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

 It is currently 18 Jun 2019, 06:01 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

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.  S is a set of integers such that i) if a is in S, then a is

Author Message
TAGS:

Hide Tags

Manager  Joined: 10 Feb 2011
Posts: 107
S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

11 00:00

Difficulty:   45% (medium)

Question Stats: 55% (01:06) correct 45% (01:23) wrong based on 310 sessions

HideShow timer Statistics

S is a set of integers such that

i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.

Is –4 in S?

(1) 1 is in S.
(2) 2 is in S.
Math Expert V
Joined: 02 Sep 2009
Posts: 55668
Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

1
1
banksy wrote:
. S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?
(1) 1 is in S.
(2) 2 is in S.

S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Similar questions:
PS:
http://gmatclub.com/forum/a-set-of-numb ... 98829.html
http://gmatclub.com/forum/for-a-certain ... 36580.html
https://gmatclub.com/forum/for-a-certai ... 61920.html
https://gmatclub.com/forum/a-set-of-num ... 60975.html
https://gmatclub.com/forum/a-set-of-num ... 68728.html

DS:
https://gmatclub.com/forum/k-is-a-set-o ... 66908.html
http://gmatclub.com/forum/if-p-is-a-set ... 96630.html
http://gmatclub.com/forum/k-is-a-set-of ... 03005.html
https://gmatclub.com/forum/s-is-a-set-o ... 30000.html
https://gmatclub.com/forum/s-is-a-set-o ... 31344.html
https://gmatclub.com/forum/s-is-a-set-o ... 09986.html
_________________
Retired Moderator Joined: 20 Dec 2010
Posts: 1745
Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

(1) 1 is in S. Thus, -1 is there. If 1 and -1 are there; then 1*-1=-1 is there; We don't know anything other than that. -4 may or may not be there. Sufficient.

(2) 2 is in S. Thus, -2 is there. If 2 and -2 are both there, -4 must be there. We know -4 is there. Don't care about anything else.
Sufficient.

Ans: "B"
_________________
Manager  G
Joined: 31 May 2015
Posts: 127
Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

1
Sorry, I am lost here, if we know that a =-2 then how do we now that b= 2 ? to reach the conclusion that -4 is in S.
_________________
GMAT loosers are born not made !!!
Math Expert V
Joined: 02 Aug 2009
Posts: 7757
Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

sony1000 wrote:
Sorry, I am lost here, if we know that a =-2 then how do we now that b= 2 ? to reach the conclusion that -4 is in S.

Hi,
you don't require to know what is a or what is b..
a and b are just two integers in the SET...
similarly when we know 2 is there, -2 will be there..
if 2 and -2 are there, 2*-2=-4 is there..

further if -4 is there, 4 is there..
so 4*-4=-16 is also there..
also 2*4=8 is there.. and so on

so a and b stand for any two integers in the set..

_________________
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1225
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: S is a set of integers such that  [#permalink]

Show Tags

1
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Posted from my mobile device
_________________
Director  D
Joined: 04 Jun 2018
Posts: 538
Location: Germany
Concentration: General Management, Finance
GPA: 3.4
WE: Analyst (Transportation)
Re: S is a set of integers such that  [#permalink]

Show Tags

1
gmatbusters wrote:
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Posted from my mobile device

How do we know -a equals b in this case?

I find the wording quite confusing _________________
A couple of things that helped me in verbal:
https://gmatclub.com/forum/verbal-strategies-268700.html#p2082192

Gmat Prep CAT #1: V42, Q34, 630
Gmat Prep CAT #2: V46, Q35, 660
Gmat Prep CAT #3: V41, Q42, 680

On the mission to improve my quant score, all help is appreciated! Intern  B
Joined: 02 Dec 2018
Posts: 17
Re: S is a set of integers such that  [#permalink]

Show Tags

Arro44 wrote:
gmatbusters wrote:
S is a set of integers such that
i) if a is in S, then –a is in S, and
ii) if each of a and b is in S, then ab is in S.
Is –4 in S?

(1) 1 is in S --> according to (i) -1 is in S. Is -4 in S? We don't know. Not sufficient.

(2) 2 is in S --> according to (i) -2 is in S --> according to (ii) -2*2=-4 is in S. Sufficient.

Posted from my mobile device

How do we know -a equals b in this case?

I find the wording quite confusing "if each of a and b is in S, then ab is in S."

All this means is that if 2 integers are in S, then the product of those 2 integers is in S.
Director  V
Joined: 27 May 2012
Posts: 800
Re: S is a set of integers such that  [#permalink]

Show Tags

gmatbusters wrote:

Project DS Butler: Day 54: Data Sufficiency (DS108)

S is a set of integers such that
i) if a is in S, then -a is in S, and
ii) if each of a and b is in S, then ab is in S.

Is -4 in S?
(1) 1 is in S.
(2) 2 is in S

Dear Moderator,
This same question has been repeated in the link below , you may wish to merge the same. Thank you.

https://gmatclub.com/forum/s-is-a-set-o ... 09986.html
_________________
- Stne
Math Expert V
Joined: 02 Sep 2009
Posts: 55668
Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

Show Tags

stne wrote:
gmatbusters wrote:

Project DS Butler: Day 54: Data Sufficiency (DS108)

S is a set of integers such that
i) if a is in S, then -a is in S, and
ii) if each of a and b is in S, then ab is in S.

Is -4 in S?
(1) 1 is in S.
(2) 2 is in S

Dear Moderator,
This same question has been repeated in the link below , you may wish to merge the same. Thank you.

https://gmatclub.com/forum/s-is-a-set-o ... 09986.html

_______________________
Topics merged. Thank you.
_________________ Re: S is a set of integers such that i) if a is in S, then a is   [#permalink] 13 Jan 2019, 21:27
Display posts from previous: Sort by

S is a set of integers such that i) if a is in S, then a is  