Q1: (x^2 + 4x + 4) / (2x^2 -x-1) >0

=> (x+2)^2/(2x+1)(x-1) >0

=>(2x+1)(x-1) >0

=> x >-1/2 , x > 1 => x >1

OR, x < -1/2 , x < 1 => x < -1/2

Hence b.

Q3:

2. ( x^2 - 7 |x| + 10) / (x^2 - 6x + 9) < 0

=>( x^2 - 7 x + 10) / (x^2 - 6x + 9) < 0(x^2 + 7 x + 10) / (x^2 - 6x + 9) < 0or

=> (x-5)(x-2)/(x-3)^2 < 0 or (x+5)(x+2)/(x-3)^2 < 0

=> (x-5)(x-2) < 0(x+5)(x+2) < 0or

=> 2 < x < 5 or -5 < x <-2

Hence b.

Modulus Problems Inequality

Q2. |x^3 - 1| >= 1-x

Here x <-1 and x >0 both satisfy this inequality, so (d) will be the answer.

But if we solve this problem, it gives imaginary values of x which is not possible in normal GMAT problems. Hence it seems difficult to arrive at real values of x by following simple mathematical steps.

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