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14 Feb 2020, 05:36
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
64% (00:58) correct
36%
(01:12)
wrong
based on 238
sessions
History
Date
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Not Attempted Yet
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. x^2 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
Are You Up For the Challenge: 700 Level Questions
I. x is negative
II. x is positive.
III. 2x is greater than or equal to x
IV. x^2 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
Are You Up For the Challenge: 700 Level Questions
14 Feb 2020, 05:48
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Bunuel
I. x is negative-------> x may be 1--Discard
II. x is positive.--------> x may be -1--Discard
III. 2x is greater than or equal to x-------> x may be -2---Discard
IV. x^2 is greater than or equal to x.-----> x may be 0.5---Discard
none is correct
Ans E
14 Feb 2020, 23:13
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Bunuel
Solution
- • It is given that x < 2.
• No further information is given so, lets directly check each statement and see which one is always true.
• I. x is negative
- o Let’s consider any 2 possible values of x which are less than 2
- Say, x = -1, in this case x is negative.
Or, x = 1, in this case x is positive
- • II. x is positive.
- o Let’s consider any 2 possible values of x which are less than 2
- Say, \(x = -1,\) in this case x is negative.
Or, \(x = 1\), in this case x is positive
- • III. 2x is greater than or equal to x
- o Let’s consider any 2 possible values of x which are less than 2
- Say, \(x = -1⟹ 2x = -2 \) which is less than -1(or x).
Or, \(x = 1, ⟹2x = 2 \) which is more than 1(or x).
- • IV. \(x^2 \) is greater than or equal to x.
- o Let’s consider any 2 possible values of x which are less than 2
- Say,\( x = \frac{1}{2} ⟹x^2 = \frac{1}{4} \)which is less than \(\frac{1}{2}\) (or x)
Or, \(x = 1, ⟹ x^2 = 1 \)which is equal to 1(or x).
Thus, the correct answer is Option E.
