why GMAT stats questions which permit repeated values always talk about "lists" of numbers, or "data sets" (which can have repeated values). So here, when you use Statement 2, you don't need to use the property that "If x is in S, then 1/x is in S" to prove that you have another '1' in the set -- you already know '1' is in the set, and there can only be one '1' in a set. The only question is, reading this, "If both x and y are in S, then so is x + y", whether x and y can represent the exact same value from the set. If so, then when 1 is in the set, so is 1+1 and so is thus 2+1, but if not, the set could just be {1}. Because of the word "both", I'd be inclined to think that x and y need to be different values, but there's no unambiguous answer to that question.

So really we're just left to guess what the question writer meant. Bunuel has certainly correctly interpreted the intentions of the question writer, but the wording of the question doesn't convey those intentions properly. There are official questions (rare ones) that test a similar concept that have none of the issues that this question has, and those might be worth looking at, but this question is not.

So really we're just left to guess what the question writer meant. Bunuel has certainly correctly interpreted the intentions of the question writer, but the wording of the question doesn't convey those intentions properly. There are official questions (rare ones) that test a similar concept that have none of the issues that this question has, and those might be worth looking at, but this question is not.

PK32 · Answer

Hi Bunuel,

If the answer is D then both the condition A & B should answer the question independently but you have use condition A & B together to answer the question.

Is it right ?

"(1) 1 is in S --> according to (i)  \frac{1}{1}=1  (another 1) must also be in S, then according to (ii)  1+1=2  must also be in S -->  1+2=3  must also be in S. Sufficient.
"
as per the condition B only one value is given So we can consider it either as X or as Y.

Bunuel · Answer

Highlighted text above is a part of the stem, NOT the statements. The statements are below, (1) and (2).

Anandita04 · Answer

This helped I had a similar doubt, thanks

Posted from my mobile device

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The set S of numbers has the following properties

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