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If k is a positive integer, is k an integer?
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Updated on: 23 Jun 2015, 00:01
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If k is a positive integer, is \(\sqrt{k}\) an integer? (1) k is even. (2) k = \(\sqrt{m}\), where m is an integer.
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Originally posted by gmatser1 on 22 Jun 2015, 16:35.
Last edited by Harley1980 on 23 Jun 2015, 00:01, edited 1 time in total.
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Re: If k is a positive integer, is k an integer?
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22 Jun 2015, 16:37
gmatser1 wrote: If k is a positive integer, is \sqrt{k} an integer?
(1) k is even. (2) k = \sqrt{m}, where m is an integer. I understand how (1) and (2) is not sufficient, but I don't get how they are not sufficient together. If k is even and k is the square root of m, shouldn't that mean that the square root of k is never an integer since 2 will be in k?



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Re: If k is a positive integer, is k an integer?
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22 Jun 2015, 16:41
When you take the square root of an even number, sometimes you get an integer, sometimes not  √2 is not an integer, but √4 is an integer. So S1 is not sufficient. Every positive integer is the square root of some other integer (2 is the square root of 4, 3 is the square root of 9, etc) so Statement 2 tells us nothing whatsoever, and since S1 is not sufficient, the answer must be E.
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Re: If k is a positive integer, is k an integer?
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23 Jun 2015, 00:03
gmatser1 wrote: gmatser1 wrote: If k is a positive integer, is \sqrt{k} an integer?
(1) k is even. (2) k = \sqrt{m}, where m is an integer. I understand how (1) and (2) is not sufficient, but I don't get how they are not sufficient together. If k is even and k is the square root of m, shouldn't that mean that the square root of k is never an integer since 2 will be in k? Hello gmatser1m can be equal to 16 and then k = 4 > integer
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Re: If k is a positive integer, is k an integer?
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23 Jun 2015, 19:57
Hi gmatser1, This question can be solved rather quickly by TESTing VALUES. We're told that K is a POSITIVE INTEGER. We're asked if √K is an integer. This is a YES/NO question. Fact 1: K is EVEN IF.... K = 2 √2 is NOT an integer, so the answer to the question is NO IF... K = 4 √4 = 2 and that IS an integer, so the answer to the question is YES Fact 1 is INSUFFICIENT Fact 2: K =√M where M is an INTEGER IF.... K = 2, M = 4 √2 is NOT an integer, so the answer to the question is NO IF... K = 4, M = 16 √4 = 2 and that IS an integer, so the answer to the question is YES Fact 2 is INSUFFICIENT Combined, we don't need to do any additional work. We already have 2 possibilities that fit BOTH Facts (one gives us a NO answer and one gives us a YES answer). Combined, INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If k is a positive integer, is k an integer?
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12 Jul 2016, 20:39
m can be equal to 16 and then k = 4 > integer



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Re: If k is a positive integer, is k an integer?
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13 Jul 2016, 05:59
gmatser1 wrote: If k is a positive integer, is \(\sqrt{k}\) an integer?
(1) k is even. (2) k = \(\sqrt{m}\), where m is an integer. (1) k is even. k can be 2, 4, 6, 8, 10.... and hence \(\sqrt{k}\) may or may not be an integer. (2) k = \(\sqrt{m}\), where m is an integer. K can be 1, 2, 3, 4, .... and hence \(\sqrt{k}\) may or may not be integer combining both statements k can be 2, 4... and hence \(\sqrt{k}\) may or may not be an integer. Both statements together are insufficient. E is the answer
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Re: If k is a positive integer, is k an integer?
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