If |x|

Question

If |x| < 4, which of the following expressions must be correct? I. x > 4 II. -x > 4 III. -4 < x < 4 A. I only B. II only C. III only D. I and II E. I, II and III

EgmatQuantExpert · Answer

Solution 
  Given:  
 • |x| < 4

To find:  
 • Among the given options, which one represents the range of values possible for x

Approach and Working:  
As per our conceptual understanding, |x| represents the distance of point x from the origin, in the number line.
 • Therefore, if we say |x| is less than 4, it means the point x is less than 4 units away from the origin.
• As x can be both positive or negative, we can say x < 4 or x > - 4
• Combining both, we can say – 4 < x < 4

Hence, the correct answer is option C.

Answer: C

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-NP-e1533292144892.png

Archit3110 · Answer

from given description
x<4 for all values would stand true at -4 < x < 4
IMO C

CrackverbalGMAT · Answer

Opening the modulus is simple, whether it be an equation or an inequality,

If |x| = 4

Then we can open the modulus as -4 = x = 4, which effectively means x = 4 and x = -4

Similarly when opening the modulus of the inequality, use the same sign on both sides.

For example if |x| < 2, then -2 < x < 2.

In the above question, we have |x| < 4.

Opening the modulus, we have -4 < x < 4 or x > -4 and x < 4

From I: x > 4. This is not true as x > -4

From II: -x > 4. Changing the signs, we get x < -4. This is untrue as x < 4

From III: -4 < x < 4. This is True.

Option C

Arun Kumar

BrushMyQuant · Answer

|x| < 4 This is of the form |x| < A => -A < x < A => -4 < x < 4 So, Answer will be C Hope it helps! Watch the following video to MASTER Absolute Values https://www.youtube.com/watch?v=huFiBk8PaGY

If |x| < 4, which of the following expressions must be correct?

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