If x is a nonzero integer, which of the following must be true: I) 3

Question

If x is a nonzero integer, which of the following must be true:

I) 3 < 3 + x 
II) −x <0 
III) x < 2x

A) none

B) I only

C) III only

D) II and III

E) I, II and III

IanStewart · Answer

If we subtract 3 on both sides of I, multiply by -1 on both sides of II (reversing the inequality when we do), and subtract x on both sides of III, each of I, II and III can be rewritten to say "x > 0". Since all we know is that x is a nonzero integer, we have no idea if x > 0 is true or false, so none of the three items needs to be true.

iamvishnu · Answer

BrentGMATPrepNow  please help. I don’t understand what is question asking.? I choose E because it satisfies x>0

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BrentGMATPrepNow · Answer

The question tells us   x is a nonzero integer  
So, x can be either negative or positive. 
When x is positive, all of the statements are true
When x is negative, none of the statements are true

The question asks us to determine what MUST be true. 
Since none of the statements are necessarily true, the correct answer is A

If x is a nonzero integer, which of the following must be true: I) 3

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If x is a nonzero integer, which of the following must be true: I) 3

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