If k not = 0, 1, -1, is 1/k >0?

[gphil]

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.

[Guest]

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.

[gphil]

It makes perfect sense. Thanks a lot!

[RonPurewal]

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.

[Raj]

So the answer is A ,correct?

[RonPurewal]

So the answer is A ,correct?

yes.

[anoo.anand]

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

[2amitprakash]

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!

[RonPurewal]

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.