|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
29 Mar 2026, 19:00
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (01:55) correct
42%
(01:54)
wrong
based on 84
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
29 Mar 2026, 22:02
Kudos
Bookmarks
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.
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
29 Mar 2026, 22:28
Kudos
Bookmarks
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
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
