Troube with Inequality... PLz help...

[Viren1808]

Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

[shankar.ashwin]

Find values in each statement, substitute in the question and find a pattern.

Statement 1:

Given x= 0.

We can find the expression becomes -1/3 < 0. Sufficient.

Statement 2:

-2<x<2

or x = (-1,0,1)

Substitute x = -1, expression becomes 0 (Numerator becomes 0)

We have already checked for x=0. So 2 contradicting answers. Insufficient.

A IMO

[rijul007]

Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

(x+1)/(x-3) < 0

Case 1- [x > 3]

(x+1)/(x-3) will be positive

Case 2- [ -1 < x < 3]

(x+1)/(x-3) will be negative

Case 3 - [x < -1]

(x+1)/(x-3) positive


Statement 1
-1 < x < 1
this satisifies case 2

Sufficient

Statement 2
x^2 - 4 < 0
(x+2)(x-2) < 0
-2 < x < 2

values of the expression in this range can either be -ve or +ve

Insufficient

Option A

[GMATGuruNY]

Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

Determine the critical points: the values of x that will make the numerator or the denominator equal to 0.
The critical points here are x=-1 and x=3.
These are the only values of x where (x+1)/(x-3) is equal to 0 or is undefined.
Thus, when x is any other value, (x+1)/(x-3) will be either greater than or less than 0.
To determine the range of x, test one value to the left and right of each critical point.

x < -1.
If x=-2, we get:
(-2+1)/(-2-3) < 0.
1/5 < 0.
Doesn't work.
x < -1 is not part of the range.

-1 < x < 3.
If x=0, we get:
(0+1)/(0-3) < 0.
-1/3 < 0.
This works.
-1<x<3 is part of the range.

x > 3.
If x=4, we get:
(4+1)/(4-3) < 0.
5 < 0.
Doesn't work.
x > 3 is not part of the range.

Question rephrased: Is -1 < x < 3?

Statement 1: -1 < x < 1.
Thus, x must be between -1 and 3.
SUFFICIENT.

Statement 2: x²<4.
Since it's possible that x = 0 (which is between -1 and 3) or that x = -3/2 (which is not between -1 and 3), INSUFFICIENT.

The correct answer is A.

[kevincanspain]

Q. Is (x+1)/(x-3) < 0 ?
(1) -1 < x < 1
(2) x^2 - 4 < 0

Request you to kindly provide some trick to tackle such problems during the test in fastest possible ways.

I believe that it is usually worthwhile to simplify the question:

Note that a fraction is negative if and only if the numerator and denominator have opposite signs: in this case, because x+1 > x-3 , the answer will be yes if and only if x+1 > 0
and x - 3 < 0
i.e. -1 < x < 3.