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Problem solving

by BTGmoderatorRO » Fri Sep 15, 2017 1:49 pm
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

OA is e
can you explain why option C is chosen over A in this question
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by Brent@GMATPrepNow » Fri Sep 15, 2017 4:35 pm
Roland2rule wrote: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
Key words: always true
So, if we can show that a statement could be false, we can eliminate that statement.

I. x is negative
If x < 2, then x COULD equal 1, in which case this statement need not be true
ELIMINATE C and D

II. x is positive.
If x < 2, then x COULD equal -1, in which case this statement need not be true

III. 2x is greater than or equal to x
If x < 2, then x COULD equal -1, in which case 2x = -2
In this case, 2x is NOT greater than x
ELIMINATE A

IV. x² is greater than or equal to x.
If x < 2, then x COULD equal 1/2, in which case x² = 1/4
So, x² is NOT greater than or equal to x.
ELIMINATE B

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by BTGmoderatorRO » Sat Sep 16, 2017 11:40 am
Brent@GMATPrepNow wrote:
Roland2rule wrote: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
Key words: always true
So, if we can show that a statement could be false, we can eliminate that statement.

I. x is negative
If x < 2, then x COULD equal 1, in which case this statement need not be true
ELIMINATE C and D

II. x is positive.
If x < 2, then x COULD equal -1, in which case this statement need not be true

III. 2x is greater than or equal to x
If x < 2, then x COULD equal -1, in which case 2x = -2
In this case, 2x is NOT greater than x
ELIMINATE A

IV. x² is greater than or equal to x.
If x < 2, then x COULD equal 1/2, in which case x² = 1/4
So, x² is NOT greater than or equal to x.
ELIMINATE B

Answer: E

Cheers,
Brent
Thanks Brent for your detailed breakdown and explanation. please endeavor to answer other questions i have been asking on this platform.
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