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# If x is less than 2, which of the following statements are always true

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If x is less than 2, which of the following statements are always true  [#permalink]

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05 Sep 2017, 10:36
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:52) correct 30% (01:18) wrong based on 54 sessions

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If x is less than 2, which of the following statements are always true?

I. x is negative
II. x is positive.
III. 2x is greater than or equal to x
IV. x² is greater than or equal to x.

A) III only

B) IV only

C) I and III only

D) I, III, and IV only

E) none of the statements

Source: 800Score

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Re: If x is less than 2, which of the following statements are always true  [#permalink]

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05 Sep 2017, 10:58
If x is less than 2, which of the following statements are always true?

I. x is negative(No, because x could be 1)
II. x is positive.(No, because x could be -2)
III. 2x is greater than or equal to x
(No, if x=-5, 2x=-10 which is smaller than x)
IV. x² is greater than or equal to x.
(No, if x=1/2,x^2=1/4, which is smaller than x)

Hence Option E(none of the statements) is the correct answer option!
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Re: If x is less than 2, which of the following statements are always true  [#permalink]

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07 Sep 2017, 01:30
If x< 2,

I. x is negative
x< 2=> x =1 , x=-1 ..ie x is negative : Not always true
II. x is positive.
x< 2=> x =1 , x=-1 ..ie x is positive : Not always true
III. 2x is greater than or equal to x
x< 2
=> x =1 => 2x> x => 2>1 true
=> x =-1 => 2x> x => -2>-1 False
IV. x² is greater than or equal to x.
x< 2
=> x =1 => x^2>= x => 1>=1 true
=> x =-1 => x^2> x => 1>= -1 true
=> x =1/2 => x^2> x => 1/4>= 1/2 False

None agree with "Must be True" condition

Re: If x is less than 2, which of the following statements are always true   [#permalink] 07 Sep 2017, 01:30
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