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gphil
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Post subject: If k not = 0, 1, -1, is 1/k >0?  Posted: Wed Oct 31, 2007 10:47 am |
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Could please somebody explain why the answer choice A)Statement (1) alone is sufficient, but statement (2) alone is not sufficient is correct? It looks like 2 statements should be sufficient. Thanks!
If k not = 0, 1, -1, is 1/k >0?
1) 1/(k-1) > 0
2) 1/(k+1) >0
1. 1/(k-1) > 0. For the expression to be >0 K could be only positive (>1), therefore 1/k>0
2. 1/(k+1) >0. It looks like the explanation is the same as for the first one.
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Guest
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Post subject: Posted: Wed Oct 31, 2007 1:27 pm |
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Does it specify if k is an integer? If it DOES NOT specify that k is an integer than k could be -1/2 and 1/(k+1) > 0 and k could be 2 and 1/(k+1) > 0. Therefore it cannot be determined.
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gphil
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Post subject: Posted: Wed Oct 31, 2007 8:08 pm |
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It makes perfect sense. Thanks a lot!
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RonPurewal
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Post subject: Posted: Fri Nov 02, 2007 2:42 pm |
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| ManhattanGMAT Staff |
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Posts: 7146
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Ok, this problem already "makes perfect sense", BUT
Make sure you understand, from the start, that the given statements and question are exactly the same as...
[same restrictions] Is K positive?
(1) K - 1 is positive
(2) K + 1 is positive
Note that #2 translates to K > -1, which includes a whole host of negative numbers between -1 and 0.
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Raj
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Post subject: Answer Posted: Mon Nov 03, 2008 6:59 pm |
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So the answer is A ,correct?
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RonPurewal
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Post subject: Re: Answer Posted: Fri Nov 14, 2008 6:43 am |
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| ManhattanGMAT Staff |
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Raj wrote: So the answer is A ,correct?
yes.
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anoo.anand
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Post subject: Re: Posted: Sun Oct 18, 2009 1:56 pm |
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Posts: 73
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RonPurewal wrote: Ok, this problem already "makes perfect sense", BUT
Make sure you understand, from the start, that the given statements and question are exactly the same as...
[same restrictions] Is K positive?
(1) K - 1 is positive
(2) K + 1 is positive
Note that #2 translates to K > -1, which includes a whole host of negative numbers between -1 and 0. hi Ron, could you please explain how are you translating 1/(k+1) > 0 to k+1 > 0 ? Thanks
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2amitprakash
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Post subject: Re: If k not = 0, 1, -1, is 1/k >0? Posted: Sun Oct 18, 2009 9:14 pm |
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I'm sure that Ron is not translating in exact mathematical equation but what you need to prove. In case of a fraction to be +ve both nom and denom must have same sign. Since the nom is 1 (and +ve), the denom must be +ve. Hope this clarifies!
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RonPurewal
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Post subject: Re: Re: Posted: Sat Oct 24, 2009 8:12 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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anoo.anand wrote: RonPurewal wrote: Ok, this problem already "makes perfect sense", BUT
Make sure you understand, from the start, that the given statements and question are exactly the same as...
[same restrictions] Is K positive?
(1) K - 1 is positive
(2) K + 1 is positive
Note that #2 translates to K > -1, which includes a whole host of negative numbers between -1 and 0. hi Ron, could you please explain how are you translating 1/(k+1) > 0 to k+1 > 0 ? Thanks if the reciprocal of a number is positive, then the number itself must be positive. if this isn't clear, then try to come up with a positive number whose reciprocal is negative (or vice versa). you should see awfully quickly that that's not gonna happen. -- alternatively, if you have wicked algebra skills, you can multiply both sides of 1/(k+1) > 0 by (k+1)^2. since that's a perfect square of a nonzero number, it's positive, and so you can do this and keep the ">" sign. but that's a bit unnecessary.
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