If x/(x 2)(x + 1) 0, which of the following specifies all the

Question

If  \frac{x }{ (x – 2)(x + 1) } ≤ 0 , which of the following specifies all the possible values of x ?

A. x < –1
B. 0 ≤ x < 2
C. x ≤ –1 and 0 ≤ x < 2
D. x < –1 and 0 ≤ x < 2
E. x ≤ –1 and x ≥ 2

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Adit_ · Answer

Denominator is a parabola facing up with 2,0 and -1,0 as the points when they meet x-axis.

Now to have a value <=0
We need to have either denominator or numerator as negative but not BOTH.

Taking critical points if we take values ranging -1 to 2 then all values of denominator are negative but between 0 to 2, x becomes positive or 0.
Hence 0 to 2 is an interval.

Now we can have denominator as positive which is when x<-1 or x>2
When x<-1 then numerator negative and denominator is positive hence satisfied.
When x>2 then numerator positive and denominator positive. Not SATISFIED.

Thus x<-1 and 0<=x<2, is the perfect relation.
Answer: Option D

__________________________

Note: Option C is wrong as x cant be equal to -1 and denominator becomes 0 that turns expression to infinity.

ExpertsGlobal5

If \(\frac{x }{ (x – 2)(x + 1) ≤ 0}\), which of the following specifies all the possible values of x ?

A. x < –1
B. 0 ≤ x < 2
C. x ≤ –1 and 0 ≤ x < 2
D. x < –1 and 0 ≤ x < 2
E. x ≤ –1 and x ≥ 2

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chloreton · Answer

If you plot the critical points on the line, you can see the points are -1,0,2

Now when x>2, the equation gives positive value.
 When x < -1, the equation gives negative value. 
 When 0 <= x < 2, the equation gives negative value. 
When -1 < x <= 0, the equation gives positive value.

Therefore,  Option D

ExpertsGlobal5 · Answer

D is the correct answer choice.  
 
  Video explanation:

https://www.youtube.com/watch?v=euq7Qhh_P0M

madhavmehtafin · Answer

I think there is a typo in the fraction, the inequality is in the denominator, please check

Bunuel · Answer

Fixed the formatting. Thank you!

If x/(x 2)(x + 1) 0, which of the following specifies all the

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GMAT Problem Solving (PS) Questions

If x/(x 2)(x + 1) 0, which of the following specifies all the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards