GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 May 2019, 02:12 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # The set S of numbers has the following properties

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  Joined: 05 Mar 2010
Posts: 165
The set S of numbers has the following properties  [#permalink]

### Show Tags

1
2 00:00

Difficulty:   85% (hard)

Question Stats: 38% (01:42) correct 62% (01:26) wrong based on 90 sessions

### HideShow timer Statistics

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.

_________________
Success is my Destiny
Intern  Joined: 02 May 2010
Posts: 46
Schools: IU, UT Dallas, Univ of Georgia, Univ of Arkansas, Miami University
WE 1: 5.5 Yrs IT
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

1
hardnstrong wrote:
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.

OA will be posted later.

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

IMO A
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

2
hardnstrong wrote:
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.

OA will be posted later.

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.
_________________
Intern  Joined: 02 May 2010
Posts: 46
Schools: IU, UT Dallas, Univ of Georgia, Univ of Arkansas, Miami University
WE 1: 5.5 Yrs IT
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

Splendid...+1! Dint look at it that way. Thanks for the explanation.
OA Please! (Not that I doubt it is D)
Manager  Joined: 05 Mar 2010
Posts: 165
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

2
Bunuel wrote:
hardnstrong wrote:
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.

OA will be posted later.

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.

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?
_________________
Success is my Destiny
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

1
hardnstrong wrote:
Bunuel wrote:
hardnstrong wrote:
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.

OA will be posted later.

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.

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?

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.
_________________
Manager  Joined: 05 Mar 2010
Posts: 165
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

Thanks for your explanation
It was helpful as always _________________
Success is my Destiny
Manager  B
Joined: 24 Jul 2016
Posts: 51
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

hardnstrong wrote:
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.

i believe this qn is poorly worded
GMAT Tutor S
Joined: 24 Jun 2008
Posts: 1520
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

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.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Intern  B
Joined: 25 Mar 2016
Posts: 40
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

Bunuel wrote:
hardnstrong wrote:
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.

OA will be posted later.

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.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
The set S of numbers has the following properties  [#permalink]

### Show Tags

PK32 wrote:
Bunuel wrote:
hardnstrong wrote:
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.

OA will be posted later.

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.

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.

Highlighted text above is a part of the stem, NOT the statements. The statements are below, (1) and (2).
_________________
Intern  Joined: 15 Apr 2017
Posts: 8
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

This helped I had a similar doubt, thanks

Posted from my mobile device
Intern  B
Joined: 25 Mar 2016
Posts: 40
Location: India
Concentration: Finance, General Management
WE: Other (Other)
Re: The set S of numbers has the following properties  [#permalink]

### Show Tags

Anandita04 wrote:
This helped I had a similar doubt, thanks

Posted from my mobile device

@Anindita04: Thanks for the clarification.
Non-Human User Joined: 09 Sep 2013
Posts: 10981
Re: The set S of numbers has the following properties: I) If x  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: The set S of numbers has the following properties: I) If x   [#permalink] 27 Nov 2018, 01:20
Display posts from previous: Sort by

# The set S of numbers has the following properties

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  