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

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S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 24 Feb 2011, 13:15
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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.
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 24 Feb 2011, 13:28
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.

Answer: B.

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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 24 Feb 2011, 13:30
(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"
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 22 Mar 2016, 01:24
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.
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 22 Mar 2016, 02:01
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..

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Re: S is a set of integers such that  [#permalink]

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New post 30 Dec 2018, 17:23
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.

Answer: B.

Posted from my mobile device
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Re: S is a set of integers such that  [#permalink]

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New post 31 Dec 2018, 01:33
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.

Answer: B.

Posted from my mobile device


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

I find the wording quite confusing :(
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Re: S is a set of integers such that  [#permalink]

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New post 31 Dec 2018, 13:38
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.

Answer: B.

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.
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Re: S is a set of integers such that  [#permalink]

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New post 13 Jan 2019, 20:24
gmatbusters wrote:

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


For DS butler Questions Click Here


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
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Re: S is a set of integers such that i) if a is in S, then a is  [#permalink]

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New post 13 Jan 2019, 20:27
stne wrote:
gmatbusters wrote:

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


For DS butler Questions Click Here


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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: S is a set of integers such that i) if a is in S, then a is &nbs [#permalink] 13 Jan 2019, 20:27
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