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

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If |x| < 4, which of the following expressions must be correct?  [#permalink]

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New post 20 Mar 2019, 19:40
1
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (00:54) correct 12% (00:54) wrong based on 105 sessions

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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

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Re: If |x| < 4, which of the following expressions must be correct?  [#permalink]

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New post 20 Mar 2019, 21:07

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

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Re: If |x| < 4, which of the following expressions must be correct?  [#permalink]

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New post 21 Mar 2019, 01:34
fitzpratik wrote:
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


from given description
x<4 for all values would stand true at -4 < x < 4
IMO C
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Re: If |x| < 4, which of the following expressions must be correct?   [#permalink] 21 Mar 2019, 01:34
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If |x| < 4, which of the following expressions must be correct?

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