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Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve

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siddharthkapoor
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Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   19 Oct 2020, 03:22
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Is x positive?

(1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1
(2) x is even
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E
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chetan2u
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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   19 Oct 2020, 03:57
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siddharthkapoor wrote:
Is x positive?

(1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1
(2) x is even


(1) \(\frac{1}{(x+1)} < \frac{1}{(x-1)}\) where x ≠ 1; x ≠ -1
\(\frac{1}{(x-1)} - \frac{1}{(x+1)}>0\)
\(\frac{x+1-(x-1)}{(x-1)(x+1)}>0\)
\(\frac{2}{x^2-1}>0...........x^2-1>0.......x^2>1\)
So x<-1 or x>1.....
Insuff

(2) x is even
Insuff

Combined
x can be -2 or 2...
Insuff

E
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Harsh9676
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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   19 Oct 2020, 20:16
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IMO E

Plugging in Nos (keep in mind ZONEF)

1. Plugging in Zero in S1, we get 1<-1, which doesn't satisfy the condition
2. We cannot take 1, since X is not equal to 1
3. Negative no>> Plugging in -2, we get -1<-1/3, which is true and X is negative here
4. Trying X =2, we get 1/3 < 1 which is true again, and X is Positive here.
5. No need to try Exponents and fractions .

St2: Insufficient,

Combined: Again 2 and -2 would give diff solutions.

Ans E
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Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   Updated on: 29 Oct 2020, 11:24
Sorry, I have a silly question: Are -2, -4, -6 etc even numbers? Negative numbers can be even or odd as well?
What about 0: Is 0 considered even or odd?

Originally posted by Pankaj0901 on 29 Oct 2020, 11:08.
Last edited by Pankaj0901 on 29 Oct 2020, 11:24, edited 1 time in total.
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Bunuel
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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   29 Oct 2020, 11:12
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PANKAJ0901 wrote:
Sorry, I have a silly question: Are -2, -4, -6 etc are even numbers? Negative numbers can be even or odd as well?
What about 0: Is 0 considered even or odd?


An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an integer that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.
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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   29 Oct 2020, 11:13
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PANKAJ0901 wrote:
Sorry, I have a silly question: Are -2, -4, -6 etc are even numbers? Negative numbers can be even or odd as well?
What about 0: Is 0 considered even or odd?


Yes negative numbers can be even or odd.

And 0 is even

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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink] New post   29 Oct 2020, 11:25
Thanks Bunuel. This is very helpful!!

Bunuel wrote:
PANKAJ0901 wrote:
Sorry, I have a silly question: Are -2, -4, -6 etc are even numbers? Negative numbers can be even or odd as well?
What about 0: Is 0 considered even or odd?


An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. So, ..., -4, -2, 0, 2, 4, ... are all even integers.

An odd number is an integer that is not evenly divisible by 2. So, ..., -3, -1, 1, 3, 5, ... are all odd integers.
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Re: Is x positive? (1) 1/(x+1) < 1/(x-1) where x ≠ 1; x ≠ -1 (2) x is eve [#permalink]
29 Oct 2020, 11:25
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Bunuel
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