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S is a set of integers such that i) if a is in S, then –a [#permalink]
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01 Apr 2012, 05:30
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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 [#permalink]
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01 Apr 2012, 07:51



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Re: S is a set of integers [#permalink]
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02 Apr 2012, 18:46
Bunuel 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.
Hope it helps. How do you know that a = b?



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Re: S is a set of integers [#permalink]
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03 Apr 2012, 02:23
bohdan01 wrote: Bunuel 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.
Hope it helps. How do you know that a = b? we can interpret if a and b are two elements in the set then product of that two numbers will be in the set.so b is just another element in the set. @Bunuel Correct me if wrong
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Re: S is a set of integers [#permalink]
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03 Apr 2012, 04:48
bohdan01 wrote: Bunuel 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.
Hope it helps. How do you know that a = b? We are told that: if some number a is in S, then –a is also in S, and if each of a and b is in S, then their product, ab is also in S. (2) says that 2 is in S, then 2 also must be in S and since both 2 and 2 are in S then their product 2*(2)=4 must also be in S. Hope it's clear.
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Re: S is a set of integers [#permalink]
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03 Apr 2012, 05:54
Bunuel 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. Similar questions: ogquant96907.htmldspisasetofintegers96630.htmlsetofintegers103005.htmlHope it helps. i agree with Bunuel's explanation.....the answer should be deduced using both the points given the question
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Re: S is a set of integers [#permalink]
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12 Oct 2012, 00:17
Bunuel wrote: bohdan01 wrote: Bunuel 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.
Hope it helps. How do you know that a = b? We are told that: if some number a is in S, then –a is also in S, and if each of a and b is in S, then their product, ab is also in S. (2) says that 2 is in S, then 2 also must be in S and since both 2 and 2 are in S then their product 2*(2)=4 must also be in S. Hope it's clear. Bunuel  Im also confused, could you kindly help? (2) says that 2 is in S so this can be a or b right? So if 2 is a then 2 is a if 2 is b then 2 is b Aren't these mutually exclusive i.e how can we take 2 to be a and 2 to be b? Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get 4 please help! cheers



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Re: S is a set of integers [#permalink]
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12 Oct 2012, 00:30
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(2) says that 2 is in S so this can be a or b right? So if 2 is a then 2 is aif 2 is b then 2 is b Aren't these mutually exclusive i.e how can we take 2 to be a and 2 to be b? Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get 4 please help! cheers  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. It doesn't matter what you call the number. i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then 1 is also in S. If 3 is in S, then (3) = 3 is also in S. ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and 2 are in S, then 2*(2) = 4 is also in S, 2*4 = 8, 2*4 = 8,...
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Re: S is a set of integers [#permalink]
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12 Oct 2012, 00:47
EvaJager wrote: (2) says that 2 is in S so this can be a or b right? So if 2 is a then 2 is a if 2 is b then 2 is b Aren't these mutually exclusive i.e how can we take 2 to be a and 2 to be b?
Also another way I (mistakenly) interpret the statements as if 2 (a or b) is in set then b (or a) can be any nos in the set? for example 5 then we cant get 4
please help!
cheers
 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.
It doesn't matter what you call the number. i) States that if a number is in S, then its opposite is also in S. Meaning, if 1 is in S, then 1 is also in S. If 3 is in S, then (3) = 3 is also in S. ii) States that if two numbers are in S, then their product is also in S. Doesn't matter even the two numbers are equal. For example, if 2 is in S, then 2*2 = 4 is also in S. If 2 and 2 are in S, then 2*(2) = 4 is also in S, 2*4 = 8, 2*4 = 8,... ahhh.. I guess i didn't give enf credit to stipulated conditions It says ii) if EACH of a and b is in S, then ab is in S. So for ANY A or B in the set then a*b in the set so we definitely know 2 and 2 are in the set hence we are Good..... thanks for your response EvaJager



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Re: S is a set of integers such that i) if a is in S, then –a [#permalink]
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24 Jun 2014, 12:19
Bunuel 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. Similar questions: kisasetofnumberssuchthatiifxisinkthenx96907.htmlifpisasetofintegersand3isinpiseverypositive96630.htmlkisasetofintegerssuchthatiftheintegerrisink103005.htmlHope it helps. Hi Bunnel , I am a little confused with this one . In stmt A ) i get the elements in the set as 1 and 1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ? However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , 1 ? Thanks and Regards , Sheldon Rodrigues



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Re: S is a set of integers such that i) if a is in S, then –a [#permalink]
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24 Jun 2014, 12:58
shelrod007 wrote: Bunuel 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. Similar questions: kisasetofnumberssuchthatiifxisinkthenx96907.htmlifpisasetofintegersand3isinpiseverypositive96630.htmlkisasetofintegerssuchthatiftheintegerrisink103005.htmlHope it helps. Hi Bunnel , I am a little confused with this one . In stmt A ) i get the elements in the set as 1 and 1 ... i did not find 12 so i thought the Set S has only two elements .. hence We could answer the question that 12 is not present in the set ? However later on i saw that this is not sufficient to answer the question how can 12 be present in the set with Stmt 1 yields on two values 1 , 1 ? Thanks and Regards , Sheldon Rodrigues 1 and 1 may NOT be the only numbers in S. S could contain a whole bunch of other numbers. For example, the set could be: {..., 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, ...} {..., 5, 3, 1, 1, 3, 5, ...} Hope it's clear.
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Re: S is a set of integers such that i) if a is in S, then –a [#permalink]
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